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.202Medium
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.203Medium
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)
Q.204Medium
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.205Medium
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)
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Q.206Medium
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.207Medium
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.208Medium
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.209Medium
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.210Medium
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.211Medium
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.212Medium
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.213Medium
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.214Medium
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.215Medium
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.216Medium
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.217Medium
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.218Medium
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.219Medium
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.220Medium
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.
