Question

A 137-turn circular coil of radius 3.41 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 14.7Ω resistor to create a closed circuit. During a time interval of 0.165 s, the magnetic field strength decreases uniformly from 0.481 T to zero. Find the energy E in millijoules that is dissipated in the resistor during this time interval. E=mJ

Answer 1

To find the energy dissipated in the resistor, calculate the induced emf using Faraday's Law of electromagnetic induction and the rate of change of magnetic flux. Then use the formula E = (emf^2) / R to find the energy dissipated in the resistor.

Step-by-step explanation:

To find the energy dissipated in the resistor, we first need to calculate the change in magnetic field strength. The rate of change of magnetic field strength is given as 0.481 T/0.165 s = -2.918 T/s. Using Faraday's Law of electromagnetic induction, we can find the induced emf in the coil:

emf = -N * (dΦ/dt)

Where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux. The magnetic flux through the coil is given by:

Φ = B * A

Where B is the magnetic field strength and A is the area of the coil. The change in magnetic flux is then:

dΦ/dt = (Φ₂ - Φ₁) / t = (B₂ * A - B₁ * A) / t

Substituting the given values, we can calculate the change in magnetic flux. Finally, the energy dissipated in the resistor is given by:

E = (emf^2) / R = (N^2 * (dΦ/dt)^2) / R