Question

A circular wire turned 5 times sits in a 2 T magnetic field. The magnetic field is increased to 10 T over a period of 25 seconds, which induces a –5.03 V emf. What is the radius of the wire loop? (Round your answer to the nearest integer value.)

Answer 1

Faraday's law of electromagnetic induction states:

$$|E|=N\frac{\Delta \Phi}{\Delta t}=N\frac{A·\Delta B}{\Delta t}$$

Express the area A in terms of radius:

$$A=\pi R^2.$$

Therefore:

$$|E|=N\frac{\pi R^2·\Delta B}{\Delta t},\\\space\\ R=\sqrt{\frac{|E|\Delta t}{N\pi\Delta B}},\\\space\\ R=\sqrt{\frac{5.03·25}{5\pi(10-2)}}=1\text{ m}.$$