The Hall effect in semiconductors is used to determine:
Answer: C
Hall voltage V_H = BId/ne·t indicates carrier sign from voltage polarity and carrier density n from magnitude. This dual information makes Hall effect powerful for semiconductor characterization.
Q.402Easy
A magnetic field B is applied perpendicular to a current-carrying wire of length L carrying current I. The magnetic force on the wire is F = BIL sin θ. What is the angle θ when the force is maximum?
Answer: A
Force F = BIL sin θ is maximum when sin θ = 1, which occurs at θ = 90°. This means the wire must be perpendicular to the magnetic field direction.
Q.403Easy
The SI unit of magnetic field intensity is Tesla. One Tesla is equivalent to which of the following?
Answer: A
1 Tesla = 1 Weber/m² = 1 kg/(A·s²). This is the correct dimensional formula for magnetic field intensity.
Q.404Medium
A solenoid with 500 turns is 0.5 m long and carries a current of 2 A. The permeability of free space is μ₀ = 4π × 10⁻⁷ T·m/A. Calculate the magnetic field inside the solenoid.
Answer: C
B = μ₀nI where n = N/L = 0500.5 = 1000 turns/m. B = 4π × 10⁻⁷ × 1000 × 2 = 2.51 × 10⁻¹ T ≈ 0.251 T.
Q.405Easy
An electron moves in a circular path in a perpendicular magnetic field. Which quantity remains constant during its motion?
Answer: A
Magnetic force is always perpendicular to velocity, so it does no work. Kinetic energy (½mv²) remains constant, but direction changes, so velocity changes while speed remains constant.
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Q.406Medium
Two parallel wires carry currents I₁ = 5 A and I₂ = 3 A in the same direction, separated by distance r = 0.1 m. The force per unit length between them is approximately:
A rectangular loop ABCD with sides 2 m × 3 m carries a current of 4 A and is placed in a uniform magnetic field of 0.5 T perpendicular to the plane of the loop. The magnetic torque on the loop is:
Answer: A
Torque τ = NIAB sin θ. When B is perpendicular to the plane of the loop, it is parallel to the normal of the loop area, so θ = 0° and τ = 0.
Q.408Easy
A charged particle with charge q and mass m enters a magnetic field region with velocity v perpendicular to B. The radius of circular motion is given by:
Answer: A
From qvB = mv²/r, we get r = mv/(qB). This is the radius of curvature for a charged particle in a perpendicular magnetic field.
Q.409Medium
A long straight wire carries a current and produces a magnetic field. At a distance of 2 cm from the wire, the field is 4 × 10⁻⁵ T. What is the current in the wire? (μ₀ = 4π × 10⁻⁷ T·m/A)
Answer: A
B = μ₀I/(2πr). So I = 2πrB/μ₀ = 2π × 0.02 × 4 × 10⁻⁵/(4π × 10⁻⁷) = 2 A.
Q.410Medium
A beam of electrons is accelerated through a potential difference V and then enters a region of perpendicular electric and magnetic fields. For the electrons to move undeflected, which condition must be satisfied?
Answer: B
For undeflected motion, electric force equals magnetic force: qE = qvB, which simplifies to E = vB. This is the velocity selector condition.
Q.411Hard
The magnetic field at the center of a circular arc of radius R subtending angle θ at the center and carrying current I is:
Answer: A
For a circular arc, B = (μ₀I/4πR) × θ, where θ is in radians. This is derived from the Biot-Savart law integrated over the arc.
Q.412Hard
A toroidal magnetic field is produced by a toroid with N turns carrying current I. If the mean radius of the toroid is R and the cross-sectional area of the core is A, the magnetic energy stored is:
Answer: A
Magnetic energy U = ½LI² where L = μ₀N²A/(2πR) for a toroid. Therefore U = μ₀N²I²A/(4πR). Note: The correct formula is actually U = ½ × μ₀N²I²A/(2πR) = μ₀N²I²A/(4πR).
Q.413Hard
An alpha particle (charge +2e, mass 4u) and a proton (charge +e, mass u) are accelerated from rest through the same potential difference. They then enter a uniform magnetic field perpendicular to their motion. The ratio of their radii of curvature is:
Answer: C
After acceleration: ½m₁v₁² = q₁V and ½m₂v₂² = q₂V. In magnetic field, r = mv/(qB). r₁/r₂ = (m₁v₁/q₁)/(m₂v₂/q₂) = (4u × √(2eV/4u)/2e)/(u × √(2eV/u)/e) = √(2u/e) × e/(√(2eV) × √(2V/u)) = 2√2:1.
Q.414Easy
The magnetic flux through a surface is Φ = ∫B·dA. For a uniform field B perpendicular to a rectangular surface of area 2 m², with B = 0.5 T, the flux is:
Answer: C
Φ = BA cos θ. Since B is perpendicular to the surface, θ = 0° and cos θ = 1. Φ = 0.5 × 2 = 1 Wb.
Q.415Easy
According to Lenz's law, the induced EMF in a coil opposes the change in magnetic flux. If the flux through a coil increases at a rate of 0.1 Wb/s and the coil has 100 turns, the induced EMF is:
Answer: A
Induced EMF ε = -N × dΦ/dt = -100 × 0.1 = -10 V. The magnitude is 10 V.
Q.416Medium
A conducting rod of length L = 0.5 m moves with velocity v = 10 m/s perpendicular to a uniform magnetic field B = 2 T. The motional EMF induced is:
Answer: B
Motional EMF ε = BLv = 2 × 0.5 × 10 = 10 V.
Q.417Medium
In a cyclotron, a charged particle spirals outward as it gains energy. The frequency of revolution is independent of:
Answer: B
The cyclotron frequency f = qB/(2πm) is independent of velocity. As velocity increases, radius increases but period remains constant (independent of v).
Q.418Easy
The magnetic field due to a solenoid inside and outside differs significantly. Which statement is correct?
Answer: A
An ideal solenoid produces a uniform, strong magnetic field inside (B = μ₀nI) and negligible field outside. This is due to cancellation of fields from adjacent turns outside.
Q.419Medium
A rectangular conducting loop is partially inside a uniform magnetic field region. If the loop is pulled out with constant velocity v, the induced EMF depends on:
Answer: A
EMF induced ε = BLv where L is the length of the conductor cutting magnetic field lines and v is the velocity. It depends on all three factors: B, L, and v.
Q.420Hard
The phenomenon where the inductance of a coil changes with the current flowing through it due to non-linear magnetic properties of the core is called:
Answer: B
When the magnetic core saturates, further increase in current produces minimal increase in magnetic flux, causing inductance to decrease. This is the saturation effect in magnetic cores.
