The magnetic field intensity at a distance r from a long straight current-carrying wire is:
Answer: B
Using Ampere's circuital law for an infinite straight wire: B = μ₀I/(2πr), where μ₀ = 4π × 10⁻⁷ T·m/A
Q.42Easy
A proton moving with velocity v perpendicular to a magnetic field B follows a circular path. The radius of this path is:
Answer: A
For circular motion in magnetic field: qvB = mv²/r, therefore r = mv/(qB)
Q.43Easy
Two parallel wires carrying currents I₁ and I₂ in the same direction, separated by distance d. The force per unit length between them is:
Answer: C
Magnetic force per unit length between parallel wires: F/L = μ₀I₁I₂/(2πd), attractive for same direction currents
Q.44Easy
A charged particle with charge q and mass m moves in a magnetic field. The cyclotron frequency is:
Answer: A
Cyclotron frequency: f = qB/(2πm) = ω/(2π), where ω = qB/m is the angular frequency
Q.45Medium
A rectangular coil of area A and N turns is rotated in a uniform magnetic field B with angular velocity ω. The maximum induced EMF is:
Answer: A
Maximum EMF in rotating coil: ε_max = NABω, where Φ = NBA cos(ωt), so ε = dΦ/dt = NABω sin(ωt)
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Q.46Medium
A solenoid of length L and cross-sectional area A has N turns. Its self-inductance is:
Answer: A
Self-inductance of solenoid: L = μ₀n²V = μ₀(N/L)²AL = μ₀N²A/L
Q.47Medium
A conducting rod of mass m slides on two parallel rails separated by distance d in a magnetic field B perpendicular to the plane. If the rod moves with constant velocity v, the magnetic force on it is:
Answer: B
Induced EMF: ε = Bdv, induced current: I = Bdv/R, magnetic force: F = BId = B²d²v/R (opposes motion)
Q.48Easy
The magnetic moment of a current loop carrying current I with area A is:
Answer: A
Magnetic moment of a current loop: μ = IA, where I is current and A is area of the loop
Q.49Medium
A bar magnet is cut into two equal halves perpendicular to its length. The magnetic moment of each half is:
Answer: A
When cut perpendicular to length, magnetic moment is halved. Each piece has half the pole strength or length.
Q.50Medium
The mutual inductance between two coils depends on:
Answer: A
Mutual inductance M₁₂ = k√(L₁L₂) depends on coil geometry, orientation, and proximity, not on current or resistance
Q.51Medium
An electron (charge -e) and a proton (charge +e) move perpendicular to the same uniform magnetic field with the same velocity. The ratio of their radii of curvature is:
Answer: B
r = mv/(eB), so r_e/r_p = (m_e/m_p) = 18361 approximately
Q.52Hard
A magnetic field B is applied perpendicular to a conductor carrying current I. The Hall coefficient is related to:
Answer: A
Hall coefficient R_H = 1/(ne), where n is charge carrier density and e is elementary charge
Q.53Easy
A transformer has primary coil with N₁ turns and secondary coil with N₂ turns. The voltage ratio is:
Answer: A
Transformer equation: V₂/V₁ = N₂/N₁ (ideal transformer with no losses)
Q.54Medium
When a conductor moves through a magnetic field, an EMF is induced. This is due to the Lorentz force on:
Answer: A
Motional EMF arises because free electrons experience Lorentz force F = -e(v × B) as conductor moves through field
Q.55Medium
A paramagnetic material placed in a magnetic field becomes magnetized. This is because:
Answer: A
In paramagnetic materials, unpaired electrons have permanent magnetic moments that align with external field
Q.56Medium
An inductor with inductance L and a resistor with resistance R are connected in series with a DC source. The time constant is:
Answer: A
For LR circuit, time constant τ = L/R. Current rises as I = (V/R)(1 - e^(-t/τ))
Q.57Hard
A charged particle enters a uniform magnetic field region at an angle θ to the field direction. Its trajectory is:
Answer: A
Velocity component parallel to B is unaffected; perpendicular component causes circular motion, resulting in helical trajectory
Q.58Medium
The energy stored in a magnetic field of an inductor carrying current I is:
Answer: A
Energy stored in inductor: U = ½LI², derived from dW = LI dI integrated from 0 to I
Q.59Hard
A superconductor exhibits the Meissner effect, which means:
Answer: A
Meissner effect: superconductor actively expels magnetic flux from its interior (B = 0), not just zero resistance
Q.60Easy
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
