Moving Charges and Magnetism: Class 12 Important Questions with Answers

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. Write the Lorentz force.
2. When is the force on a current-carrying wire in B zero?
3. Define 1 tesla.
4. What is the value of ${\mu }_0$?
5. Write the condition for a helical path.
6. Why is a radial field used in a galvanometer?
7. State Ampere's circuital law.
8. B far along the axis of a small loop varies as?
9. A wire of 1 m with 2 A at 90° to 0.5 T: force?
10. Ideal ammeter resistance?

D. Short answer I (2 marks each)

1. Derive $r=mv/qB$ and show that T is independent of v.
2. State Biot–Savart law in vector form and give the direction of dB.
3. Define one ampere.
4. Derive B inside a long solenoid using Ampere's law.
5. A 50 Ω galvanometer gives full deflection at 1 mA. Make it a 0–5 V voltmeter.
6. Find B at the centre of a semicircular wire of radius 5 cm with 4 A (leads radial).
7. Why does a flexible current loop in B become circular?
8. Compare current and voltage sensitivity of a galvanometer.

Rough work

E. Short answer II (3 marks each)

1. Derive B on the axis of a circular loop. Find B at the centre.
2. Derive the force per unit length between two parallel wires and state its nature for opposite currents.
3. Derive $\vec{F}=I\vec{l}\times \vec{B}$ from the Lorentz force.
4. Derive B inside and outside a long thick wire carrying I uniformly; sketch B against r.
5. A proton enters B = 0.2 T at $3\times 10^6$ m/s at 30° to B. Find the radius and pitch of the helix.
6. Three wires, A, B, C, parallel and coplanar, 5 cm apart, carry 2 A, 3 A, 4 A in the same direction. Find the force per metre on B.

F. Long answer (5 marks each)

1. Derive the torque on a rectangular coil in a uniform B. A coil of 50 turns, area 4 cm², 2 A, in 0.5 T: find the maximum torque and the work to turn it from 0° to 180°.
2. Explain the principle, construction and working of a moving coil galvanometer. How is it converted to (a) an ammeter, (b) a voltmeter? Derive the required resistances.
3. State Ampere's law. Use it for a long straight wire and a long solenoid. A solenoid of 50 cm, 1000 turns, 2 A: find B inside.
4. Show that a charged particle moves in a circle when v ⊥ B and derive its frequency. An α-particle and a proton have the same KE in the same B: compare their radii and periods.

G. HOTS (higher-order thinking)

1. An electron beam passes undeflected through a region. Can you be sure there is no magnetic field there? Explain.
2. Why do the wires of a household cable carrying ac not fly apart, though they repel?
3. A current loop is placed in a non-uniform B. Can there be a net force? Give a reason.
4. Why does a galvanometer have a scale with zero at the centre?

20 MCQs

1. The SI unit of B is
   (a) weber (b) gauss (c) tesla (d) henry
2. The magnetic force on a charge is maximum when θ between v and B is
   (a) 90° (b) 45° (c) 0° (d) 180°
3. Work done by the magnetic force on a moving charge is
   (a) qvB (b) negative (c) maximum (d) zero
4. Radius of a charge in B is
   (a) qB/mv (b) mv/qB (c) qv/mB (d) mB/qv
5. B at the centre of a loop is
   (a) ${\mu }_{0}I/2\pi R$ (b) ${\mu }_{0}I/2R$ (c) ${\mu }_{0}I/4R$ (d) ${\mu }_{0}IR$
6. B inside a long solenoid
   (a) zero (b) ${\mu }_{0}I/2\pi r$ (c) ${\mu }_{0}nI/2$ (d) ${\mu }_{0}nI$
7. Field of a long wire at distance r
   (a) ${\mu }_{0}I/2\pi r$ (b) ${\mu }_{0}Ir$ (c) ${\mu }_{0}I/2r$ (d) ${\mu }_{0}I/4\pi r^2$
8. Parallel wires with opposite currents
   (a) attract (b) no force (c) repel (d) rotate
9. Torque on a coil is
   (a) $\vec{m}\cdot \vec{B}$ (b) zero always (c) mB (d) $\vec{m}\times \vec{B}$
10. A galvanometer becomes an ammeter with
    (a) high R in series (b) low R in parallel (c) low R in series (d) high R in parallel
11. Current sensitivity of a galvanometer
    (a) NAB/kR (b) k/NAB (c) NAB/k (d) NIAB
12. Frequency of a charge in B depends on
    (a) q/m and B (b) radius (c) speed (d) KE
13. Electron and proton with the same momentum in B: radii ratio
    (a) $m_p/m_e$ (b) 1 (c) $m_e/m_p$ (d) 2
14. Magnetic moment of a loop of area A, current I, N turns
    (a) I/A (b) NI/A (c) NIA (d) NA/I
15. Path when v is at 30° to B
    (a) circle (b) straight line (c) parabola (d) helix
16. μ₀ equals
    (a) $4\pi \times 10^{-7}$ T m/A (b) $10^{-7}$ T m/A (c) $8.85\times 10^{-12}$ (d) $9\times 10^9$
17. The core of a galvanometer coil is made of
    (a) soft iron (b) steel (c) copper (d) aluminium
18. B at the centre of a semicircle (leads radial)
    (a) ${\mu }_{0}I/2R$ (b) zero (c) ${\mu }_{0}I/\pi R$ (d) ${\mu }_{0}I/4R$
19. Force on 2 m of wire with 3 A ⊥ B = 0.1 T
    (a) 0.3 N (b) 0.6 N (c) 6 N (d) 0.06 N
20. A voltmeter is made by joining
    (a) small R in parallel (b) large R in parallel (c) large R in series (d) small R in series

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: The kinetic energy of a charge moving in a magnetic field stays constant. R: The magnetic force is perpendicular to the velocity.
2. A: The period of a charge in a uniform B is independent of its speed. R: The radius is proportional to the speed.
3. A: An ammeter is connected in parallel with the circuit element. R: An ammeter has low resistance.
4. A: Two parallel wires carrying currents in the same direction attract. R: Like currents produce opposite fields between them.
5. A: Torque on a current loop is zero when its plane is perpendicular to B. R: Then $\vec{m}$ is parallel to $\vec{B}$.
6. A: A radial field gives a linear scale in a galvanometer. R: The soft-iron core reduces the magnetic field.

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

Answers to the practice set