Question

A horizontal circular wire loop of radius 0.7 m lies in a plane perpendicular to a uniform magnetic field that is pointing down from above into the plane of the loop, and has a constant magnitude of 0.44 T. If in 0.14 s the wire is reshaped from a circle into a square, but remains in the same plane, what is the magnitude of the average induced?

Answer 1

Answer:

$\epsilon=1.10\ V$

Explanation:

It is given that,

Radius of the circular loop, r = 0.7 m

Magnetic field, B = 0.44 T

In 0.14 s the wire is reshaped from a circle into a square, but remains in the same plane.

Area of the circular wire,

$A_1=\pi r^2$

$A_1=\pi (0.7)^2=1.539\ m^2$

For the area of square,

The circumference of wire, $C=2\pi r=2\pi \times 0.7=4.39\ m$

Side of square, $l=\dfrac{4.39}{4}=1.09\ m$

Area of square, $A_2=1.09^2=1.188\ m^2$

An emf is induced in the loop due to change in its area. The induced emf is given by :

$\epsilon=-B\dfrac{dA}{dt}$

$\epsilon=-B\dfrac{A_2-A_1}{t}$

$\epsilon=-0.44\times \dfrac{1.188-1.539}{0.14}$  

$\epsilon=1.10\ V$

So, the magnitude of the average induced emf is 1.10 volts. Hence, this is the required solution.