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Electric Charges and Fields
Physics · Class 12 · Part 1NCERT pp. 1–372 sets × 25 questionsFree
Key facts and formulas for Electric Charges and Fields, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Quantisation and conservation | q = n e, e = 1.6 × 10⁻¹⁹ C; total charge of an isolated system is conserved |
| Coulomb's law | F = k q₁q₂ / r², k = 9 × 10⁹ N m² C⁻²; in a medium F = F₀ / K |
| Electric field | E = F/q; point charge E = kQ/r²; force on charge F = qE |
| Dipole | p = q × 2a; axial E = 2kp/r³, equatorial E = kp/r³; τ = pE sin θ; U = −pE cos θ |
| Electric flux | φ = E S cos θ (θ with the normal); Gauss's law Φ = q_enc / ε₀ |
| Line and sheet | Infinite line E = 2kλ/r; infinite sheet E = σ/(2ε₀); just outside a conductor E = σ/ε₀ |
| Shell and ball | Outside a shell E = kQ/r²; inside a shell E = 0; uniform ball charge within r is Q(r/R)³ |
| Charge sharing | Identical spheres share total charge equally on touching |
| Cube and corner | Centre charge: q/(6ε₀) per face; corner charge: q/(24ε₀) per far face |
| Parallel sheets | Opposite sheets: σ/ε₀ between, 0 outside; like sheets: 0 between, σ/ε₀ outside |
Three sample questions
Q1. When glass is rubbed with silk, electrons pass from the glass to the silk. After rubbing, the silk is
- positively charged
- negatively charged
- neutral
- positively charged because it gains protons
Hint and solution
Hint: Electrons are negative. Does silk gain them or lose them?
- Rubbing transfers electrons only — In friction, loosely bound outer electrons move from one body to the other. Protons stay put.
- Glass loses e⁻, silk gains e⁻ — Electrons pass from glass to silk, so silk has more electrons than protons.
- Excess electrons → negative charge — A body with extra electrons is negatively charged, so silk is negative. Option B.
Answer: B. The silk gains electrons, so it is negatively charged.
Q2. Charges of +5 µC, −3 µC, +8 µC and −6 µC are brought together. The total charge is
- +22 µC
- −4 µC
- +14 µC
- +4 µC
Hint and solution
Hint: Charge is a scalar with sign. Just add them algebraically.
- Q = q₁ + q₂ + q₃ + q₄ — Charge is a scalar, so we add with signs, not as vectors.
- Positives: 5 + 8 = +13 µC — Add all the positive charges first.
- Negatives: −3 − 6 = −9 µC — Add the negative charges together.
- Q = 13 − 9 = +4 µC — The total is plus 4 microcoulomb. Option D.
Answer: D. 5 − 3 + 8 − 6 = +4 µC. Charge is a signed scalar.
Q3. Which statements are correct? (i) Net charge of an isolated system is conserved. (ii) A body can have a charge of 2.5 e. (iii) Charge is a scalar. (iv) In rubbing of solids, protons are transferred.
- (i), (ii) and (iii)
- (i) and (iii) only
- (ii) and (iv) only
- (i), (iii) and (iv)
Hint and solution
Hint: Check each statement: is charge quantised, and which particles move in rubbing?
- (i) Conservation of charge: true — The total charge of an isolated system stays constant.
- (ii) q = n e, n whole number: false — Charge is quantised, so 2.5 e cannot exist.
- (iii) true, (iv) false — Charge is a scalar. In rubbing, electrons move, not protons.
- True statements: (i) and (iii) — Only (i) and (iii) are correct. Option B.
Answer: B. Charge comes in whole multiples of e, so (ii) is false. Only electrons move, so (iv) is false.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.