Question

A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.060 t. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.50 s, the magnetic field changes to the opposite direction with a magnitude of 0.040 t. What is the magnitude of the average emf induced in the loop?

Answer 1

Given:

Radius of loop $r = 4 \times 10^{-2}$ m

Change in magnetic field $\Delta B = 0.060 -0.040 = 0.02$ T

Time interval $\Delta t = 0.50$ sec

To Find: Magnitude of average emf,

According to the faraday's law,

Induced emf = $-N\frac{\Delta \phi}{\Delta t}$

Where $\Delta \phi = \Delta B A$, $A =$ area of the loop,

So average emf is given by,

Induced emf = $\frac{\Delta BA}{\Delta t}$

Induced emf $= \frac{0.02 \times \pi (4 \times 10^{-2} )^{2} }{0.50}$

Induced emf = $2 \times 10^{-4}$ V

Therefore, the magnitude of the average emf induced in the loop is $2 \times 10^{-4}$ V