A charged particle moves in a uniform magnetic field perpendicular to its velocity. Which of the following remains constant?
Answer: A
When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force is always perpendicular to velocity, so it does no work. Hence kinetic energy remains constant. However, direction changes continuously.
Q.2Easy
The magnetic field at the center of a circular loop of radius R carrying current I is:
Answer: C
Using Biot-Savart law, the magnetic field at the center of a circular loop of radius R carrying current I is B = μ₀I/2R. This is a fundamental formula in magnetism.
Q.3Easy
A bar magnet is cut into two equal halves along its length. The magnetic moment of each half is:
Answer: A
When a bar magnet is cut along its length, each half has half the number of magnetic dipoles. Since magnetic moment is the sum of individual dipole moments, each half has magnetic moment M/2.
Q.4Easy
The SI unit of magnetic flux density is:
Answer: B
Magnetic flux density (B) is measured in Tesla (T) in SI units. 1 Tesla = 1 Weber/m². Gauss is CGS unit, Weber is unit of flux, and Henry is unit of inductance.
Q.5Easy
A solenoid of length L, cross-sectional area A, and N turns carries current I. The magnetic field inside the solenoid is:
Answer: A
The magnetic field inside a solenoid is uniform and given by B = μ₀nI, where n = N/L is the number of turns per unit length. This is independent of the cross-sectional area A.
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Q.6Medium
An electron enters a region of uniform magnetic field with velocity v perpendicular to the field. If the magnetic field strength is B, the radius of curvature is:
Answer: A
For a charged particle in a magnetic field, centripetal force equals magnetic force: mv²/r = evB, giving r = mv/eB. This is the radius of the circular path.
Q.7Medium
Two parallel wires carrying currents I₁ and I₂ in opposite directions are separated by distance d. The force between them is:
Answer: C
Currents in opposite directions repel each other. The force per unit length is F/ℓ = μ₀I₁I₂/2πd, making total force F = μ₀I₁I₂ℓ/2πd (repulsive).
Q.8Medium
A rectangular loop of dimensions a × b carrying current I is placed in a uniform magnetic field B. The maximum torque on the loop is:
Answer: A
Torque on a current loop in a magnetic field is τ = NIAB sin(θ), where A is the area and θ is the angle. Maximum torque occurs when sin(θ) = 1, giving τ_max = BIab for N=1.
Q.9Medium
The magnetic moment of an electron orbiting in the first Bohr orbit is approximately:
Answer: A
The magnetic moment of an electron in the first Bohr orbit equals 1 Bohr magneton (μ_B = eℏ/2m_e ≈ 9.27 × 10⁻²⁴ J/T). This is a fundamental quantum result.
Q.10Easy
A moving charge experiences a magnetic force. This force is always:
Answer: B
Magnetic force is given by F = q(v × B), which is the cross product of velocity and field. Cross product is always perpendicular to both vectors.
Q.11Medium
The magnetic field due to a long straight wire carrying current I at perpendicular distance r is:
Answer: A
Using Ampere's law for a long straight wire, ∮B·dl = μ₀I_enclosed. For a circular path of radius r: B(2πr) = μ₀I, giving B = μ₀I/2πr.
Q.12Medium
A proton and an electron, both accelerated through the same potential difference, enter a uniform magnetic field perpendicularly. Which has a larger radius of curvature?
Answer: A
Both particles gain same kinetic energy, so mv²/2 is same. Since r = mv/eB and proton has much larger mass than electron, proton has larger radius of curvature.
Q.13Medium
The period of revolution of a charged particle in a magnetic field is independent of:
Answer: C
Period T = 2πm/eB is independent of velocity. This remarkable result means all particles with same m and q have same period regardless of speed in a given B field.
Q.14Medium
A compass needle placed in a magnetic field experiences a maximum torque when the needle is:
Answer: C
Torque τ = m × B has magnitude τ = mB sin(θ). Maximum occurs when sin(θ) = 1, i.e., θ = 90° (perpendicular orientation).
Q.15Medium
The self-inductance of a solenoid with N turns, length L, and cross-sectional area A is:
Answer: A
Self-inductance of solenoid is derived from L = NΦ/I where Φ = μ₀nIA. This gives L = μ₀N²A/L, proportional to N² and inversely proportional to length.
Q.16Hard
A circular loop and a square loop of equal perimeter are placed in the same uniform magnetic field. Their magnetic moments are:
Answer: B
For equal perimeter, circle encloses maximum area (isoperimetric inequality). Since magnetic moment m = IA, circular loop with larger area has larger magnetic moment.
Q.17Hard
A charged particle moves in crossed electric and magnetic fields. For the particle to move undeflected, the condition is:
Answer: A
For undeflected motion, electric and magnetic forces must balance: qE = qvB, giving E = vB. This is the principle of velocity selector used in mass spectrometers.
Q.18Hard
The magnetic field inside a toroid with N turns, major radius R, and carrying current I is:
Answer: D
In a toroid, using Ampere's law on circular path of radius r (inside toroid): B(2πr) = μ₀NI, so B = μ₀NI/2πr. Field varies inversely with distance from toroid center.
Q.19Hard
Two identical coils are placed coaxially with separation much larger than their radius. Their mutual inductance is:
Answer: B
For coaxial coils with large separation d >> radius, mutual inductance M ∝ 1/d² due to spreading of magnetic field lines. This is used in wireless power transfer systems.
Q.20Hard
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.
