A rectangular loop of wire with dimensions 5 cm × 10 cm is placed in a uniform magnetic field of 2 T perpendicular to its plane. If the loop is rotated by 90° in 0.1 s, what is the average induced EMF?
Answer: A
Using Faraday's law: EMF = ΔΦ/Δt = BA/Δt = 2 × (0.05 × 0.1)/0.1 = 1 V
Q.442Easy
Which of the following materials is diamagnetic?
Answer: A
Bismuth is a diamagnetic material that gets repelled by magnetic fields. Iron, cobalt, and nickel are ferromagnetic materials.
Q.443Easy
The magnetic field at the center of a circular loop carrying current I with radius R is given by:
Answer: A
Using Biot-Savart law for a circular loop, the magnetic field at center is B = μ₀I/(2R)
Q.444Easy
Two parallel wires carrying currents I₁ and I₂ in the same direction are separated by distance d. The force per unit length between them is:
Answer: A
Parallel currents in same direction attract each other with force per unit length F/L = μ₀I₁I₂/(2πd)
Q.445Easy
A proton and an electron, both moving with the same velocity perpendicular to a uniform magnetic field, experience forces in the ratio:
Answer: A
Magnetic force F = qvB. Since both have same charge magnitude and velocity, forces are equal in magnitude (directions opposite due to opposite charges)
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Q.446Easy
The radius of circular motion of a charged particle in a magnetic field is r = mv/(qB). If the magnetic field is doubled, the radius becomes:
Answer: A
r ∝ 1/B. When B is doubled, r becomes r/2
Q.447Easy
A solenoid has 1000 turns, length 1 m, and carries a current of 2 A. The magnetic field inside the solenoid is (μ₀ = 4π × 10⁻⁷ T·m/A):
Answer: A
B = μ₀nI = μ₀(N/L)I = 4π × 10⁻⁷ × 1000 × 2 = 8π × 10⁻⁴ T
Q.448Easy
A galvanometer can be converted into an ammeter by connecting a:
Answer: A
A shunt (low resistance in parallel) diverts excess current, protecting the galvanometer coil
Q.449Easy
A conducting rod of length L moves with velocity v perpendicular to a magnetic field B. The induced EMF across the rod is:
Answer: A
Motional EMF = BLv (where L is perpendicular to both B and v)
Q.450Medium
The self-inductance of a solenoid depends on:
Answer: A
L = μ₀n²AL, where n = N/l. Self-inductance depends on geometry and material properties, not on current.
Q.451Medium
A charged particle moves in a helical path in a uniform magnetic field. This happens when the particle's velocity has:
Answer: A
Perpendicular component causes circular motion, parallel component causes linear motion, resulting in helical path
Q.452Medium
In a Hall effect experiment with a rectangular conductor in a magnetic field, the Hall voltage is proportional to:
Answer: A
Hall voltage V_H = (1/ne) × (IB/t), proportional to B and I, inversely proportional to carrier concentration n
Q.453Medium
A rectangular loop is placed in a non-uniform magnetic field. The loop will experience:
Answer: A
Non-uniform field causes net force on the loop due to unequal forces on different sides, plus torque due to magnetic moment
Q.454Medium
The energy density of a magnetic field is given by:
Answer: A
Magnetic energy density u = B²/(2μ₀), similar to electric field energy density
Q.455Medium
Two coils have self-inductances L₁ and L₂ with coupling coefficient k. Their mutual inductance is:
Answer: A
Mutual inductance M = k√(L₁L₂), where 0 ≤ k ≤ 1 is the coupling coefficient
Q.456Medium
A particle with charge q and mass m undergoes circular motion in a magnetic field. Its cyclotron frequency is independent of:
Answer: A
Cyclotron frequency f = qB/(2πm). It depends on q, B, and m, but not on velocity v
Q.457Hard
A toroidal coil has N turns and inner radius r₁, outer radius r₂. The self-inductance is approximately:
Answer: A
For a toroidal coil: L = (μ₀N²h/(2π)) × ln(r₂/r₁), where h is the height of the toroid
Q.458Hard
In a cyclotron, the time period of revolution of a particle is independent of its energy because:
Answer: A
T = 2πm/(qB), independent of v and r. As energy increases, velocity and radius increase proportionally, keeping period constant
Q.459Easy
A magnetic field B is perpendicular to a plane containing a circular loop of radius r. If the magnetic field increases uniformly from 0 to B₀ in time t, what is the magnitude of induced EMF in the loop?
Answer: A
By Faraday's law, induced EMF = -dΦ/dt. Magnetic flux Φ = BA = πr²B. As B changes from 0 to B₀ in time t, EMF = πr²(B₀-0)/t = πr²B₀/t
Q.460Easy
Which of the following is NOT a property of magnetic field lines?
Answer: D
Magnetic field lines always form closed loops and cannot exist in isolation. Unlike electric field lines which start from positive charges and end at negative charges, magnetic field lines have no beginning or end.
