Physics is where JEE ranks are usually won or lost, since a single conceptual slip changes the whole answer. Questions here span mechanics, rotational motion, thermodynamics, waves and oscillations, electrostatics, current electricity, magnetism, optics, and modern physics. Numerical problems carry full derivations so you can see which step you skipped, not just which option was right.
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.2Hard
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.3Hard
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.4Hard
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.5Hard
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.
Q.6Hard
The magnetic field at the center of a circular arc of radius R subtending angle θ at the center and carrying current I is:
Answer: A
For a circular arc, B = (μ₀I/4πR) × θ, where θ is in radians. This is derived from the Biot-Savart law integrated over the arc.
Q.7Hard
A toroidal magnetic field is produced by a toroid with N turns carrying current I. If the mean radius of the toroid is R and the cross-sectional area of the core is A, the magnetic energy stored is:
Answer: A
Magnetic energy U = ½LI² where L = μ₀N²A/(2πR) for a toroid. Therefore U = μ₀N²I²A/(4πR). Note: The correct formula is actually U = ½ × μ₀N²I²A/(2πR) = μ₀N²I²A/(4πR).
Q.8Hard
An alpha particle (charge +2e, mass 4u) and a proton (charge +e, mass u) are accelerated from rest through the same potential difference. They then enter a uniform magnetic field perpendicular to their motion. The ratio of their radii of curvature is:
Answer: C
After acceleration: ½m₁v₁² = q₁V and ½m₂v₂² = q₂V. In magnetic field, r = mv/(qB). r₁/r₂ = (m₁v₁/q₁)/(m₂v₂/q₂) = (4u × √(2eV/4u)/2e)/(u × √(2eV/u)/e) = √(2u/e) × e/(√(2eV) × √(2V/u)) = 2√2:1.
Q.9Hard
The phenomenon where the inductance of a coil changes with the current flowing through it due to non-linear magnetic properties of the core is called:
Answer: B
When the magnetic core saturates, further increase in current produces minimal increase in magnetic flux, causing inductance to decrease. This is the saturation effect in magnetic cores.
Q.10Hard
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.11Hard
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.12Hard
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.13Hard
A toroidal coil has N turns and inner radius r₁, outer radius r₂. The self-inductance is approximately:
Answer: A
For a toroidal coil: L = (μ₀N²h/(2π)) × ln(r₂/r₁), where h is the height of the toroid
Q.14Hard
In a cyclotron, the time period of revolution of a particle is independent of its energy because:
Answer: A
T = 2πm/(qB), independent of v and r. As energy increases, velocity and radius increase proportionally, keeping period constant
Q.15Hard
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.16Hard
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.17Hard
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.18Hard
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)
