Exams › JEE Advanced › Physics
A conducting solid sphere of radius R carries a uniform total charge Q and rotates with angular velocity omega about its axis. A uniform external magnetic field B is applied perpendicular to the axis of rotation. Find the torque experienced by the sphere.
- Q*omega*R²*B / 5
- Q*omega*R²*B / 3
- Q*omega*R²*B / 4
- Q*omega*R²*B / 2
Correct answer: Q*omega*R²*B / 5
Solution
A rotating charged solid sphere with uniform volume charge density rho = Q / (4/3 * pi * R³). Consider a thin shell at radius r with thickness dr: charge dq = rho * 4*pi*r² * dr. This shell rotates with omega, acting as a current loop. Magnetic moment of shell: dM = (1/3)*dq*omega*r² (for a spherical shell, dM = dq*omega*r²/3... actually for a ring at colatitude theta: dM contribution). For a uniformly charged solid sphere: M_total = Q*omega*R²/5. Torque = M * B = Q*omega*R²*B/5.
Related JEE Advanced Physics questions
- Two parallel conductors lie in the plane of the paper, separated by a distance X₀. A charged particle travels with velocity v between these wires, maintaining a distance X₁ from one of them. When both wires carry identical currents I flowing in the same direction, the particle's trajectory has a curvature radius of R₁. Conversely, if the currents in the wires flow in opposite directions, the curvature radius becomes R₂. Given that X₁/X₀ equals 3, determine the ratio R₁/R₂.
- A current-carrying wire of infinite length is placed along the z-axis, carrying current I in the positive z-direction, generating a magnetic field B. What is the value of the line integral ∮ B⋅dℓ along a straight path connecting the points (−√3a, a, 0) and (a, a, 0)? [Here, μ₀ represents the permeability of free space.]
- A charged particle has specific charge (charge-to-mass ratio) alpha. It starts from rest at the origin at t = 0 with initial velocity v0*i_hat + v0*j_hat in a uniform magnetic field B0*i_hat. Find the coordinates of the particle at time t = pi / (alpha * B0).
- Two infinitely long, thin, straight parallel wires are separated by a distance of 0.1 m and each carries a current of 10 A. A point P is equidistant from both wires at a distance of 0.1 m from each. Find the magnitude of the net magnetic field at P when the currents flow in (i) the same direction and (ii) opposite directions.
- A straight conducting wire of length 2*pi*R carries a steady current I. It is bent so that it forms an arc of a circle of radius R, leaving a gap of angle theta (in radians) at the top. Find the magnitude of the magnetic field at the centre O of the circle. (Assume the two short straight ends at the gap meet at the centre and contribute zero field.)
- A particle of charge 20 μC and mass 20 μg moves in a circular orbit of radius 5 cm under the influence of a uniform magnetic field B = 0.1 T. At point P on the circle, a uniform electric field is suddenly switched on, after which the particle moves along the tangent at P with constant velocity. What is the magnitude of the electric field?
⚔️ Practice JEE Advanced Physics free + battle 1v1 →