Question

A single loop of wire with an area of 0.0820 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.220 T/s .
Required:
a. What emf is induced in this loop?
b. If the loop has a resistance of 0.600Ω, find the current induced in the loop.

Answer 1

Answer:

a) emf = 0.01804 V

b) I = 0.03 A

Explanation:

a) The emf is calculated by using the following formula:

$|emf|=|\frac{d\Phi_B}{dt}|=|\frac{d(A\cdot B)}{dt}|$ $=A|\frac{dB}{dt}|$

A: area of the loop = 0.0820m^2

B: magnitude of the magnetic field

dB/dt: change of the magnetic field, in time: 0.220 T/s

Where ФB is the magnetic flux, the surface vector and magnetic vector are perpendicular between them, and the area A is constant.

You replace the values of A and dB/dt in the equation (1):

$|emf|=(0.082m^2)(0.220T/s)=0.01804V$

b) The current in the loop is:

$I=\frac{emf}{R}$

R: resistance of the loop = 0.600Ω

$I=\frac{0.01804V}{0.600\Omega}=0.03A=30mA$