A 113 ‑turn circular coil of radius 2.71 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 10.3 Ω resistor to create a closed circuit. During a time interval of 0.153 s, the magnetic field strength decreases uniformly from 0.441 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

357 mJ

Explanation:

Parameters given:

Number of turns, N = 113

Radius, r = 2.71 cm = 0.0271 m

Resistance connected to coil, R = 10.3 ohms

Time interval, dt = 0.153 s

Change in magnetic field, dB = 0 - 0.441 T = - 0.441 T

First, we need to find the induced EMF in the coil. It is given as:

V = - (N * A * dB) / dt

A = area of coil = pi * r² = 3.142 * 0.0271² = 0.0023 m²

Therefore:

V = - (113 * 0.0023 * - 0.441) / 0.153

V = 0.75 V

Electrical energy dissipated in the resistor is given as:

E = V² / (R * t)

Where t is the time (0.153 secs)

E = (0.75²) / (10.3 * 0.153)

E = 0.357 J = 357 mJ

The energy dissipated in the resistor is 357 mJ