Vidaara.orgClass 12 · Physics
CodeVID-P12-01-CH-01
Chapter Assignment — Electrostatics
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A (1 mark each)
6 × 1 = 6 marks
1.
The SI unit of charge is the:
- A.volt
- B.coulomb
- C.farad
- D.ampere
2.
Coulomb force between charges varies as:
- A.$1/r$
- B.$1/r^2$
- C.$r$
- D.$r^2$
3.
Torque on a dipole is:
- A.$pE\cos\theta$
- B.$pE\sin\theta$
- C.$pE$
- D.$p/E$
4.
Field inside a charged spherical shell is:
- A.maximum
- B.zero
- C.constant
- D.infinite
5.
Electric potential is a:
- A.vector
- B.scalar
- C.tensor
- D.pseudovector
6.
Energy stored in a capacitor is:
- A.$\frac12 CV$
- B.$\frac12 CV^2$
- C.$CV^2$
- D.$C^2 V$
Section B (2 marks)
4 × 2 = 8 marks
7.
State Coulomb\u2019s law in vector form.
8.
Define electric flux and give its SI unit.
9.
A $5\ \mu\text{F}$ capacitor is charged to 100 V. Find the charge.
10.
Find the field 0.2 m from a $+4\ \mu\text{C}$ charge.
Section C (3 marks)
2 × 3 = 6 marks
11.
Using Gauss\u2019s law, derive the field of an infinite line charge of density $\lambda$.
12.
Two capacitors $6\ \mu\text{F}$ and $3\ \mu\text{F}$ are in series across 9 V. Find the charge on each.
Section D (5 marks)
2 × 5 = 10 marks
13.
Derive the expression for the electric field on the axial line of a short dipole and state the direction of the field.
14.
Derive the energy stored in a parallel-plate capacitor and express it as energy density.
Answer Key
Section A (1 mark each)
- (B) coulomb
- (B) $1/r^2$
- (B) $pE\sin\theta$
- (B) zero
- (B) scalar
- (B) $\frac12 CV^2$
Section B (2 marks)
- $\vec{F}_{12}=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}\hat{r}$, directed along the line joining the charges.
- Flux $\phi=\vec{E}\cdot\vec{A}=EA\cos\theta$; SI unit $\text{N}\,\text{m}^2\,\text{C}^{-1}$.
- $Q=CV=5\times10^{-6}\times100=5\times10^{-4}\ \text{C}$.
- $E=9\times10^{9}\times\frac{4\times10^{-6}}{0.04}=9\times10^{5}\ \text{N/C}$.
Section C (3 marks)
- Coaxial cylinder of radius $r$, length $l$: flux $=E(2\pi r l)=\frac{\lambda l}{\epsilon_0}$, giving $E=\frac{\lambda}{2\pi\epsilon_0 r}$.
- $C_s=2\ \mu\text{F}$; $Q=C_sV=2\times10^{-6}\times9=1.8\times10^{-5}\ \text{C}$ on each.
Section D (5 marks)
- For axial point at $r$: $E=\frac{1}{4\pi\epsilon_0}\left[\frac{q}{(r-a)^2}-\frac{q}{(r+a)^2}\right]$; for $r\gg a$ this reduces to $E=\frac{1}{4\pi\epsilon_0}\frac{2p}{r^3}$, directed along $\vec{p}$.
- $U=\frac12 CV^2=\frac{Q^2}{2C}$. With $C=\frac{\epsilon_0 A}{d}$ and $V=Ed$, $U=\frac12\epsilon_0 E^2 (Ad)$, so energy per unit volume $u=\frac12\epsilon_0 E^2$.
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