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.
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.62Hard
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.63Hard
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.64Hard
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.65Hard
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.66Hard
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.67Hard
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.68Hard
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.69Hard
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.70Hard
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.71Hard
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.72Hard
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.73Hard
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.74Hard
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.75Hard
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.76Hard
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)
Q.77Hard
In Young's double slit experiment, if one slit is covered with a transparent film of thickness t and refractive index μ, the path difference changes by:
Answer: A
Optical path = μt, geometrical path = t. Additional path difference = μt - t = (μ-1)t
Q.78Hard
When a convex lens is immersed in water (n=34), its focal length compared to air is:
Answer: A
Lens maker's formula: 1/f = (n_lens/n_medium - 1)(1/R₁ - 1/R₂). When medium changes from air to water, (n_lens/n_medium) decreases, so f increases.
Q.79Hard
The minimum deviation through a prism occurs when:
Answer: D
All three conditions are equivalent and occur at minimum deviation: symmetric path, equal angles, and ray parallel to base.
Q.80Hard
The Brewster angle for glass-air interface (n_glass = 1.5) is approximately:
Answer: C
tan(θ_B) = n = 1.5. θ_B = arctan(1.5) = 56.31°. At this angle, reflected light is completely polarized.
