Question

A single circular loop with a radius of 35 cm is placed in a uniform external magnetic field with a strength of 0.50 T so that the plane of the coil is perpendicular to the field. The coil is pulled steadily out of the field in 15 s. Find the magnitude of the average induced emf during this interval. Show all work and include units of measure.

Answer 1

Answer:

0.0129 V

Explanation:

The average emf induced in the coil is given by Faraday-Newmann-Lenz:

$\epsilon=-\frac{\Delta \Phi_B}{\Delta t}$

where

$\Delta \Phi_B$ is the variation of magnetic flux through the coil

$\Delta t = 15 s$ is the time interval

Here we have

B = 0.50 T is the strength of the magnetic field

The radius of the coil is

r = 35 cm = 0.35 m

So the area is

$A=\pi r^2 = \pi (0.35 m)^2=0.385 m^2$

The initial flux through the coil is

$\Phi_i = BA = (0.50 T)(0.385 m^2)=0.193 Wb$

while the final flux is zero, since the coil has been completely removed from the magnetic field region; so, the variation of magnetic flux is

$\Delta \Phi = \Phi_f - \Phi_i = -0.193 Wb$

and so, the average emf induced is

$\epsilon=-\frac{-0.193 Wb}{15 s}=0.0129 V$