A square loop of metal wire lies in a region where a uniform magnetic field B is perpendicular to the plane of the loop. The wire has diameter 4 mm and total length 30 cm. The field increases steadily at dB/dt = 0.032 T/s. Taking the metal's resistivity as 1.23*10⁻⁸ ohm*m, find the magnitu

Question

A square loop of metal wire lies in a region where a uniform magnetic field B is perpendicular to the plane of the loop. The wire has diameter 4 mm and total length 30 cm. The field increases steadily at dB/dt = 0.032 T/s. Taking the metal's resistivity as 1.23*10⁻⁸ ohm*m, find the magnitude of the induced current in the loop (closest value).

Accepted Answer

0.61 A. Side length = total length/4 = 0.30/4 = 0.075 m, so loop area A = 0.075² = 5.625*10⁻³ m². EMF = A*dB/dt = 5.625*10⁻³ * 0.032 = 1.8*10⁻⁴ V. The wire cross-sectional area is a = pi*(d/2)² = pi*(0.002)² = 1.2566*10⁻⁵ m². Resistance R = rho*L/a = (1.23*10⁻⁸ * 0.30)/1.2566*10⁻⁵ = 3.69*10⁻⁹/1.2566*10⁻⁵ = 2.936*10⁻⁴ ohm. Current I = EMF/R = 1.8*10⁻⁴ / 2.936*10⁻⁴ = 0.613 A, i.e. about 0.61 A.

Solution

Related JEE Main Physics questions