Electric Charges and Fields: Class 12 Important Questions with Answers

More NCERT-style worked problems

Case-based practice

Practice set: test yourself

Try every question before looking at the answers below. 64 or more out of 80 means you are ready for the board.

C. Very short answer (1 mark each)

1. What is the net charge of an electric dipole?
2. Name the experiment that showed charge is quantised.
3. Flux through a closed surface with $+q$ and $-q$ inside?
4. Why is $\vec{E}$ normal to a charged conductor's surface?
5. Two charges attract with force F. If each charge and the distance are doubled, the force is?
6. Write the dimensional formula of ${\epsilon }_0$.
7. At what angle between $\vec{p}$ and $\vec{E}$ is the torque maximum?
8. Field at the centre of a uniformly charged ring?
9. Ratio of axial to equatorial field of a short dipole at the same distance?
10. How many electrons make $-1$ C?

D. Short answer I (2 marks each)

1. State and explain the principle of superposition of electric forces.
2. Write four properties of electric field lines.
3. Draw the field lines of (a) two equal positive charges, (b) a dipole.
4. A charge $q$ is at the centre of a cube. Find the flux through (a) the whole cube, (b) one face.
5. Two charges $+9$ μC and $+1$ μC are 40 cm apart. Where is the field zero?
6. Derive the torque on a dipole in a uniform field. When is it zero?
7. Explain charging by induction with diagrams.
8. Find the force on $-2$ μC at 3 cm from an infinite line charge of $\lambda =3$ μC/m.

Rough work

E. Short answer II (3 marks each)

1. Use Gauss's law to find the field due to an infinitely long straight wire with linear charge density λ.
2. Four charges $+q$, $+q$, $-q$, $-q$ are at the corners of a square of side $a$ (like charges adjacent). Find the field at the centre.
3. $\vec{E}=200x\hat{i}$ N/C. Find the flux through a cube of side 0.2 m whose faces are at x = 0.2 m and x = 0.4 m, and the charge inside.
4. Show that the electric field of a charged conducting plate is twice that of a charged non-conducting sheet of the same σ.
5. Three charges $q$, $q$ and $-2q$ are at the corners of an equilateral triangle of side $l$. Find the dipole moment of the system.
6. A proton enters a uniform field of $3\times 10^4$ N/C at right angles with speed $2\times 10^6$ m/s. Find its deflection after 10 cm. ($m_p=1.67\times 10^{-27}$ kg)

F. Long answer (5 marks each)

1. Derive the field of a dipole at a point on its axis. Show that for $r\gg a$ it is $2kp/r^3$. Find the field on the axis 20 cm from the centre of a dipole of $p=2\times 10^{-8}$ C m.
2. State Gauss's law. Use it to find E due to a uniformly charged thin shell outside and inside. Draw the E–r graph.
3. Derive the field on the equatorial line of a dipole. A dipole of charges ±2 μC, 2 cm apart, is placed at 30° to a field of $5\times 10^5$ N/C: find the torque.
4. (a) Derive E due to an infinite plane sheet. (b) Two parallel sheets carry +2σ and −σ. Find E in the three regions.

G. HOTS (higher-order thinking)

1. A charge $q$ is at the centre of the open face of a hemisphere-shaped bowl. What is the flux through the curved surface?
2. Why is it safer to sit inside a car than under a tree during lightning?
3. A small charged ball hangs on a silk thread. A charged rod is brought near and the ball is attracted. Can you conclude the ball and rod have opposite charges? Explain.
4. The field just outside a charged conductor is $\sigma /{\epsilon }_0$, yet the field of a sheet is $\sigma /2{\epsilon }_0$. Explain the factor of 2 using superposition.

20 MCQs

1. The minimum charge a body can have is
   (a) 1 C (b) $3.2\times 10^{-19}$ C (c) $1.6\times 10^{-19}$ C (d) $0.8\times 10^{-19}$ C
2. If the distance between two charges is halved, the force becomes
   (a) 4F (b) 2F (c) F/2 (d) F/4
3. The SI unit of electric field is
   (a) N C (b) N m²/C (c) C/N (d) N/C
4. Field lines of an isolated positive charge are
   (a) radially inward (b) radially outward (c) circles (d) parallel lines
5. The flux through a closed surface enclosing a dipole is
   (a) $q/{\epsilon }_0$ (b) zero (c) $2q/{\epsilon }_0$ (d) $q/2{\epsilon }_0$
6. The field of a short dipole at a distance r varies as
   (a) $1/r$ (b) $1/r^2$ (c) $1/r^4$ (d) $1/r^3$
7. Torque on a dipole is maximum when θ is
   (a) 90° (b) 0° (c) 180° (d) 45°
8. Field of an infinite line charge at distance r is
   (a) $\lambda /2{\epsilon }_0$ (b) $\lambda /4\pi {\epsilon }_0{r}^2$ (c) $\lambda /2\pi {\epsilon }_{0}r$ (d) zero
9. Field near an infinite plane sheet of charge is
   (a) $\sigma /{\epsilon }_0$ (b) $2\sigma /{\epsilon }_0$ (c) $\sigma /4{\epsilon }_0$ (d) $\sigma /2{\epsilon }_0$
10. Field inside a charged thin spherical shell is
    (a) maximum (b) zero (c) $kq/R^2$ (d) $kq/r^2$
11. A charge q at the centre of a cube: flux through one face is
    (a) $q/{\epsilon }_0$ (b) $q/4{\epsilon }_0$ (c) $q/6{\epsilon }_0$ (d) $q/8{\epsilon }_0$
12. Rubbing glass with silk, the glass
    (a) loses electrons (b) gains electrons (c) gains protons (d) loses protons
13. A dipole in a non-uniform field experiences
    (a) only a torque (b) a force and possibly a torque (c) neither (d) only a force, never torque
14. The unit of electric flux is
    (a) N/C (b) N C m (c) N m²/C (d) C/m²
15. The force between two charges in water (K = 80) compared with air is
    (a) 80 times (b) 1/√80 times (c) the same (d) 1/80 times
16. At a far point, $E_{\text{axial}}/E_{\text{equatorial}}$ of a dipole is
    (a) 2 (b) 1/2 (c) 4 (d) 1
17. Two plates with +σ and −σ: field between them is
    (a) $\sigma /{\epsilon }_0$ (b) $\sigma /2{\epsilon }_0$ (c) zero (d) $2\sigma /{\epsilon }_0$
18. Dimensions of ${\epsilon }_0$
    (a) $[{\text{M}}^{-1}{\text{L}}^3{\text{T}}^4\text{A}]$ (b) $[{\text{ML}}^3{\text{T}}^{-3}{\text{A}}^{-1}]$ (c) $[{\text{MLT}}^{-2}]$ (d) $[{\text{M}}^{-1}{\text{L}}^{-3}{\text{T}}^4{\text{A}}^2]$
19. A proton and an electron in the same field have accelerations in the ratio $a_p/a_e$
    (a) 1 (b) $m_e/m_p$ (c) $m_p/m_e$ (d) $\sqrt{m_e/m_p}$
20. Number of electrons in $-3.2$ μC
    (a) $2\times 10^{12}$ (b) $5\times 10^{12}$ (c) $2\times 10^{13}$ (d) $3.2\times 10^{13}$

1 (c) · 2 (a) · 3 (d) · 4 (b) · 5 (b) · 6 (d) · 7 (a) · 8 (c) · 9 (d) · 10 (b) · 11 (c) · 12 (a) · 13 (b) · 14 (c) · 15 (d) · 16 (a) · 17 (a) · 18 (d) · 19 (b) · 20 (c)

Assertion–Reason (6)

(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

1. A: Two field lines never intersect. R: At a point the field has a unique direction.
2. A: The net flux through a closed surface with a charge outside it is zero. R: Field lines from an outside charge that enter the surface also leave it.
3. A: A dipole in a uniform field has zero net force. R: A dipole in a uniform field has zero torque at all angles.
4. A: The field inside a uniformly charged thin shell is zero. R: A Gaussian sphere drawn inside the shell encloses no charge.
5. A: Charge is quantised. R: The total charge of an isolated system is conserved.
6. A: The field of an infinite sheet varies as $1/r$. R: The field lines of an infinite sheet are parallel.

Key: 1 (a) · 2 (a) · 3 (c) · 4 (a) · 5 (b) · 6 (d)

Answers to the practice set