Exams › JEE Advanced › Physics
Two long cylindrical wires carry different but uniform current densities. The radius of wire 2 is twice the radius of wire 1. The B vs r graphs (magnetic field vs radial distance from axis) for the two wires are plotted on the same axes; the decreasing (outer) curved portions of the two graphs exactly overlap each other. If B1 and B2 denote the maximum magnetic fields at the surfaces of wire 1 and wire 2 respectively, and x = B1/B2, find 2x.
- 2
- 4
- 8
- 16
Correct answer: 4
Solution
Equal outer B(r) curves imply equal total currents: J1*R1² = J2*(2R1)², so J1 = 4J2. Surface field ratio B1/B2 = (J1*R1)/(J2*R2) = (4J2*R1)/(J2*2R1) = 2, so x = 2 and 2x = 4.
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 →