Question 1

A charged particle with charge q = 2 C moves with velocity v = 5 m/s perpendicular to a magnetic field B = 0.4 T. Calculate the magnetic force acting on the particle.

Accepted Answer

Using F = qvB sin(θ), where θ = 90°, F = 2 × 5 × 0.4 × 1 = 4 N.

Question 2

An electron moves in a circular path in a uniform magnetic field. If the magnetic field strength is doubled, what happens to the radius of the circular path?

Accepted Answer

Since r = mv/(qB), radius is inversely proportional to magnetic field; doubling B halves the radius.

Question 3

A proton enters a magnetic field of 0.5 T at an angle of 30° to the field direction with speed 2 × 10⁶ m/s. The magnetic force on the proton is (charge of proton = 1.6 × 10⁻¹⁹ C):

Accepted Answer

F = qvB sin(30°) = 1.6 × 10⁻¹⁹ × 2 × 10⁶ × 0.5 × 0.5 = 8 × 10⁻¹⁴ N.

Question 4

Which of the following statements about the Lorentz force on a moving charge is correct?

Accepted Answer

The magnetic force F = q(v × B) is perpendicular to both v and B by the cross-product definition.

Question 5

A charged particle moves through crossed electric and magnetic fields without deflection. If E = 3 × 10⁵ V/m and B = 0.6 T, calculate the velocity of the particle.

Accepted Answer

For no deflection, electric and magnetic forces balance: qE = qvB, so v = E/B = 3 × 10⁵ / 0.6 = 5 × 10⁵ m/s.

Question 6

A rectangular loop with sides 4 cm and 6 cm carries 2 A current in a uniform magnetic field of 1.5 T. The plane of the loop is parallel to the field. What is the net force on the loop?

Accepted Answer

Net force on a closed current loop in a uniform magnetic field is zero because forces on opposite sides cancel.

Question 7

An electron moves with speed 10⁷ m/s in a magnetic field of 0.1 T perpendicular to its motion. Find the angular frequency (cyclotron frequency) of its motion.

Accepted Answer

Angular frequency ω = qB/m = (1.6×10⁻¹⁹ × 0.1)/(9.1×10⁻³¹) ≈ 1.76×10⁹ rad/s.

Question 8

A dipole moment of 0.4 A·m² is placed in a magnetic field of 2 T at an angle of 60°. Calculate the torque on the dipole.

Accepted Answer

τ = μB sin(θ) = 0.4 × 2 × sin(60°) = 0.8 × (√3/2) = 0.4√3 N·m.

Question 9

A solenoid has 200 turns and carries a current of 3 A. If the solenoid is 0.4 m long, find the magnetic field inside it.

Accepted Answer

B = μ₀nI = (4π×10⁻⁷) × (200/0.4) × 3 ≈ 1.88×10⁻¹ T.

Question 10

A charged particle moves perpendicular to a uniform magnetic field with speed 2×10⁶ m/s. If the magnetic field strength is 0.5 T and the particle has charge 1.6×10⁻¹⁹ C and mass 1.67×10⁻²⁷ kg, find the radius of circular motion.

Accepted Answer

Using r = mv/(qB) = (1.67×10⁻²⁷ × 2×10⁶)/(1.6×10⁻¹⁹ × 0.5) = 4.18 m.

Question 11

An electron enters a magnetic field of 2 T at an angle of 30° to the field direction with speed 3×10⁶ m/s. What is the radius of the helical path?

Accepted Answer

The perpendicular component of velocity is v⊥ = v sin(30°) = 1.5×10⁶ m/s; r = m v⊥/(eB) ≈ 2.21 cm.

Question 12

A proton and an alpha particle (He nucleus) are accelerated through the same potential difference and then enter perpendicular to a magnetic field. What is the ratio of their radii of curvature?

Accepted Answer

Since KE is same, r ∝ √(m/q); for proton m/q = 1, for alpha m/q = 4/2 = 2, so r_p : r_α = √1:√2 = 1:√2.

Question 13

A current-carrying wire of length 0.5 m carrying 10 A is placed perpendicular to a magnetic field of 0.8 T. Calculate the force on the wire.

Accepted Answer

Using F = BIL = 0.8 × 10 × 0.5 = 4 N.

Question 14

Two parallel wires carry currents of 5 A and 10 A in opposite directions. If they are separated by 20 cm, what is the nature of force between them?

Accepted Answer

Opposite currents repel; F/L = (μ₀ I₁I₂)/(2πd) = (2×10⁻⁷ × 5 × 10)/0.2 = 5×10⁻⁵ N/m.

Question 15

A straight conductor of length 0.5 m carrying a current of 4 A is placed perpendicular to a uniform magnetic field of 2 T. Calculate the magnetic force acting on the conductor.

Accepted Answer

Using F = BIL sin(θ), where B = 2 T, I = 4 A, L = 0.5 m, and θ = 90°, we get F = 2 × 4 × 0.5 × 1 = 4 N.

Question 16

Two parallel conductors carry currents of 5 A and 3 A in the same direction, separated by a distance of 20 cm. What is the nature and magnitude of force per unit length between them?

Accepted Answer

For parallel currents in the same direction, force is attractive; F/L = (μ₀I₁I₂)/(2πd) = (2×10⁻⁷ × 5 × 3)/0.2 = 1.5 × 10⁻⁵ N/m.

Question 17

An electron moves horizontally with velocity 2 × 10⁶ m/s perpendicular to a magnetic field of 0.01 T. What is the radius of the circular path traced by the electron? (Take m = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C)

Accepted Answer

Using r = mv/(eB) = (9.1 × 10⁻³¹ × 2 × 10⁶)/(1.6 × 10⁻¹⁹ × 0.01) = 0.114 m = 11.4 cm.

Question 18

A rectangular coil with 100 turns, area 0.02 m², carries a current of 2 A and is placed in a uniform magnetic field of 0.5 T at an angle of 60° to the field. Calculate the magnetic torque on the coil.

Accepted Answer

Using τ = NBIA sin(θ) = 100 × 0.5 × 2 × 0.02 × sin(60°) = 2 × 0.866 = 1.73 N·m.

CAPF AC Moving Charges & Magnetism

Moving Charges & Magnetism — Practice Questions