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.22Medium
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.23Medium
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.24Medium
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.25Medium
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
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Q.26Medium
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.27Medium
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.28Medium
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.29Medium
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.30Medium
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.31Medium
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.32Medium
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.33Medium
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.34Medium
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.35Medium
The magnetic field between the poles of a permanent magnet is approximately:
Answer: B
Between the parallel poles of a strong permanent magnet (in the central region), the magnetic field is approximately uniform. However, it becomes non-uniform near the pole edges.
Q.36Medium
A rectangular conducting loop ABCD with sides a and b is rotated with angular velocity ω in a uniform magnetic field B perpendicular to the plane of rotation. The induced EMF is:
Answer: B
When the loop rotates, the magnetic flux through it varies as Φ = BA·cosωt. The induced EMF = -dΦ/dt = BA·ω·sinωt = Bab·ω·sinωt
Q.37Medium
Two magnets are placed with their north poles facing each other. The force between them varies with distance r as:
Answer: D
Two magnetic dipoles interact with force F ∝ 1/r⁴ when aligned along the same axis. This is because the magnetic field of a dipole varies as 1/r³, and force on a dipole is proportional to the field gradient.
Q.38Medium
A conducting rod of length L moves with velocity v perpendicular to its length in a magnetic field B. The motional EMF induced is maximum when:
Answer: B
Motional EMF = B·L·v·sinθ, where θ is the angle between v and B. EMF is maximum when sinθ = 1, i.e., when v is perpendicular to B.
Q.39Medium
The magnetic susceptibility of a paramagnetic material is:
Answer: B
Paramagnetic materials have positive but small magnetic susceptibility (χ > 0, typically 10⁻⁵ to 10⁻³). Diamagnetic materials have small negative susceptibility, and ferromagnetic materials have large positive susceptibility.
Q.40Medium
A charged particle with charge q and mass m is moving with speed v in a circular path of radius r in a magnetic field. The magnetic field strength is:
Answer: A
From qvB = mv²/r (centripetal force equals magnetic force), we get B = mv/(qr). This is the relationship between field strength, particle properties, and circular path radius.
