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.82Easy
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.83Easy
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.84Easy
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.85Easy
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).
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Q.86Medium
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.87Medium
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.88Medium
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.89Medium
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.90Medium
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.91Medium
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.
Q.92Medium
The permeability of free space μ₀ has the value:
Answer: B
The permeability of free space μ₀ = 4π × 10⁻⁷ T·m/A. Option A is permittivity ε₀, option C is speed of light, and option D is Planck's constant.
Q.93Medium
A long straight wire carrying current I produces a magnetic field at distance r. If the current is doubled and distance is halved, the magnetic field becomes:
Answer: B
B = μ₀I/(2πr). If I → 2I and r → r/2, then B_new = μ₀(2I)/(2π(r/2)) = 4·μ₀I/(2πr) = 4B_initial
Q.94Medium
The SI unit of magnetic flux density (magnetic field) is:
Answer: B
The SI unit of magnetic field (flux density) is Tesla (T). 1 T = 1 Wb/m² = 1 kg/(A·s²). Weber is the unit of magnetic flux, Gauss is CGS unit, and Henry is unit of inductance.
Q.95Hard
A proton and an alpha particle (He²⁺ nucleus) are accelerated through the same potential difference. They are then made to move perpendicular to a uniform magnetic field. The ratio of their radii of curvature is:
Answer: C
From qVB = mv²/2 and r = mv/(qB), we get r = √(2mV/q)/B. For proton (m=m_p, q=e) and alpha (m=4m_p, q=2e): r_p/r_α = √(m_p/(4m_p))·√(2e/e) = √(41)·√2 = √(21)·√2 = 12
Q.96Hard
A rectangular loop of dimensions a × b is placed in a non-uniform magnetic field where B varies as B = B₀(1 + kx), where x is the distance from a reference line. The net force on the loop is:
Answer: C
In a non-uniform field, the forces on opposite sides of the loop are unequal. The net force depends on the field gradient. F = I·∫(dB/dx)·dA = I·b·∫B₀k·da = B₀kIab (approximately, for small variations).
Q.97Hard
A charged particle enters a region with perpendicular electric and magnetic fields with velocity v. For the particle to pass undeflected, the condition is:
Answer: A
For undeflected motion, electric force equals magnetic force: qE = qvB, which gives E = vB. This is the principle of a velocity selector.
Q.98Hard
A solenoid with N turns, length L, and cross-sectional area A is wound with wire of resistance R. When connected to a voltage source V, the magnetic energy stored is:
Answer: C
Current I = V/R. Self-inductance L = μ₀N²A/L. Magnetic energy = LI²/2 = (μ₀N²A/L)·(V²/R²)/2 = V²μ₀N²A/(2R²L)
