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.22Easy
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.23Easy
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.24Easy
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.25Easy
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.26Easy
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.27Easy
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.28Easy
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.29Easy
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.30Easy
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.31Easy
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.
Q.32Easy
A straight wire carrying current I is placed in a uniform magnetic field B at an angle θ to the magnetic field. If the length of the wire is L, the magnetic force on the wire is:
Answer: B
The magnetic force on a current-carrying conductor is F = BIL sinθ, where θ is the angle between the current direction and the magnetic field. When θ = 90°, force is maximum (BIL), and when θ = 0°, force is zero.
Q.33Easy
Two parallel wires carry currents I₁ and I₂ in the same direction, separated by distance d. The force per unit length between them is:
Answer: B
Parallel wires carrying currents in the same direction experience attractive force. Force per unit length = μ₀I₁I₂/(2πd). If currents are opposite, the force is repulsive.
Q.34Easy
A charged particle enters a uniform magnetic field with velocity perpendicular to the field. The particle will move in:
Answer: B
When a charged particle moves perpendicular to a uniform magnetic field, the Lorentz force acts as centripetal force, causing circular motion. The radius is r = mv/(qB).
Q.35Easy
A solenoid has n turns per unit length and carries current I. The magnetic field inside the solenoid is:
Answer: A
The magnetic field inside an ideal long solenoid is B = μ₀nI, independent of the solenoid's radius and position along the axis (away from ends). This assumes n is the number of turns per unit length.
Q.36Easy
The magnetic moment of a current loop is defined as:
Answer: A
Magnetic moment M = IA, where I is the current and A is the area enclosed by the loop. For N turns, M = NIA. The SI unit is A·m².
Q.37Easy
An electron moves in a plane perpendicular to a uniform magnetic field. If the radius of its circular path is r, the momentum of the electron is:
Answer: A
For circular motion in a magnetic field: qvB = mv²/r, which gives r = mv/(qB). Therefore, momentum p = mv = qBr = eBr (for an electron where q = e).
