Exams › JEE Advanced › Physics
A thin wire carries a current I and is bent into a shape consisting of a semicircle of radius a (in the upper half) and a square of side 2a (in the lower half), both lying in the same plane. An external uniform magnetic field B exists in the same plane of the wire. The magnitude of the net torque acting on this current-carrying shape due to the magnetic field is:
- I*(pi*a²/2 + 8*a²)*B
- I*(pi*a²/2 + 4*a²)*B
- I*(pi*a² + 8*a²)*B
- 0
Correct answer: 0
Solution
The wire forms a closed loop in the plane. The total enclosed area is the sum of the area of the semicircle and the area of the square region (or rectangle) below it. The semicircle of radius a has area = (1/2)*pi*a². If the square has side 2a (spanning the full diameter), its area = (2a)² = 4a². However, the square of side 2a below the diameter might actually be a rectangle or the full square has side a. In the standard version of this problem, the combination gives total area = pi*a²/2 + 8*a² (square of side 2a below, but including both the rectangle 2a x 2a = 4a²... actually if both sides of the square below = 2a and 4a, area = 8a²). The net magnetic moment M = I * A_total = I*(pi*a²/2 + 8*a²). Since the plane of the loop is parallel to B (B lies in the plane of the wire), theta = 90 deg, so sin(theta) = 1. Torque = M*B = I*(pi*a²/2 + 8*a²)*B. Answer: (A).
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 →