Zero net force does not mean nothing happens. A loop can be pulled open, squashed inward, or turned — and the orientation decides which.
Part 1 — The concept, explained simply
Put a current loop in a field and ask not "which way does it move" but "what does it feel". The answer is a stretch, a squeeze, or a twist — and each has a different cause.
1. Net force zero does not mean nothing happens
We know a closed loop in a uniform field feels no net force. Students then assume nothing at all happens to it. But "no net force" only means the loop will not travel. It can still be pulled outward, squashed inward, or turned.
Picture it: grab a rubber band with both hands and pull outwards equally. Your two pulls cancel, so the band goes nowhere — but it is stretched hard. Net force zero, plenty happening.
2. What each element of the loop feels
Take a circular loop carrying current I with the field B perpendicular to its plane (pointing out of the page). Apply F = I l × B to each little piece:
Every element carries current along the rim, i.e. tangentially.
The field is perpendicular to the page.
So each force is perpendicular to both — that is, radially, straight out from the centre or straight in.
Add the arrows and they cancel in pairs, so the loop stays put. But every single element is being pulled outwards, so the wire is stretched — just like the rubber band.
3. Stretch or squeeze?
Reverse either the current or the field and every arrow flips inward, so the loop is compressed instead. Which one you get depends on the two directions together:
Current sense
Field
Effect
Anticlockwise
Out of the page
Outward forces → stretching
Clockwise
Out of the page
Inward forces → compression
Either
In the plane of the loop
No radial forces → a torque instead
The deciding question: is the field perpendicular to the loop's plane or in it?
Perpendicular → radial forces → stretch or squeeze, no torque.
In the plane → no radial forces → a torque, and the loop turns.
4. The tension in the wire
If the loop is being stretched, the wire itself must carry a tension holding it together. Balancing forces on a small arc gives a strikingly simple result:
T = B I R
Bigger field, bigger current or bigger loop all mean more tension — and enough of any of them will snap the wire.
5. Why a floppy loop becomes a circle
Now make the wire flexible. Every element is pushed outward, so the loop opens up as far as it can. The wire length cannot change, so the only way to gain area is to become the shape that encloses the most area for a given perimeter — a circle.
Do not confuse the two "becomes a circle" arguments. Field perpendicular to the plane: radial outward forces physically push the loop open into a circle. Field in the plane, loop free to turn: a torque rotates it until its plane is perpendicular to B, maximising the flux.
Both end with a circle facing the field, but for different reasons.
Part 2 — Formula sheet
Situation
Result
Note
Net force on a closed loop, uniform field
0
It will not travel — but it may deform.
Force on each element
dF = I dā × B
Radial when B ⊥ the loop's plane.
B perpendicular to the plane
stretching or compression
No torque in this orientation.
B in the plane of the loop
τ = mB sinθ
A torque, no radial stretching.
Tension in a circular loop
T = B I R
From balancing forces on a small arc.
Flexible loop, B ⊥ plane
opens into a circle
Outward forces plus fixed perimeter.
Flexible loop, free to turn
turns to face B
Maximises flux; stable equilibrium.
Magnetic moment
m = NIA
Largest for a circle at fixed perimeter.
Loop in a NON-uniform field
Fnet ≠ 0
e.g. a loop near a straight wire.
Maximum area for a given perimeter
the circle
Why every "becomes circular" answer is a circle.
Three questions that settle any loop-in-a-field problem
Is the field uniform? If not, expect a net force.
Is B perpendicular to the plane or in it? Perpendicular → stretch/squeeze. In the plane → torque.
Is the wire rigid or flexible? Flexible plus outward forces → it opens into a circle.
Part 3 — 20 questions with step-by-step solutions
Attempt each on paper first. Every solution follows the same five steps: Given → Asked → Concept → Formula → Solution.
Q1Elastic loop
A current I is carried by an elastic circular wire of length L. It is placed in a uniform field B out of the page, with its plane perpendicular to B. What happens to the wire?
(a) no force
(b) a stretching force
(c) a compressive force
(d) a torque
Show step-by-step solution
GivenElastic circular loop, B perpendicular to its plane
AskedEffect on the wire
ConceptEach element feels a radial force. With this sense of current and field the forces point outward.
FormuladF = I dā × B
SolutionCurrent runs tangentially; B is perpendicular to the plane. dā × B is therefore radial for every element. With the given senses the forces point outward from the centre. The loop is pulled open — a stretching force. (The net force is still zero.)
Answer: a stretching force
Q2Net force
For that same loop, the NET force is:
(a) outward
(b) inward
(c) zero
(d) perpendicular to the plane
Show step-by-step solution
GivenClosed loop in a uniform field
AskedNet force
ConceptRadial forces on opposite elements are equal and opposite, so they cancel in pairs.
FormulaFnet = 0 in a uniform field
SolutionTake any element and the one diametrically opposite it. Their outward forces point in exactly opposite directions and are equal. Summing over the whole loop gives zero — the loop does not travel.
Answer: zero
Q3Tension
The tension in a circular current loop of radius R carrying current I in a field B perpendicular to its plane is:
(a) BIR
(b) BI/R
(c) BIR²
(d) BI/2R
Show step-by-step solution
GivenCircular loop, radius R, current I, field B perpendicular
AskedTension in the wire
ConceptBalance the outward magnetic force on a small arc against the inward pull of the tension at its two ends.
FormulaT = B I R
SolutionConsider a small arc subtending angle dθ. Outward magnetic force on it = BI(R dθ). The tensions at its two ends give an inward component T dθ. Equating: T dθ = BIR dθ ⇒ T = BIR.
Answer: BIR
Q4Reversal
If the direction of the current in a stretched loop is reversed while the field stays the same, the loop will be:
(a) stretched more
(b) compressed
(c) unaffected
(d) rotated
Show step-by-step solution
GivenCurrent reversed, field unchanged
AskedNew effect
ConceptReversing the current reverses every element's force, so radial outward becomes radial inward.
FormuladF = I dā × B
SolutionEach element's force reverses direction. Outward forces become inward. The loop is squeezed instead of stretched — compression.
Answer: compressed
Q5Orientation
A current loop is placed in a uniform field lying IN the plane of the loop. It will experience:
(a) a stretching force
(b) a compressive force
(c) a torque
(d) a net force
Show step-by-step solution
GivenField in the plane of the loop
AskedEffect on the loop
ConceptWith B in the plane, the forces are perpendicular to the plane rather than radial, producing a couple.
Formulaτ = mB sinθ
SolutionTwo opposite arms feel forces out of and into the plane. These are equal and opposite but on different lines ⇒ a couple. So the loop experiences a torque and turns; there is no radial stretching.
Answer: a torque
Q6Numerical
A circular loop of radius 20 cm carries 5 A in a field of 0.4 T perpendicular to its plane. The tension in the wire is:
(a) 0.2 N
(b) 0.4 N
(c) 0.8 N
(d) 1.0 N
Show step-by-step solution
GivenR = 0.2 m, I = 5 A, B = 0.4 T
AskedTension
ConceptDirect substitution into the tension formula.
FormulaT = B I R
SolutionT = 0.4 × 5 × 0.2 = 0.4 N.
Answer: 0.4 N
Q7Flexible
A flexible loop of irregular shape carrying current is placed in a uniform field with the field perpendicular to its plane. The loop:
(a) stays irregular
(b) becomes circular
(c) collapses to a point
(d) becomes square
Show step-by-step solution
GivenFlexible irregular loop, B perpendicular to its plane
AskedFinal shape
ConceptOutward forces push it open; the perimeter is fixed, so it takes the shape of maximum area.
Formulacircle maximises area for a fixed perimeter
SolutionEvery element is pushed outward, so the loop opens up. The wire length cannot change. For a fixed perimeter, a circle encloses the greatest area — so it becomes circular.
Answer: becomes circular
Q8Concept
A loop in a uniform field has zero net force. This means:
(a) nothing happens to it
(b) it cannot translate, but it may deform or rotate
(c) it must be at rest
(d) the field is zero
Show step-by-step solution
GivenClosed loop in a uniform field
AskedCorrect interpretation of zero net force
ConceptZero net force forbids translation only.
FormulaFnet = 0
SolutionZero net force means no acceleration of the loop as a whole. But individual elements still feel forces. Those can stretch, compress or rotate the loop.
Answer: it cannot translate, but it may deform or rotate
Q9Non-uniform
A loop placed in a NON-uniform magnetic field experiences:
(a) zero net force
(b) a net force as well as possibly a torque
(c) only a torque
(d) only compression
Show step-by-step solution
GivenLoop in a non-uniform field
AskedNet force
ConceptThe cancellation of forces relies on both sides sitting in equal fields.
FormulaFnet = ∑ I dā × B
SolutionIn a uniform field, opposite elements feel equal and opposite forces. In a non-uniform field the field strengths differ, so cancellation fails. A net force therefore survives — as with a loop near a straight wire.
Answer: a net force as well as possibly a torque
Q10Direction
For a loop carrying anticlockwise current in a field out of the page, the force on each element is directed:
(a) radially outward
(b) radially inward
(c) tangentially
(d) out of the page
Show step-by-step solution
GivenAnticlockwise current, B out of the page
AskedDirection of the element forces
ConceptApply dā × B at one element and the rest follow by symmetry.
FormuladF = I dā × B
SolutionAt the top of the loop the current runs to the left (anticlockwise). B is out of the page. dā × B then points upward, i.e. away from the centre. By symmetry every element is pushed radially outward.
Answer: radially outward
Q11Tension scaling
If both the current and the radius of a loop are doubled, the tension in the wire becomes:
(a) twice
(b) four times
(c) half
(d) unchanged
Show step-by-step solution
GivenI → 2I, R → 2R, same B
AskedNew tension
ConceptThe tension is proportional to the product of I and R.
FormulaT = B I R
SolutionDoubling I doubles T. Doubling R doubles T again. T becomes four times its original value.
Answer: four times
Q12Comparison
A rigid loop and a flexible loop, otherwise identical, are placed in the same perpendicular field. The difference is that:
(a) only the flexible one feels forces
(b) both feel the same forces, but only the flexible one changes shape
(c) the rigid one feels a torque
(d) neither feels anything
Show step-by-step solution
GivenRigid vs flexible loop in a perpendicular field
AskedThe difference
ConceptThe forces are the same; only the response differs.
FormuladF = I dā × B
SolutionThe magnetic forces on each element are identical in both cases. The rigid loop resists, so it merely develops tension. The flexible one deforms, opening out into a circle.
Answer: both feel the same forces, but only the flexible one changes shape
Q13Two reasons
A flexible current loop free to move and turn in a uniform field finally settles as a circle with its plane perpendicular to B. The two effects responsible are:
(a) stretching only
(b) torque only
(c) radial forces opening it out, and torque turning it to face the field
(d) gravity
Show step-by-step solution
GivenFlexible loop, free to move and turn
AskedThe effects at work
ConceptTwo separate mechanisms happen to give the same final configuration.
Formularadial forces; τ = mB sinθ
SolutionRadial outward forces push the loop open into a circle (maximum area). The torque turns it until its area vector lines up with B. Together these give a circular loop facing the field — maximum flux.
Answer: radial forces opening it out, and torque turning it to face the field
Q14Numerical
A circular loop of radius 0.5 m carries 2 A in a perpendicular field of 0.1 T. The tension in the wire is:
(a) 0.1 N
(b) 0.2 N
(c) 0.5 N
(d) 1.0 N
Show step-by-step solution
GivenR = 0.5 m, I = 2 A, B = 0.1 T
AskedTension
ConceptSubstitute into T = BIR.
FormulaT = B I R
SolutionT = 0.1 × 2 × 0.5 = 0.1 N.
Answer: 0.1 N
Q15Torque zero
A current loop lies with its plane perpendicular to a uniform field. The torque on it is:
(a) maximum
(b) mB
(c) zero
(d) mB/2
Show step-by-step solution
GivenPlane perpendicular to B, so the normal is along B
AskedTorque
ConceptCareful: the plane being perpendicular means the moment is PARALLEL to B, giving θ = 0.
Formulaτ = mB sinθ
SolutionPlane ⊥ B ⇒ the area vector (and m) is parallel to B. θ = 0°, so sinθ = 0. τ = 0. This is exactly the orientation in which stretching, not turning, occurs.
Answer: zero
Q16Combined
In the orientation where a loop is stretched most strongly, the torque on it is:
(a) also maximum
(b) zero
(c) half of maximum
(d) undefined
Show step-by-step solution
GivenLoop with B perpendicular to its plane
AskedTorque in that orientation
ConceptRadial stretching and torque occur in opposite orientations, never together.
Formulaτ = mB sinθ, θ = 0
SolutionMaximum stretching happens when B is perpendicular to the plane. That is exactly θ = 0 between m and B. So the torque is zero there. The two effects are mutually exclusive.
Answer: zero
Q17Square loop
A flexible SQUARE loop carrying current is placed in a field perpendicular to its plane, with the forces directed outward. The loop tends to:
(a) stay square
(b) become circular
(c) collapse
(d) become triangular
Show step-by-step solution
GivenFlexible square loop, outward radial forces
AskedTendency of the shape
ConceptOutward forces plus a fixed perimeter drive it towards maximum area.
Formulacircle maximises area
SolutionEach side is pushed outward, bowing it into a curve. The perimeter stays fixed at 4a. The shape of greatest area for that perimeter is a circle, so it rounds out.
Answer: become circular
Q18Concept
The tension formula T = BIR is obtained by:
(a) applying Ampere's law
(b) balancing the outward magnetic force on a small arc against the inward pull of the tensions
(c) using τ = mB sinθ
(d) measuring the magnetic moment
Show step-by-step solution
GivenDerivation of the tension in a current loop
AskedMethod used
ConceptIt is a force-balance on a small element, exactly like the tension in a spinning ring.
FormulaT dθ = BIR dθ
SolutionTake a small arc subtending dθ at the centre. Its outward magnetic force is BI(R dθ). The two end tensions have a combined inward component T dθ. Equate and cancel dθ: T = BIR.
Answer: balancing the outward magnetic force on a small arc against the inward pull of the tensions
Q19Trap
A student says: 'the net force on the loop is zero, so the wire is under no stress'. This reasoning is:
(a) correct
(b) wrong — zero net force does not mean zero force on each element
(c) correct only for circular loops
(d) correct only in a non-uniform field
Show step-by-step solution
GivenZero net force on a closed loop
AskedIs the reasoning sound?
ConceptThe net force is a sum; individual terms can be large while the total vanishes.
FormulaFnet = 0 but dF ≠ 0
SolutionEvery element feels a real outward force. Those forces cancel when summed over the loop. But each element is still being pulled, so the wire carries tension — exactly like the stretched rubber band.
Answer: wrong — zero net force does not mean zero force on each element
Q20Summary
Which pairing is correct?
(a) B perpendicular to the plane → torque; B in the plane → stretching
(b) B perpendicular to the plane → stretching or compression; B in the plane → torque
(c) both orientations give a torque
(d) both orientations give stretching
Show step-by-step solution
GivenLoop in a uniform field, two orientations
AskedCorrect pairing
ConceptThe orientation decides which effect appears; they never occur together.
FormuladF radial when B ⊥ plane; τ = mB sinθ when B in plane
SolutionB perpendicular to the plane ⇒ forces are radial ⇒ stretch or squeeze, torque zero. B in the plane ⇒ forces are perpendicular to the plane on opposite arms ⇒ a couple. So the second pairing is the correct one.
Answer: B perpendicular to the plane → stretching or compression; B in the plane → torque