Question

A single-turn circular loop of wire of radius 5.0 cm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.05480.0548-\text{s}s time interval, the magnitude of the field increases uniformly from 200 to 300 mT. Determine the magnitude of the emf induced in the loop.

Answer 1

Answer:

Induced EMF,$\epsilon=0.0143\ volts$

Explanation:

Given that,

Radius of the circular loop, r = 5 cm = 0.05 m

Time, t = 0.0548 s

Initial magnetic field, $B_i=200\ mT=0.2\ T$

Final magnetic field, $B_f=300\ mT=0.3\ T$

The expression for the induced emf is given by :

$\epsilon=\dfrac{d\phi}{dt}$

$\phi$ = magnetic flux

$\epsilon=\dfrac{d(BA)}{dt}$

$\epsilon=A\dfrac{d(B)}{dt}$

$\epsilon=A\dfrac{B_f-B_i}{t}$

$\epsilon=\pi (0.05)^2\times \dfrac{0.3-0.2}{0.0548}$

$\epsilon=0.0143\ volts$

So, the induced emf in the loop is 0.0143 volts. Hence, this is the required solution.