Question

An emf is induced in a conducting loop of wire 1.07 m long as its shape is changed from square to circular. Find the average magnitude of the induced emf if the change in shape occurs in 4.36 s and the local 0.115-T magnetic field is perpendicular to the plane of the loop.

Answer 1

0.517 mV

Step-by-step explanation:

Length of wire = 1.07 m

For square:

Perimeter = 1.07 m

Let a be the side of square

So, 4a = 1.07

a = 0.2675 m

Area of square, A 1 = side x side = 0.2675 x 0.2675 = 0.07156 m^2

For circle:

Circumference = 1.07 m

Let r be the radius of circle

So, 2 π r = 1.07

2 x 3.14 x r = 1.07

r = 0.1704 m

Area of circle, A 2 = π r^2 = 3.14 x 0.1704 x 0.1704 = 0.09115 m^2

Change in area, dA = A2 - A1 = 0.09115 - 0.07156 = 0.0196 m^2

Time taken in changing the area, dt = 4.36 s

Magnetic field, B = 0.115 T

According to the Farady's law of electromagnetic induction

`e = (d\phi )/(dt)=(dBA )/(dt)=B(dA )/(dt)`

`e = 0.115* (0.0196)/(4.36)`

e = 5.17 x 10^-4 V

e = 0.517 mV

Thus, the induced emf is 0.517 mV.