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Lenz's law and the direction of induced current

Faraday tells you how big the emf is. Lenz tells you which way it pushes. Every answer here comes from one idea: the induced current fights the change that made it.

NCERTAllen module pages 100–102 and 105Illustrations 9, 10, 12, 13, Beginner's Box 2

Nature pushes back

Picture it

Imagine a ring that hates surprises. Push more field through it and it grumbles and tries to push some back out. Take field away and it tries to hold on to what it had. It cannot stop the change. It can only resist it, a little, by making its own current and so its own small magnet.

That is all of Lenz's law. The induced current always acts against the change in flux. Not against the field. Against the change.

In exam language

Lenz's law: the direction of the induced current (or emf) is such that it opposes the change in magnetic flux that produces it.

e = −N dφ/dt the minus sign is Lenz's law
Trap

"The induced current opposes the magnetic field" is false. When the flux is decreasing, the induced current's field points the same way as the original field, trying to keep it up.

Four steps that always work

Direction of induced current for four field casesOut of the page and increasing gives clockwise. Into the page and increasing gives anticlockwise. Out and decreasing gives anticlockwise. Into and decreasing gives clockwise. All seen from the front.out of pagegrowinginduced fieldclockwise(opposes)into pagegrowinginduced fieldanticlockwise(opposes)out of pageshrinkinginduced fieldanticlockwise(keeps it up)into pageshrinkinginduced fieldclockwise(keeps it up)Seen from the front. Growing: induced field against B. Shrinking: along B.
Four cases. The symbols grow or shrink to show the field changing. The travelling arrowheads show the induced current, as seen from the front. Growing flux gets an opposing field; shrinking flux gets a supporting field.
  1. Which way does the field go through the loop? Out of the page (dots) or into the page (crosses).
  2. Is the flux growing or shrinking? Check B, the area inside the field, and the angle.
  3. Which way must the induced field point? Growing: opposite to B. Shrinking: same as B.
  4. Turn that field into a current. Curl your right hand so your thumb points along the induced field. Your fingers show the current. Thumb towards you (out of page) gives anticlockwise; thumb away from you (into page) gives clockwise.
FieldChangeInduced fieldCurrent (seen from the front)
Out of pageGrowingInto pageClockwise
Into pageGrowingOut of pageAnticlockwise
Out of pageShrinkingOut of pageAnticlockwise
Into pageShrinkingInto pageClockwise

The flat-hand margin note on page 100 (B growing: read the answer directly; B shrinking: read it and reverse) gives these same four answers. The handwritten answers under Illustration 9(a) are all correct.

Magnets, coils and poles

Magnet approaching and leaving a ringWhen the N pole approaches, the near face of the ring becomes N and the current looks anticlockwise from the magnet's side; the ring pushes the magnet back. When it leaves, the near face becomes S, the current looks clockwise and the ring pulls the magnet back.ringSNNSpushed backpulled backseen from the magnet's sideNSno currentanticlockwiseclockwiseN pole coming in → near face N → anticlockwise from the magnet → repelsN pole going out → near face S → clockwise from the magnet → attractsEither way the ring fights the motion. That fight is Lenz's law.
Magnet and ring. Left: side view. Right: the ring as seen from the magnet. While the N pole comes in, the ring makes an N face towards it and pushes back. While it goes out, the ring makes an S face and pulls back. Still magnet: no current.

A loop carrying current is a small magnet. The face where the current looks anticlockwise to you is its N face. The face where it looks clockwise is its S face.

A memory trick

A memory picture: draw the letter N and put little arrows on its tips; they curl anticlockwise. Draw S; its ends curl clockwise.

Magnet does thisNear face of the coil becomesCurrent seen from the magnetForce on the magnet
N pole comes closerNAnticlockwiseRepulsion
N pole moves awaySClockwiseAttraction
S pole comes closerSClockwiseRepulsion
S pole moves awayNAnticlockwiseAttraction

Coming closer always gives repulsion. Moving away always gives attraction. The coil always resists the relative motion.

Always say where you are looking from

The same current looks clockwise from one side and anticlockwise from the otherA loop carries one current. Its own field points to the left. The observer on the left sees anticlockwise; the observer on the right sees clockwise.field of the currentseen from the leftanticlockwiseseen from the rightclockwiseAlways say which side you are looking from.
Two observers, one current. Nothing about the current changes. Only the observer moves. So every clockwise or anticlockwise answer must name the side it is seen from.

A clock seen through a glass table from underneath runs backwards. A loop is the same. If a question says "as seen from the magnet" or shows an eye, use that side. If it shows the loop flat in the page, the viewer is you, in front of the page.

Correction to the Allen module

Illustration 9 (p. 101). The printed answers are right, but the first block of reasoning has "B increasing" and "B decreasing" swapped for cases (ii) and (iii), and the solution for the magnet part never says which side the clockwise and anticlockwise answers are seen from. They hold when viewed from the magnet's side. Copying that reasoning as written leads straight to a reversed answer, which is her most frequent direction error.

Wires, beams and loops in the page

For a long straight wire in the page, curl your right hand around the wire with your thumb along the current. On one side the field goes into the page, on the other side out of it. For current flowing up the page, the field is into the page on the right and out of the page on the left.

SituationField at the loopChangeInduced current
Current up, loop on the right, current increasingInto pageGrowingAnticlockwise
Current up, loop on the right moving awayInto pageShrinkingClockwise
Current up, loop on the left, current decreasingOut of pageShrinkingAnticlockwise
Loop moving parallel to the wireUnchangedNoneNo current
Trap

Beams: the current of an electron beam flows opposite to the electrons' motion. A positive beam (protons, alpha particles, positrons) carries current along its motion. An accelerating beam means growing current; a slowing beam means shrinking current; a steady beam means no induced current at all.

Loops that change shape

If a circular loop in a steady field is pulled into an ellipse with the same wire, its area falls, because a circle encloses the most area for a given length. Less area means shrinking flux, so the induced current tries to keep the flux up. Stretching a loop open does the reverse.

Special loops

LoopWhat happens
Figure-of-eight with a twist, two equal halvesThe emfs in the two halves oppose each other: no current
Figure-of-eight with a twist, unequal halvesThe bigger half wins; the current looks opposite in the two halves
Ring with a cutEmf across the cut, no current, no opposing force
Loop with a capacitorA brief current charges the plates; find which plate the current flows onto
Two concentric rings joined by one straight wireEach ring carries its own current; nothing flows in the joining wire, because it has no return path

Two coils facing each other

Two coaxial coils with currents in the same directionAs the coils approach each other both currents shrink. As they separate both currents grow.coil Acoil Bgreen bar = currentMoving together: both currents decreaseMoving apart: both currents increaseAt rest: currents unchangedCurrents in the same direction attract, so the change always fights the motion.
Allen Illustration 10. Currents in the same direction attract. Moving the coils together increases each coil's flux from the other, so both currents dip to resist. Moving them apart does the opposite.
Currents in the two coilsCoils move togetherCoils move apart
Same directionBoth currents decreaseBoth currents increase
Opposite directionsBoth currents increaseBoth currents decrease

Check with forces. Same-direction currents attract. Moving together, a weaker current weakens that attraction, which resists the motion. Opposite currents repel. Moving together, a stronger current strengthens the repulsion, which again resists the motion.

The same idea gives the jumping ring: a metal ring sitting on an iron core is thrown upward when the coil below is switched on (the induced current is opposite, so it is repelled) and is briefly tugged down when the coil is switched off.

Why the push-back must happen: energy

A magnet falls more slowly through a copper ringTwo magnets are dropped together. The one falling through a copper ring is slowed as it approaches and as it leaves, and reaches the floor later.NSno ringNScopper ringlands firstComing in: ring repelsGoing out: ring attractsBoth slow it: a < g
Two magnets dropped together. The one falling through the copper ring is slowed both on the way in and on the way out, and lands later. Its lost kinetic energy becomes heat in the ring.
Picture it

Suppose the ring helped instead of resisted. A magnet nudged towards it would be pulled in faster, which would make a bigger current, which would pull harder, and so on. The magnet would speed up forever and the ring would get hotter forever, all from one small nudge. That is energy out of nothing, which never happens. So the induced current has to resist.

In exam language

Lenz's law is a consequence of the law of conservation of energy. The work done against the opposing magnetic force is what becomes electrical energy, and then heat in the resistance.

Allen Illustration 12 uses this directly: all the kinetic energy a magnet loses in a ring appears as heat, so ½Mv² (lost) = ms Δθ in the ring. Illustration 13 models the opposing force as F = −bv, which gives m dv/dt = −bv and so v = v₀ e−bt/m: the speed dies away exponentially and never quite reaches zero. Both are correct in the module.

Falling magnetAcceleration
Free fall, no ringa = g
Approaching a closed ringa < g (repelled)
Leaving a closed ringa < g (attracted back)
Ring with a cuta = g (emf but no current)
Long copper tubea falls towards zero; speed approaches a steady terminal value

Rules and formula sheet

Rule or formulaMeaningUse it forWatch out
e = −N dφ/dtMinus sign = Lenz's lawSign of emfSize from Faraday, direction from Lenz
Growing flux → induced field oppositeOpposes increaseDirection stepsNot 'opposes the field'
Shrinking flux → induced field same wayOpposes decreaseDirection stepsMost-missed case
Anticlockwise face = NClock ruleMagnet–coil questionsName the viewing side
Approach → repel; recede → attractForce always opposes relative motionForce questionsHolds for poles and coils
½Mv² = ms ΔθKinetic energy lost → heatIllustration 12 typeUse the ring's mass for heat
v = v₀ e−bt/mOpposing force F = −bvIllustration 13 typeExponential, not linear
a < gMagnet through a closed ring or tubeFalling-magnet questionsCut ring: a = g

Allen pages 100–102 and 105 checked

ItemCheck
Lenz's law statement and minus signCorrect
Illustration 9(a): four induced-current answersAnswers correct
Illustration 9: reasoning lines for cases (ii) and (iii)"Increasing" and "decreasing" are swapped
Illustration 9: magnet partAnswers hold as seen from the magnet's side; the page does not say so
Illustration 10: coaxial coilsCorrect
Illustration 12: kinetic energy converted to heat in the ringCorrect method
Illustration 13: F = −bv, exponential fall of speedCorrect
Lenz's law and conservation of energy (p. 105)Correct

Beginner's Box 2 answer key

The module prints no key for this box. Each answer below comes from the four-step method. "Seen from the front" means seen by you, looking at the page.

PartAnswerReason
Q1 (i)AnticlockwiseCurrent up, loop on the right: field into the page, growing.
Q1 (ii)ClockwiseLoop moves away from the wire: field into the page, shrinking.
Q1 (iii)Plate A positive, plate B negativeField out of page, growing: current clockwise, which runs down the right arm onto the upper plate A.
Q1 (iv)AnticlockwiseElectrons to the right = current to the left. Above it the field is into the page, and it grows as the beam speeds up.
Q1 (v)AnticlockwisePositrons to the right = current to the right. Above it the field is out of the page, and it shrinks as the beam slows.
Q1 (vi)No currentUniform alpha beam: steady current, steady field.
Q1 (vii) (a)Anticlockwise around the whole loopThe two bulges without a crossing make one simple loop. Field into the page, growing.
Q1 (vii) (b)Anticlockwise in the larger half, clockwise in the smaller halfThe crossing makes the halves oppose; the larger half has the larger emf and sets the current.
Q1 (vii) (c)No current (emf across the gap)The ring is not closed.
Q1 (vii) (d)Anticlockwise in both rings; zero in the connecting wireEach ring is its own closed loop; the single joining wire has no return path.
Q1 (viii)AnticlockwiseCircle to ellipse: area falls, flux out of the page shrinks.
Q2 (i) (a)Same sense as the source currentThe loop moves away, so the source's flux through it shrinks; the induced current supports it (and attracts).
Q2 (i) (b)Opposite sense to the source currentSource current growing: induced current opposes it (and repels).
Q2 (ii)Through R from N to LN pole approaching: the solenoid's left face becomes N, so the current is anticlockwise as seen from the magnet. Tracing the winding in the figure, that current leaves the coil through the right-hand lead, so it enters R at the N end.
Q2 (iii)Clockwise as seen by the observer; plate signs depend on which half holds the capacitor (see note)The field runs from the N pole-piece to the S pole-piece, towards the observer. The S piece moves closer, so this flux grows. The induced field must point away from the observer, which the observer sees as clockwise. Capacitor on the half farther from the reader: current runs down past it, so A is positive and B negative. Capacitor on the nearer half: current runs up past it, so B is positive and A negative.
A drawing that cannot be read two ways

Note on Q2 (i) and Q2 (iii). These loops are drawn as tilted ellipses, and a flat scan cannot show which half of each ellipse is nearer to the reader. The answers "same sense" and "opposite sense" in Q2 (i) do not depend on that. For Q2 (iii), clockwise for the observer is certain, but the plate signs are not: both readings are given above. Check this one with the teacher, and use whichever convention the class uses for tilted loops.

NEET practice: 43 questions

Direction questions are where marks leak in this chapter, so most questions here are about which way the current goes. Every clockwise or anticlockwise answer states where it is seen from.

Q1Direction
A square loop lies in the plane of the page in a field pointing out of the page. The field is increasing. Seen from the front, the induced current is
Loop in a magnetic fieldfield out of the page, increasingfield out of the page, increasing
  1. (A)No induced current
  2. (B)Anticlockwise
  3. (C)Clockwise
  4. (D)Clockwise, then anticlockwise
Show the solution
Given
Field out of the page, growing
Asked
Direction of induced current
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Field: out of page.
  2. Flux: growing.
  3. Induced field: into the page.
  4. Thumb into page → fingers curl clockwise.
Answer
(C) Clockwise
Why not the others
Anticlockwise would add to the growth. No current ignores the change. A reversal would need the change to reverse.
Shortcut
Out and growing → clockwise.
Where it went wrong
Making the induced field point along B.
Q2Direction
A loop lies in the page in a field pointing into the page. The field is decreasing. Seen from the front, the induced current is
Loop in a magnetic fieldfield into the page, decreasingfield into the page, decreasing
  1. (A)Clockwise
  2. (B)Anticlockwise
  3. (C)No induced current
  4. (D)Anticlockwise, then clockwise
Show the solution
Given
Field into the page, shrinking
Asked
Direction of induced current
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Field: into page.
  2. Flux: shrinking.
  3. Induced field: into page (keeps it up).
  4. Thumb into page → clockwise.
Answer
(A) Clockwise
Why not the others
Anticlockwise would make the loss worse. No current ignores the change. Nothing reverses the change.
Shortcut
Into and shrinking → clockwise.
Where it went wrong
Opposing the field instead of opposing the change.
Q3Direction
A loop lies in the page in a field pointing into the page. The field is increasing. Seen from the front, the induced current is
Loop in a magnetic fieldfield into the page, increasingfield into the page, increasing
  1. (A)Clockwise, then anticlockwise
  2. (B)Clockwise
  3. (C)No induced current
  4. (D)Anticlockwise
Show the solution
Given
Field into the page, growing
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Induced field must point out of the page.
  2. Thumb out of page → anticlockwise.
Answer
(D) Anticlockwise
Why not the others
Clockwise would strengthen the growing flux. The other two ignore the steady growth.
Shortcut
Into and growing → anticlockwise.
Where it went wrong
Getting the right-hand curl backwards.
Q4Direction
The N pole of a bar magnet is moved towards a circular coil along its axis. Seen from the magnet's side, the induced current in the coil is
  1. (A)Clockwise
  2. (B)Anticlockwise
  3. (C)No induced current
  4. (D)Clockwise, then anticlockwise
Show the solution
Given
N pole approaching; viewer on the magnet's side
Asked
Direction
Concept
The coil opposes the approach by making a like pole on the near face.
Formula
Anticlockwise face = N
Baby steps
  1. The coil must repel the N pole, so its near face becomes N.
  2. A face that shows anticlockwise current is N.
  3. Seen from the magnet (looking at that face): anticlockwise.
Answer
(B) Anticlockwise
Why not the others
Clockwise would make an S face, which would attract. No current ignores the motion.
Shortcut
N approaching → N face → anticlockwise (from the magnet).
Where it went wrong
Answering for the far side without noticing.
Q5Direction
The S pole of a bar magnet is moved away from a coil along its axis. Seen from the magnet's side, the induced current is
  1. (A)No induced current
  2. (B)Clockwise
  3. (C)Anticlockwise
  4. (D)Clockwise, then anticlockwise
Show the solution
Given
S pole receding; viewer on the magnet's side
Asked
Direction
Concept
The coil opposes the departure by attracting.
Formula
Anticlockwise face = N
Baby steps
  1. To oppose the S pole leaving, the coil attracts it.
  2. So the near face becomes N.
  3. N face seen from the front: anticlockwise.
Answer
(C) Anticlockwise
Why not the others
Clockwise would make an S face, which would repel the S pole away even faster. No current ignores the motion.
Shortcut
Receding → opposite pole on the near face.
Where it went wrong
Making a like pole when the magnet is leaving.
Q6Direction
The N pole of a magnet moves towards a coil. An observer stands on the far side of the coil, looking towards the magnet. To this observer the induced current is
  1. (A)No induced current
  2. (B)Anticlockwise
  3. (C)Clockwise
  4. (D)Anticlockwise, then clockwise
Show the solution
Given
N pole approaching; viewer on the far side
Asked
Direction as seen by this viewer
Concept
Clockwise and anticlockwise depend on where you look from.
Formula
Flip viewpoint → reverse sense
Baby steps
  1. From the magnet's side the current is anticlockwise.
  2. The far-side observer looks at the loop from behind.
  3. The same current appears clockwise.
Answer
(C) Clockwise
Why not the others
Anticlockwise is the magnet-side answer. The other two ignore the steady approach.
Shortcut
Change sides → swap CW and ACW.
Where it went wrong
Giving the magnet-side answer for the wrong observer.
Q7Direction
The S pole of a magnet is pushed towards a coil. The face of the coil nearer the magnet behaves as
  1. (A)an S pole
  2. (B)an N pole
  3. (C)no pole, because no current flows
  4. (D)an N pole, then an S pole
Show the solution
Given
S pole approaching
Asked
Polarity of the near face
Concept
Opposing an approach means repelling.
Formula
Approach → like pole
Baby steps
  1. Approaching magnet → coil repels.
  2. Like poles repel, so the near face is S.
Answer
(A) an S pole
Why not the others
An N face would attract, helping the motion. Current does flow while the magnet moves. Nothing reverses during a steady approach.
Shortcut
Approach → same pole.
Where it went wrong
Choosing the opposite pole by habit ('opposite attracts').
Q8Direction
The N pole of a magnet is pulled away from a nearby closed coil. The force between the coil and the magnet is
  1. (A)zero
  2. (B)repulsive
  3. (C)attractive
  4. (D)attractive, then repulsive
Show the solution
Given
N pole receding
Asked
Nature of force
Concept
The force always opposes relative motion.
Formula
Recede → attract
Baby steps
  1. The coil opposes the magnet leaving.
  2. It does that by pulling the magnet back: attraction.
  3. (Its near face becomes S.)
Answer
(C) attractive
Why not the others
Repulsion would help the magnet leave. Zero ignores the induced current. No reversal happens during a steady pull.
Shortcut
Receding → attraction.
Where it went wrong
Thinking an induced current always repels.
Q9Direction
A long straight wire in the page carries a current up the page. A loop lies in the page to the right of the wire. The current in the wire is increasing. Seen from the front, the current induced in the loop is
Long straight wire and a loopI increasingII increasing
  1. (A)Clockwise
  2. (B)Anticlockwise
  3. (C)No induced current
  4. (D)Clockwise in the half nearer the wire only
Show the solution
Given
Current up, loop on the right, current growing
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Current up: into page on the right
Baby steps
  1. Right-hand rule: for current up, the field on the right is into the page.
  2. Growing current → growing flux into the page.
  3. Induced field out of the page → anticlockwise.
Answer
(B) Anticlockwise
Why not the others
Clockwise would add to the growth. No current ignores the change. A loop carries one current all the way round.
Shortcut
Right of an upward current: into page.
Where it went wrong
Getting the side of the wire wrong for 'into' and 'out'.
Q10Direction
A wire in the page carries a steady current up the page. A loop to its right is moved directly away from the wire. Seen from the front, the induced current is
Long straight wire and a looploop moves awayIvloop moves away
  1. (A)Clockwise, then anticlockwise
  2. (B)Anticlockwise
  3. (C)No induced current
  4. (D)Clockwise
Show the solution
Given
Steady current up, loop on the right moving away
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Current up: into page on the right
Baby steps
  1. Field at the loop: into the page.
  2. Moving away → field weaker → flux shrinking.
  3. Induced field into page → clockwise.
Answer
(D) Clockwise
Why not the others
Anticlockwise would speed the loss. No current forgets that the field weakens with distance. The change does not reverse.
Shortcut
Moving away = shrinking flux.
Where it went wrong
Treating a steady current as 'no change' even though the loop moves.
Q11Direction
A wire in the page carries a steady current. A loop beside it moves parallel to the wire, keeping the same distance. The induced current is
Long straight wire and a looploop moves parallel to the wireIvloop moves parallel to the wire
  1. (A)Anticlockwise
  2. (B)Clockwise
  3. (C)No induced current
  4. (D)Clockwise, then anticlockwise
Show the solution
Given
Loop moves along the wire at a fixed distance
Asked
Induced current
Concept
Flux changes only if the distance from the wire changes.
Formula
B = μ₀I/2πr
Baby steps
  1. The field depends only on distance from the wire.
  2. The distance does not change, so the flux does not change.
  3. No emf, no current.
Answer
(C) No induced current
Why not the others
Clockwise and anticlockwise both need a change in flux. A reversal needs a change that reverses.
Shortcut
Same distance from a long wire = same flux.
Where it went wrong
Assuming any motion near a wire induces current.
Q12Direction
A wire in the page carries a current up the page. A loop lies to the left of the wire. The current is decreasing. Seen from the front, the induced current is
Long straight wire and a loopI decreasingII decreasing
  1. (A)Clockwise, then anticlockwise
  2. (B)Clockwise
  3. (C)No induced current
  4. (D)Anticlockwise
Show the solution
Given
Current up, loop on the left, current shrinking
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Current up: out of page on the left
Baby steps
  1. For current up, the field on the left is out of the page.
  2. Current falling → flux out of page shrinking.
  3. Induced field out of page → anticlockwise.
Answer
(D) Anticlockwise
Why not the others
Clockwise is the answer for a loop on the right with the same change, or on the left with growing current. The other options ignore the change.
Shortcut
Left of an upward current: out of page.
Where it went wrong
Using the right-side field for a loop on the left.
Q13Direction
Two coaxial circular loops face each other. The current in loop 1 is increasing. The induced current in loop 2 is
  1. (A)in the same sense, and the loops repel
  2. (B)in the same sense as loop 1's current, and the loops attract
  3. (C)opposite in sense, and the loops attract
  4. (D)opposite in sense to loop 1's current, and the loops repel
Show the solution
Given
Loop 1 current growing
Asked
Sense of induced current and force
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Loop 1's flux through loop 2 grows.
  2. Loop 2's current must oppose: opposite sense.
  3. Opposite currents repel.
Answer
(D) opposite in sense to loop 1's current, and the loops repel
Why not the others
Same sense would help the growth. Opposite currents cannot attract. Same-sense currents cannot repel.
Shortcut
Growing neighbour → opposite current → repel.
Where it went wrong
Pairing the right current with the wrong force.
Q14Direction
Loop 1 carries a steady current. A coaxial loop 2 is moved away from it. The induced current in loop 2 is
  1. (A)in the same sense as loop 1's, and the loops attract
  2. (B)opposite to loop 1's, and the loops repel
  3. (C)in the same sense, and the loops repel
  4. (D)zero, because loop 1's current is steady
Show the solution
Given
Steady current in loop 1; loop 2 receding
Asked
Sense and force
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Loop 2 moves away → flux from loop 1 shrinks.
  2. Induced current supports it: same sense.
  3. Same-sense currents attract, resisting the separation.
Answer
(A) in the same sense as loop 1's, and the loops attract
Why not the others
Opposite current would speed the loss of flux. Same-sense currents attract, not repel. The current being steady does not matter; the distance is changing.
Shortcut
Receding → same sense → attract.
Where it went wrong
Saying 'steady current, so nothing happens'.
Q15Direction
Two coaxial coils carry equal currents in the same direction. They are moved towards each other. During the motion the currents in the coils
  1. (A)both decrease
  2. (B)both increase
  3. (C)stay the same
  4. (D)one increases and the other decreases
Show the solution
Given
Same-direction currents, coils approaching (Allen Illustration 10)
Asked
Change in currents
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Each coil's flux from the other grows as they approach.
  2. Each induced current opposes that: it runs against the coil's own current.
  3. So both currents decrease.
Answer
(A) both decrease
Why not the others
Increase would strengthen the attraction and help the approach. Staying the same ignores induction. The situation is symmetric, so both coils change the same way.
Shortcut
Same currents, approaching → both dip.
Where it went wrong
Forgetting the symmetry.
Q16Direction
Two coaxial coils carry equal currents in opposite directions. They are moved apart. During the motion the currents
  1. (A)both increase
  2. (B)both decrease
  3. (C)stay the same
  4. (D)one increases and the other decreases
Show the solution
Given
Opposite currents, coils separating
Asked
Change in currents
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Opposite currents repel. Moving apart, the induced currents must resist the separation.
  2. Weaker repulsion resists separation, so both currents decrease.
  3. (Moving together they would both increase.)
Answer
(B) both decrease
Why not the others
Increase is the answer for moving together. Staying the same ignores induction. Symmetry rules out one up and one down.
Shortcut
Opposite currents: together ↑, apart ↓.
Where it went wrong
Using the same-direction table for opposite currents.
Q17Direction
A bar magnet is dropped with its length vertical through a horizontal closed metal ring. Its acceleration is
  1. (A)less than g both while approaching and while leaving the ring
  2. (B)less than g while approaching and greater than g while leaving
  3. (C)equal to g throughout
  4. (D)greater than g while approaching and less than g while leaving
Show the solution
Given
Magnet falling through a closed ring
Asked
Acceleration while approaching and leaving
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Approaching: the ring repels → upward force → a < g.
  2. Leaving: the ring attracts it back → upward force → a < g.
  3. Both forces oppose the motion.
Answer
(A) less than g both while approaching and while leaving the ring
Why not the others
Greater than g would mean the ring helps the fall, which would create energy. Equal to g needs no current.
Shortcut
The ring always pulls against the fall.
Where it went wrong
Thinking attraction on the way out speeds the magnet up. The attraction is upward.
Q18Direction
Identical magnets are dropped through equal-length vertical tubes of copper and of PVC. Compared with the PVC tube, the magnet in the copper tube takes
  1. (A)a longer time
  2. (B)a shorter time
  3. (C)the same time
  4. (D)the same time, but lands with more speed
Show the solution
Given
Copper (conductor) versus PVC (insulator)
Asked
Time of fall
Concept
Induced currents in a conductor oppose the relative motion.
Formula
a < g inside a conducting tube
Baby steps
  1. Changing flux induces currents in the copper walls.
  2. These currents oppose the magnet's motion.
  3. PVC has no induced currents, so the magnet falls freely.
Answer
(A) a longer time
Why not the others
Shorter would need a helping force. Same time would need no opposition in copper. More speed contradicts the slowing.
Shortcut
Conductor slows it.
Where it went wrong
Thinking only iron tubes affect magnets.
Q19Direction
A magnet is dropped through a metal ring that has a narrow cut in it. Ignoring air resistance, its acceleration is
  1. (A)greater than g
  2. (B)less than g
  3. (C)g
  4. (D)zero at the centre of the ring
Show the solution
Given
Ring with a cut
Asked
Acceleration
Concept
Opposing force needs a current, and a current needs a closed path.
Formula
I = 0 in an open ring
Baby steps
  1. An emf is induced across the cut.
  2. The ring is open, so no current flows.
  3. No current means no opposing force: a = g.
Answer
(C) g
Why not the others
Less than g needs a current. Greater than g is never possible. Zero acceleration would need a force equal to the weight.
Shortcut
No closed path → no current → free fall.
Where it went wrong
Confusing 'emf induced' with 'current induced'.
Q20Direction
Lenz's law is a consequence of the law of conservation of
  1. (A)charge
  2. (B)energy
  3. (C)linear momentum
  4. (D)mass
Show the solution
Given
Lenz's law
Asked
Underlying conservation law
Concept
Work done against the opposing force becomes electrical energy.
Formula
Mechanical work → electrical energy → heat
Baby steps
  1. If the induced current helped the change, the motion would speed itself up.
  2. Energy would appear from nothing.
  3. So the opposition is required by conservation of energy.
Answer
(B) energy
Why not the others
Charge conservation gives Kirchhoff's junction rule. Momentum and mass are not what the opposition protects.
Shortcut
Lenz = energy.
Where it went wrong
Attribution error: picking charge because currents are involved.
Q21Direction
Suppose the induced current in a coil helped the motion of an approaching magnet instead of opposing it. Then
  1. (A)no current would flow at all
  2. (B)the coil would get colder
  3. (C)the magnet would keep speeding up, creating energy from nothing
  4. (D)the emf would be zero
Show the solution
Given
Imagined 'helping' induced current
Asked
Consequence
Concept
Conservation of energy forbids self-amplifying induction.
Formula
—
Baby steps
  1. Helping force → magnet speeds up.
  2. Faster magnet → bigger current → bigger helping force.
  3. Runaway growth of kinetic and electrical energy with no input: impossible.
Answer
(C) the magnet would keep speeding up, creating energy from nothing
Why not the others
Cooling, zero current or zero emf do not follow from a helping force.
Shortcut
Help would mean a perpetual motion machine.
Where it went wrong
Missing the feedback loop in the argument.
Q22Direction
A circular loop sits in a uniform field pointing out of the page. It is suddenly pulled into an ellipse using the same length of wire. Seen from the front, the induced current is
  1. (A)Clockwise
  2. (B)Anticlockwise
  3. (C)No induced current
  4. (D)Clockwise, then anticlockwise
Show the solution
Given
Circle → ellipse, same perimeter, field out of page
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
φ = BA; A falls
Baby steps
  1. For a fixed length of wire, a circle encloses the largest area.
  2. The ellipse has less area → flux out of page shrinks.
  3. Induced field out of page → anticlockwise.
Answer
(B) Anticlockwise
Why not the others
Clockwise would need the flux to grow. No current ignores the change in area. The area only falls.
Shortcut
Circle has maximum area → any squeeze reduces flux.
Where it went wrong
Assuming same wire length means same area.
Q23Direction
A flexible loop lies in a field pointing into the page and is stretched so that its area increases. Seen from the front, the induced current is
  1. (A)Clockwise
  2. (B)Anticlockwise
  3. (C)No induced current
  4. (D)Clockwise, then anticlockwise
Show the solution
Given
Field into page, area growing
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
φ = BA; A rises
Baby steps
  1. Flux into page grows.
  2. Induced field out of page.
  3. Anticlockwise.
Answer
(B) Anticlockwise
Why not the others
Clockwise would add to the growth. The other two ignore the growing area.
Shortcut
Into and growing → anticlockwise, whatever makes it grow.
Where it went wrong
Thinking only a changing B counts.
Q24Direction
A loop is twisted into a figure-of-eight with two equal halves and placed flat in a uniform field that is increasing. The induced current in the loop is
  1. (A)zero
  2. (B)clockwise in both halves
  3. (C)anticlockwise in both halves
  4. (D)twice that in a single loop of the same half-area
Show the solution
Given
Twisted figure-of-eight, equal halves
Asked
Induced current
Concept
Around the whole circuit, a twist reverses one half's contribution.
Formula
enet = e₁ − e₂ = 0
Baby steps
  1. The twist makes the circulation in one half opposite to the other.
  2. Equal halves → equal and opposite emfs around the circuit.
  3. Net emf = 0 → no current.
Answer
(A) zero
Why not the others
Same-sense currents in both halves would need no twist. Doubling would need the emfs to add.
Shortcut
Twisted equal halves cancel.
Where it went wrong
Adding the two halves' emfs.
Q25Direction
A rectangular loop in the page contains a capacitor in its right-hand arm, with plate P above plate Q. A field into the page through the loop is decreasing. Which plate becomes positive?
Rectangular loop containing a capacitor in a decreasing fieldUpper plate P, lower plate QPQfield into the page, decreasing
  1. (A)Both plates become positive
  2. (B)Q
  3. (C)Neither plate is charged
  4. (D)P
Show the solution
Given
Field into page, shrinking; capacitor in the right arm
Asked
Positive plate
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Shrinking into page → clockwise
Baby steps
  1. Induced field into page → current clockwise.
  2. Clockwise: along the top to the right, then down the right arm.
  3. Current coming down the right arm arrives at the upper plate P first.
  4. P becomes positive, Q negative.
Answer
(D) P
Why not the others
Q positive would need anticlockwise current. The brief charging current does charge the plates. Both positive is impossible for a capacitor.
Shortcut
Find the direction, then follow the current onto a plate.
Where it went wrong
Direction reversal, then the wrong plate.
Q26Direction
A beam of protons travels to the left, just below a circular loop in the page, and is slowing down. Seen from the front, the current induced in the loop is
  1. (A)Anticlockwise
  2. (B)Clockwise
  3. (C)No induced current
  4. (D)Anticlockwise, then clockwise
Show the solution
Given
Protons moving left below the loop, slowing
Asked
Direction
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Current left: into page above it
Baby steps
  1. Protons are positive: current flows to the left.
  2. Above a leftward current the field is into the page.
  3. Slowing beam → smaller current → flux into page shrinks.
  4. Induced field into page → clockwise.
Answer
(B) Clockwise
Why not the others
Anticlockwise would be right for a speeding-up beam. No current needs a steady beam. The change does not reverse.
Shortcut
Positive beam: current along motion.
Where it went wrong
Taking the current opposite to the protons' motion (that rule is for electrons).
Q27Numerical
A magnet loses 360 J of kinetic energy while passing through a metal ring of mass 0.5 kg and specific heat 400 J kg⁻¹ K⁻¹. If all of it becomes heat in the ring, the rise in the ring's temperature is
  1. (A)1.8 K
  2. (B)0.9 K
  3. (C)0.45 K
  4. (D)3.6 K
Show the solution
Given
Energy lost = 360 J, m = 0.5 kg, s = 400 J kg⁻¹ K⁻¹
Asked
Δθ
Concept
Lenz's law and energy conservation: work against the opposing force becomes heat (Allen Illustration 12).
Formula
KE lost = ms Δθ
Baby steps
  1. 360 = 0.5 × 400 × Δθ.
  2. 0.5 × 400 = 200.
  3. Δθ = 360/200 = 1.8 K.
Answer
(A) 1.8 K
Why not the others
0.9 K forgets the 0.5 kg. 0.45 K multiplies by the mass instead of dividing. 3.6 K doubles the energy.
Shortcut
Δθ = E/(ms).
Where it went wrong
Putting the mass on the wrong side of the fraction.
Q28Numerical
A conducting body of mass 2 kg moves through a magnetic field that exerts an opposing force F = −bv with b = 0.5 kg s⁻¹. Its initial speed is 10 m/s and no other force acts. Its speed after 4 s is about
  1. (A)3.7 m/s
  2. (B)6.3 m/s
  3. (C)0.18 m/s
  4. (D)5.0 m/s
Show the solution
Given
m = 2 kg, b = 0.5 kg s⁻¹, v₀ = 10 m/s, t = 4 s
Asked
v(4 s)
Concept
An opposing force proportional to speed gives exponential decay (Allen Illustration 13).
Formula
v = v₀ e−bt/m
Baby steps
  1. bt/m = 0.5 × 4/2 = 1.
  2. v = 10 e⁻¹ = 10 × 0.368.
  3. v ≈ 3.7 m/s.
Answer
(A) 3.7 m/s
Why not the others
6.3 m/s is 10(1 − e⁻¹), the speed lost. 0.18 m/s uses e⁻⁴ (forgets b/m). 5.0 m/s assumes a straight-line fall.
Shortcut
bt/m = 1 → v₀/e.
Where it went wrong
Using e−t without b/m.
Q29Direction
A conducting rod slides to the right along two rails in a magnetic field, forming a closed circuit. The magnetic force on the rod due to the induced current is
  1. (A)perpendicular to the rails
  2. (B)to the right, along its motion
  3. (C)zero
  4. (D)to the left, opposing its motion
Show the solution
Given
Rod moving right, closed circuit
Asked
Direction of the magnetic force on the rod
Concept
Lenz's law applied to motion: the induced force opposes the velocity.
Formula
F = BIℓ, opposite to v
Baby steps
  1. The rod's motion changes the flux, inducing a current.
  2. By Lenz's law the effect opposes the cause (the motion).
  3. So the force on the rod is to the left.
Answer
(D) to the left, opposing its motion
Why not the others
A force along the motion would create energy. Zero needs no current. The force from the current in the rod is along the rails, not across them.
Shortcut
Induced force always brakes the motion.
Where it went wrong
Working out the current correctly, then applying the force rule backwards.
Q30Direction
A light aluminium ring rests on a vertical iron core that passes through a coil. The coil is suddenly connected to a battery. The ring
  1. (A)spins about the core
  2. (B)is pulled down onto the coil
  3. (C)stays at rest
  4. (D)is thrown upward
Show the solution
Given
Coil switched on; ring on the core
Asked
What the ring does
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Switching on → flux through the ring grows quickly.
  2. Induced current in the ring is opposite to the coil's current.
  3. Opposite currents repel → ring jumps up.
Answer
(D) is thrown upward
Why not the others
Being pulled down would need a same-sense current (that happens when switching off). At rest ignores the induced current. The force is along the axis, not a twist.
Shortcut
Switch on → repel → jump.
Where it went wrong
Mixing up the switch-on and switch-off cases.
Q31Direction
In the same set-up, after the current has become steady, the coil is suddenly disconnected. At that moment the ring
  1. (A)is unaffected
  2. (B)is thrown upward
  3. (C)is briefly pulled towards the coil
  4. (D)is thrown upward even harder
Show the solution
Given
Coil switched off
Asked
Momentary effect on the ring
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Flux through the ring collapses.
  2. The induced current supports the flux: same sense as the coil's current.
  3. Same-sense currents attract → a brief pull towards the coil.
Answer
(C) is briefly pulled towards the coil
Why not the others
Upward throw belongs to switching on. 'Unaffected' ignores the collapsing flux.
Shortcut
Switch off → attract.
Where it went wrong
Assuming every sudden change throws the ring.
Q32Direction
A key in a primary coil's circuit is held down, and then released. At the moment of release, the current induced in a nearby secondary coil flows
  1. (A)opposite to the primary current
  2. (B)in the same sense as the primary current was flowing
  3. (C)only while the key stays released
  4. (D)in no particular direction
Show the solution
Given
Primary current falling to zero
Asked
Sense of induced current in the secondary
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Primary current falls → its flux in the secondary shrinks.
  2. Induced current supports the flux.
  3. So it flows in the same sense as the primary current.
Answer
(B) in the same sense as the primary current was flowing
Why not the others
Opposite sense belongs to switching on. It lasts only while the flux falls, not while the key stays released. Lenz's law always fixes a direction.
Shortcut
Falling primary → same-sense secondary.
Where it went wrong
Using the switch-on answer for switch-off.
Q33Direction
A bar magnet falls with its N pole downward, along the axis of a horizontal ring, and passes right through it. Seen from above, the induced current in the ring is
  1. (A)clockwise throughout
  2. (B)clockwise while it approaches, then anticlockwise after
  3. (C)anticlockwise throughout
  4. (D)anticlockwise while the magnet approaches, then clockwise after it has passed through
Show the solution
Given
N pole down, magnet falling through a horizontal ring; viewer above
Asked
Direction before and after
Concept
Lenz's law: the induced current opposes the change in flux.
Formula
Growing → induced field opposite; shrinking → same
Baby steps
  1. Approaching from above: the ring repels the N pole, so its top face becomes N.
  2. Top face N seen from above: anticlockwise.
  3. After passing: the S end (top of the magnet) moves away below the ring; the ring attracts it, so its bottom face becomes N.
  4. Bottom face N looks anticlockwise from below, which is clockwise from above.
Answer
(D) anticlockwise while the magnet approaches, then clockwise after it has passed through
Why not the others
Clockwise-first gives the ring an S top face, which would attract the approaching N pole. A single direction throughout ignores that the flux first grows, then shrinks.
Shortcut
Growing then shrinking flux → current reverses.
Where it went wrong
Forgetting to switch to the bottom face (and the viewpoint) after the magnet passes.
Q34Graph
A magnet is dropped from rest so that it falls through a horizontal coil connected to a resistor. Which graph best shows the induced current against time?
  1. (A)Graph of I against tIt
  2. (B)Graph of I against tIt
  3. (C)Graph of I against tIt
  4. (D)Graph of I against tIt
Show the solution
Given
Magnet speeding up as it falls through the coil
Asked
I against t
Concept
Flux grows as the magnet enters and shrinks as it leaves; the magnet moves faster on the way out.
Formula
e = −N dφ/dt
Baby steps
  1. Entering: current in one direction.
  2. At the middle: flux is at its peak, rate of change zero, current zero.
  3. Leaving: current reverses.
  4. It is moving faster now, so the second pulse is taller and shorter.
Answer
(A) the graph in option A
Why not the others
Equal pulses would need constant speed. Two pulses of the same sign ignore the reversal. A single pulse ignores the leaving stage.
Shortcut
Opposite signs; the second pulse is taller and narrower.
Where it went wrong
Drawing equal pulses because 'in and out are symmetric'.
Q35Graph
The current in a primary coil is switched on, held steady, and then switched off, as shown. Which graph shows the current induced in a nearby secondary coil?
Graph of I₁ against tI₁t
  1. (A)Graph of I₂ against tI₂t
  2. (B)Graph of I₂ against tI₂t
  3. (C)Graph of I₂ against tI₂t
  4. (D)Graph of I₂ against tI₂t
Show the solution
Given
Primary: rise, steady, fall
Asked
I₂ against t
Concept
Induced current depends on the rate of change of the primary current, with Lenz's law setting its sign.
Formula
I₂ ∝ −dI₁/dt
Baby steps
  1. Switch on: I₁ rises → a brief pulse one way.
  2. Steady: no change → zero.
  3. Switch off: I₁ falls → a brief pulse the other way.
Answer
(D) the graph in option D
Why not the others
Same-sign pulses ignore Lenz's law. A flat-topped copy of I₁ confuses current with its rate of change. A constant line needs a constant rate.
Shortcut
Spikes at the switching moments, opposite signs.
Where it went wrong
Copying the primary current's shape.
Q36Graph
A strong magnet is released from rest inside a long vertical copper tube. Which graph shows its speed against time?
  1. (A)Graph of v against tvt
  2. (B)Graph of v against tvt
  3. (C)Graph of v against tvt
  4. (D)Graph of v against tvt
Show the solution
Given
Magnet falling inside a long conducting tube
Asked
v against t
Concept
The opposing force grows with speed until it balances the weight.
Formula
mg − bv = m dv/dt
Baby steps
  1. At first the speed is small, so the opposing force is small: a ≈ g.
  2. As speed grows, the opposing force grows.
  3. When bv = mg the speed stops changing: terminal speed.
Answer
(C) the graph in option C
Why not the others
The straight line is free fall (no tube). The rise-and-fall curve would need the force to exceed the weight and stop the magnet. A constant speed from the start is impossible from rest.
Shortcut
Rises and levels off.
Where it went wrong
Picking free fall because the tube is not magnetic.
Q37Graph
A conductor moving through a magnetic field feels only an opposing force proportional to its speed, F = −bv. Which graph shows its speed against time?
  1. (A)Graph of v against tvt
  2. (B)Graph of v against tvt
  3. (C)Graph of v against tvt
  4. (D)Graph of v against tvt
Show the solution
Given
F = −bv, no other forces
Asked
v against t
Concept
dv/dt ∝ −v gives exponential decay.
Formula
v = v₀ e−bt/m
Baby steps
  1. Force proportional to speed → the speed falls by the same fraction in equal times.
  2. That is an exponential curve.
  3. It approaches zero but never reaches it.
Answer
(B) the graph in option B
Why not the others
The straight line reaching zero is constant deceleration (constant force). The flat line has no force. The 1/(1 + kt) curve falls too slowly at late times and has a different shape.
Shortcut
Force ∝ v → exponential.
Where it went wrong
Drawing a straight line to zero.
Q38Assertion–reason
Assertion (A): A magnet dropped through a vertical copper tube falls with an acceleration less than g.
Reason (R): The currents induced in the tube oppose the relative motion of the magnet.
  1. (A)Both A and R are true, and R is the correct explanation of A.
  2. (B)Both A and R are true, but R is not the correct explanation of A.
  3. (C)A is true, but R is false.
  4. (D)A is false, but R is true.
Show the solution
Given
A: slower fall. R: induced currents oppose motion.
Asked
Truth and link
Concept
Lenz's law.
Formula
a < g
Baby steps
  1. A is true.
  2. R is true.
  3. The opposing force from the induced currents is exactly why a < g.
Answer
(A) Both A and R are true, and R is the correct explanation of A.
Why not the others
(B) denies a direct link. (C) and (D) need a false statement.
Shortcut
'Slower because the currents oppose' reads correctly.
Where it went wrong
Choosing (B) out of caution.
Q39Assertion–reason
Assertion (A): A current that looks clockwise from one side of a loop looks anticlockwise from the other side.
Reason (R): The face of a loop on which the current looks anticlockwise behaves as a north pole.
  1. (A)Both A and R are true, and R is the correct explanation of A.
  2. (B)Both A and R are true, but R is not the correct explanation of A.
  3. (C)A is true, but R is false.
  4. (D)A is false, but R is true.
Show the solution
Given
A: viewpoint reverses sense. R: clock rule for poles.
Asked
Truth and link
Concept
Clockwise and anticlockwise are relative to the observer.
Formula
Anticlockwise face = N
Baby steps
  1. A is true: it is a fact about viewing, true for any rotation.
  2. R is true.
  3. But A would be true even if loops had no poles at all, so R does not explain A.
Answer
(B) Both A and R are true, but R is not the correct explanation of A.
Why not the others
(A) needs R to be the reason. (C) and (D) need a false statement.
Shortcut
A is geometry; R is magnetism.
Where it went wrong
Linking two true facts that sit next to each other in the notes.
Q40Assertion–reason
Assertion (A): A magnet dropped through a metal ring with a narrow cut falls freely.
Reason (R): An emf is still induced across the cut.
  1. (A)Both A and R are true, and R is the correct explanation of A.
  2. (B)Both A and R are true, but R is not the correct explanation of A.
  3. (C)A is true, but R is false.
  4. (D)A is false, but R is true.
Show the solution
Given
A: free fall through a cut ring. R: emf across the cut.
Asked
Truth and link
Concept
Force needs current; current needs a closed path.
Formula
I = 0 in an open ring
Baby steps
  1. A is true: no current, no opposing force.
  2. R is true: the flux still changes.
  3. But free fall happens because there is no current, not because there is an emf. R does not explain A.
Answer
(B) Both A and R are true, but R is not the correct explanation of A.
Why not the others
(A) would claim the emf causes free fall. (C) and (D) need a false statement.
Shortcut
The explanation of A would be 'no closed path', which R does not say.
Where it went wrong
Treating any true, related R as the explanation.
Q41Assertion–reason
Assertion (A): Lenz's law is a consequence of the law of conservation of energy.
Reason (R): The induced emf always acts to help the change in flux that produces it.
  1. (A)Both A and R are true, and R is the correct explanation of A.
  2. (B)Both A and R are true, but R is not the correct explanation of A.
  3. (C)A is true, but R is false.
  4. (D)A is false, but R is true.
Show the solution
Given
A: Lenz follows from energy. R: induced emf helps the change.
Asked
Truth and link
Concept
Lenz's law: the induced emf opposes the change.
Formula
e = −N dφ/dt
Baby steps
  1. A is true.
  2. R is false: the emf opposes, it never helps.
  3. A true, R false.
Answer
(C) A is true, but R is false.
Why not the others
(A) and (B) need R true. (D) needs A false.
Shortcut
Any statement with 'helps' in Lenz's law is false.
Where it went wrong
Misreading 'opposes' in a hurry.
Q42Two statements
Statement I: When the N pole of a magnet approaches a coil, the near face of the coil becomes an N pole.
Statement II: When the S pole of a magnet moves away from a coil, the near face of the coil becomes an S pole.
  1. (A)Both Statement I and Statement II are true.
  2. (B)Both Statement I and Statement II are false.
  3. (C)Statement I is true, but Statement II is false.
  4. (D)Statement I is false, but Statement II is true.
Show the solution
Given
Two pole claims
Asked
Which are true
Concept
Approach → like pole (repel). Recede → unlike pole (attract).
Formula
Coil opposes the relative motion
Baby steps
  1. Statement I: approach → N face → true.
  2. Statement II: receding S must be attracted → near face N, not S → false.
Answer
(C) Statement I is true, but Statement II is false.
Why not the others
Both-true fails on II. Both-false fails on I. I-false-II-true has them reversed.
Shortcut
Recede → opposite pole.
Where it went wrong
Using the approach rule for a receding magnet.
Q43Two statements
Statement I: The induced current in a loop always produces a magnetic field opposite to the external field through the loop.
Statement II: The induced current opposes the change in magnetic flux through the loop.
  1. (A)Both Statement I and Statement II are true.
  2. (B)Both Statement I and Statement II are false.
  3. (C)Statement I is true, but Statement II is false.
  4. (D)Statement I is false, but Statement II is true.
Show the solution
Given
Opposing the field versus opposing the change
Asked
Which are true
Concept
Lenz's law opposes the change, not the field.
Formula
Shrinking flux → induced field along B
Baby steps
  1. Statement I is false: for shrinking flux the induced field is along the external field.
  2. Statement II is the correct law: true.
Answer
(D) Statement I is false, but Statement II is true.
Why not the others
Both-true would make the common misconception correct. Both-false rejects Lenz's law. I-true-II-false reverses them.
Shortcut
'Opposes the change' is right; 'opposes the field' is wrong.
Where it went wrong
The most common Lenz's law error.

Answer key

1 C
2 A
3 D
4 B
5 C
6 C
7 A
8 C
9 B
10 D
11 C
12 D
13 D
14 A
15 A
16 B
17 A
18 A
19 C
20 B
21 C
22 B
23 B
24 A
25 D
26 B
27 A
28 A
29 D
30 D
31 C
32 B
33 D
34 A
35 D
36 C
37 B
38 A
39 B
40 B
41 C
42 C
43 D

Spread across letters: A 11, B 11, C 11, D 10. No letter repeats more than twice in a row. Question mix: Direction 31, Numerical 2, Graph 4, Assertion–reason 4, Two statements 2. Balancing seed 5.