Question

A single-turn circular loop of wire that has a radius of 3.5 cm lies in the plane perpendicular to a spatially uniform magnetic field. During a 0.12-s time interval, the magnitude of the field increases uniformly from 0.2 T to 0.5 T.
a. Determine the magnitude of the emf induced in the loop during the time interval.
b. Determine the direction of the induced current in the loop.

Answer 1

Explanation:

Given that,

Radius of the circular loop, r = 3.5 cm = 0.035 m

(a) During a 0.12-s time interval, the magnitude of the field increases uniformly from 0.2 T to 0.5 T. Due to the change in the magnetic field, an emf will induced in it. The magnitude of induced emf is given by :

$\epsilon=-\dfrac{d(BA)}{dt}\\\\\epsilon=-\pi r^2\dfrac{B_f-B_i}{dt}\\\\\epsilon=-\pi (0.035)^2\dfrac{0.5-0.2}{0.12}\\\\\epsilon=-9.62\times 10^{-3}\ volts$

So, the magnitude of the emf induced in the loop during the time interval is $9.62\times 10^{-3}\ V$.

(b) The negative sign shows that the direction of induced emf in the loop is in anitclockwise direction.