1 The NEET Cheat Sheet — Core Concepts & Exceptions
Some objects carry an invisible property called charge. Charges of the same kind push each other apart, opposite kinds pull together. The push/pull at any point is what we call the electric field. The whole chapter is just rules for finding that field.
Properties of Electric Charge
Quantisation of charge
💡 Charge comes only in whole packets — never half an electron. The smallest packet is the charge of one electron (e).
Every charge is q = ± n·e, where n ∈ ℤ and e = 1.602 × 10⁻¹⁹ C.
📌 Charge of an α-particle = +2e; a Cl⁻ ion = −e.
⚠ Fails at quark level (±⅓ e, ±⅔ e), but quarks are never free — so quantisation holds for all observable charges.
Conservation of charge
💡 Charge is never created or destroyed — it only moves from one object to another (like a thread of beads being passed around).
Total charge of an isolated system stays constant in any process — even nuclear reactions.
📌 Beta decay: n → p + e⁻ + ν̄. Net charge before (0) = after (+1 − 1 + 0) = 0. ✓
Additivity
💡 If a body has many tiny charges sitting on it, the body's total charge is just their sum — with signs.
Qtotal = q₁ + q₂ + q₃ + … (algebraic sum).
📌 +5 μC plus −3 μC on the same body ⇒ net +2 μC.
Conductors, insulators & charging
Conductor vs Insulator
💡 In conductors (metals, salt water) charges can walk around freely. In insulators (plastic, glass) they're stuck where they are.
Conductors: free electrons → very low resistance. Insulators: bound electrons → resist motion.
⚠ A charged conductor at equilibrium has all extra charge on its outer surface and E = 0 inside.
3 ways to charge a body
💡 You can give an object charge by rubbing (friction), by touching (conduction), or by simply bringing a charged thing nearby (induction).
Friction (rubbing) · Conduction (direct contact) · Induction (no contact — separates charges, then ground).
📌 Earthing a conductor in induction removes the unwanted same-sign charge; left with opposite sign.
Coulomb's law — the foundation
Coulomb's law
💡 Two charges push/pull each other harder if they're bigger, and much weaker if farther apart (squared!).
F = k·q₁q₂/r², where k = 1/(4πε₀) ≈ 9 × 10⁹ N m²/C²; ε₀ = 8.854 × 10⁻¹² C²/N·m².
📌 The force is along the line joining the two charges — attractive for opposite signs, repulsive for like signs.
⚠ Valid for point charges at rest in vacuum. In a medium of dielectric constant K: Fmed = Fvac/K.
Superposition principle
💡 If many charges are around, the total force on one of them is just the vector sum of forces from each, one at a time.
Fnet = F₁ + F₂ + F₃ + … (vectors).
📌 Always resolve into x and y components first, then add.
Electric field & field lines
Electric field E
💡 An invisible arrow at every point — telling you which way and how strongly a +1 C test charge would be pushed.
E = F / q₀ (q₀ → 0); SI unit: N/C = V/m.
Field of a point charge: E = kq/r², radial (outward for +, inward for −).
Field-line rules
💡 Field lines are visual maps of the electric field — like wind-direction streaks.
- Start on + charges, end on − charges (or at infinity).
- Never cross (single E direction at each point).
- Density of lines ∝ field strength.
- Tangent to a field line = direction of E.
- Continuous in free space (don't form closed loops in electrostatics).
Positive point charge
Lines radiate outward.
Dipole (+q, −q)
From + to −, curved outside.
Two like (+, +)
Lines repel; neutral point midway.
Electric dipole
Dipole moment & field
💡 Two equal & opposite charges a tiny distance apart act together like a single "arrow" called the dipole moment, pointing from − to +.
p = q · 2a; SI unit: C·m. Direction: −q → +q.
Axial (end-on) field: E = (2kp)/r³ — along p.
Equatorial (broadside): E = kp/r³ — anti-parallel to p.
⚠ Both formulas assume r >> a (short / point dipole).
Dipole in uniform field
💡 Place a dipole in a uniform field and it rotates to align with the field — like a compass needle.
Torque τ = p × E ⇒ |τ| = pE sinθ. Stable equilibrium at θ = 0°; unstable at 180°.
Potential energy U = −p·E = −pE cosθ. Net force = 0 in uniform field.
Electric flux & Gauss's law
Electric flux ϕE
💡 Imagine field lines piercing a surface. Count the lines passing through — that "count" is the flux.
ϕE = ∫ E · dA = EA cosθ (uniform field). SI unit: V·m or N·m²/C.
📌 If E is parallel to surface (θ = 90°): ϕ = 0.
Gauss's law
💡 Total field lines piercing any closed surface depend only on the charge it encloses — nothing else inside or outside the box matters.
∮ E · dA = qenc / ε₀ — for any closed surface.
📌 Charge q at centre of a cube: flux through cube = q/ε₀; through one face = q/(6ε₀).
⚠ Charge outside the surface contributes zero net flux (in = out).
Exceptions, limits & common errors
- Coulomb's law fails for charges in motion (then magnetism enters) and at sub-atomic distances (quantum effects). It is valid for stationary point charges.
- The formula E = kq/r² applies only outside a uniformly charged sphere or shell. Inside a uniformly charged shell, E = 0; inside a uniformly charged solid sphere, E = kQr/R³ (linear in r).
- For an infinite line charge: E = λ/(2πε₀ r) — 1/r dependence, not 1/r².
- For an infinite plane sheet: E = σ/(2ε₀) — independent of distance!
- For a charged conductor's surface: E = σ/ε₀ just outside (twice that of a sheet, because field is one-sided).
- Gauss's law gives you the field quickly only when the surface has high symmetry (sphere, cylinder, plane). Otherwise it just gives you the flux.
2 The Formula & Approximation Bank
Every formula NEET tests, grouped by topic — with the time-saving notes beside each. A one-line plain summary sits above each group.
Coulomb force & field
💡 Two big "musts": k = 9 × 10⁹ in vacuum, and force/field always shrink as 1/r².
| Formula | Notes / Approximation |
|---|---|
| F = (1/4πε₀)·q₁q₂/r² = kq₁q₂/r² | k = 9 × 10⁹ N m²/C² (vacuum); ε₀ = 8.854 × 10⁻¹² C²/N·m². |
| Fmed = Fvac / K | K = relative permittivity (dielectric constant) of the medium. |
| E = F / q₀ = kq/r² (point charge) | Direction: away from +q, toward −q. |
| q = ± n·e ; e = 1.6 × 10⁻¹⁹ C | Quantisation; integer multiples only. |
| 1 C ≈ 6.25 × 10¹⁸ electron charges | Handy for "number of electrons" type Qs. |
Continuous charge distributions
💡 When charge is spread out, "shrink" the distribution to a tiny piece dq, find its dE, then add (integrate).
| Formula | Notes |
|---|---|
| Line: λ = dq/dl ; E = λ/(2πε₀ r) | Infinite straight line. Radial; falls as 1/r. |
| Surface: σ = dq/dA ; E = σ/(2ε₀) | Infinite plane sheet. Independent of distance. |
| Volume: ρ = dq/dV | Use Gauss for high-symmetry volumes. |
| Two parallel sheets (opposite signs): Ebetween = σ/ε₀; outside = 0 | Useful in capacitor / Q5-style problems. |
Electric dipole
💡 A dipole's field falls off faster than a single charge (1/r³ versus 1/r²) — because the + and − partially cancel far away.
| Formula | Notes |
|---|---|
| p = q · 2a (from −q to +q) | SI: C·m. Vector. |
| Eaxial = (2kp)/r³ | End-on; same direction as p; twice equatorial. |
| Eequatorial = kp/r³ | Broadside; opposite to p. |
| Egeneral = (kp/r³)·√(1 + 3cos²θ) | θ measured from the dipole axis. |
| τ = pE sinθ ; U = −pE cosθ | Torque & potential energy in uniform field. |
Flux & Gauss's Law applications
💡 Pick a "Gaussian surface" so that E is either perpendicular & constant (then EA = q/ε₀) or parallel (then contributes zero).
| Formula | Notes |
|---|---|
| ϕE = EA cosθ ; ∮ E·dA = qenc/ε₀ | Closed surface only; charge outside contributes 0. |
| Point charge at cube centre: ϕtotal = q/ε₀ ; per face = q/(6ε₀) | At a corner: per face touching = 0; total = q/(8ε₀). |
| Solid sphere (uniform ρ): Ein = kQr/R³ ; Eout = kQ/r² | Inside: linear in r; outside: as point charge at centre. |
| Spherical shell: Ein = 0 ; Esurface = kQ/R² ; Eout = kQ/r² | Inside any hollow conductor / shell, field is zero. |
| Conductor surface: E = σ/ε₀ | Twice a sheet because field exists on one side only. |
Useful constants
📈 Interactive Field-vs-Distance Graph
Different shapes of charge give different "falloff" laws for the electric field. A point charge falls as 1/r², a line as 1/r, and a sheet doesn't fall at all. Pick a configuration and watch the graph.
Sliders update the curve in real time. Notice: sheet is a flat line (E independent of r), line falls as 1/r, point as 1/r², and shell jumps from 0 (inside) to kQ/R² (surface) then falls.
3 The "Trap Avoidance" & Shortcut Guide
These are the exact spots where students lose easy marks. Each card shows the trap, then the quick fix.
Coulomb's law in a medium
⚡ For water K ≈ 80 — the force becomes 80 times weaker, not the same.
"Inside vs Outside" of a charged sphere/shell
A favourite NEET twist. Use this table:
| Region | Uniform shell | Solid sphere (uniform ρ) |
|---|---|---|
| Inside (r < R) | E = 0 | E = kQr/R³ (linear in r) |
| At surface | E = kQ/R² | E = kQ/R² |
| Outside (r > R) | E = kQ/r² | E = kQ/r² |
⚡ Inside a hollow conductor / shell: E = 0, V = constant = kQ/R. NEET classics.
Flux through a cube — corner trick
⚡ At face centre: ϕ = q/(2ε₀). At edge midpoint: ϕ = q/(4ε₀). At centre: ϕ = q/ε₀.
Dipole — axial vs equatorial
- Axial field is twice equatorial: Eaxial = 2·Eequatorial (at same r).
- Both fall as 1/r³, faster than a single point charge.
- On axial line E is parallel to p; on equatorial line E is anti-parallel to p.
- Net force on a dipole in uniform field = 0; only torque.
⚡ Memory hook: "A"xial means "A"head, "2x" the strength.
Sheet vs Conductor surface — the factor of 2
⚡ The "2" disappears for a conductor because all the flux has only one side to go through.
Superposition signs
- Always work with vectors: resolve each force into x and y, then add.
- For three equal charges at corners of an equilateral triangle (side a), force on any one = √3·kq²/a², directed outward along the bisector.
- For four equal charges at corners of a square, force on each charge ≠ zero — there is a net outward push along the diagonal.
Common numerical shortcuts
Memorise these to save 30+ seconds per problem:
4 High-Yield Practice MCQs
Try each question first, then open the solution to see the quickest route — using the formulas and shortcuts from above, not long textbook working.
10 NEET-level questions with numerically close options — 2 theory, 2 Coulomb, 3 field/dipole, 3 Gauss/flux. Tap "Show fastest solution".
TheoryQ1. Which of the following is NOT a correct property of electric field lines?
- They start from +ve and end on −ve charges.
- They can cross each other in regions of strong field.
- The tangent at any point gives the direction of E at that point.
- Their density at a point is proportional to the magnitude of E.
Show fastest solution
Answer: (b)Two crossing lines would give two directions for E at the crossing point — impossible. So field lines never cross. The other three are standard properties.
TheoryQ2. A point charge +q is placed at the centre of a cubical Gaussian surface. The flux through one face is:
- q/ε₀
- q/(2ε₀)
- q/(6ε₀)
- q/(8ε₀)
Show fastest solution
Answer: (c) q/(6ε₀)Total flux through the closed cube = q/ε₀. By symmetry six faces share it equally ⇒ q/(6ε₀) per face.
CoulombQ3. Two point charges +1 μC and +1 μC are placed 1 m apart in vacuum. The force on each is:
- 9 × 10⁻³ N (repulsive)
- 9 × 10⁻⁶ N (attractive)
- 9 × 10⁹ N (repulsive)
- 9 N (repulsive)
Show fastest solution
Answer: (a)F = kq₁q₂/r² = 9 × 10⁹ × (10⁻⁶)² / 1² = 9 × 10⁻³ N. Like charges → repulsive.
CoulombQ4. Two point charges +4q and +q lie on a line at distance d. The point on the line joining them where the net field is zero is at distance from +4q:
- d/3
- 2d/3
- d/2
- d/4
Show fastest solution
Answer: (b) 2d/3For E = 0 between the charges: k(4q)/x² = kq/(d−x)² ⇒ 2(d−x) = x ⇒ x = 2d/3. Closer to the smaller charge, as expected.
Field / DipoleQ5. An electric dipole of moment p is placed at angle θ with a uniform field E. Torque on it is:
- pE
- pE cosθ
- pE sinθ
- 0
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Answer: (c) pE sinθτ = p × E ⇒ magnitude = pE sinθ. Maximum at θ = 90°; zero at θ = 0° or 180°.
Field / DipoleQ6. At a point on the axial line of a short dipole (moment p) at distance r (r >> a), the field is E. The field at the same distance on the equatorial line is:
- E
- E/2
- 2E
- E/4
Show fastest solution
Answer: (b) E/2Eaxial = 2kp/r³ and Eequatorial = kp/r³ ⇒ ratio 2 : 1. So equatorial = E/2.
Field / DipoleQ7. Two large parallel sheets carry surface charge densities +σ and −σ. The field in the region between the sheets is:
- σ/(2ε₀)
- σ/ε₀
- 2σ/ε₀
- 0
Show fastest solution
Answer: (b) σ/ε₀Each sheet alone gives σ/(2ε₀). Between, the two fields add (opposite signs of σ, fields in same direction) ⇒ σ/ε₀. Outside, they cancel.
Gauss / FluxQ8. A charge of 8 μC is placed at the centre of a sphere of radius 2 m. The total electric flux out of the sphere is:
- 9 × 10⁵ V·m
- 9 × 10⁴ V·m
- 9 × 10⁵ V·m²/C
- (8/ε₀) μV·m
Show fastest solution
Answer: (a)ϕ = qenc/ε₀ = (8 × 10⁻⁶)/(8.854 × 10⁻¹²) ≈ 9.04 × 10⁵ V·m. Note: independent of radius.
Gauss / FluxQ9. A point charge q is placed at one corner of a cube. The total electric flux through the cube is:
- q/ε₀
- q/(2ε₀)
- q/(8ε₀)
- q/(6ε₀)
Show fastest solution
Answer: (c) q/(8ε₀)Surround the corner with 8 identical cubes; by symmetry, each gets q/8 of the total flux. Total enclosed (over 8 cubes) = q ⇒ each cube has q/(8ε₀).
Gauss / FluxQ10. A solid metallic sphere of radius R carries a charge Q. Field at distance r = R/2 from its centre is:
- kQ/R²
- kQr/R³
- 0
- kQ/r²
Show fastest solution
Answer: (c) 0Inside a metallic (conductor) sphere, all charge sits on the surface and the field inside is zero. Don't confuse with a solid insulator (uniform ρ) where Ein = kQr/R³.
★ Godmode
Opens every "Show fastest solution" reveal on the page at once and stays unlocked. Use it for revision day, when you just want to see all answers in order without clicking each one.