Answer:
[tex]\epsilon=1.10\ V[/tex]
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,
[tex]A_1=\pi r^2[/tex]
[tex]A_1=\pi (0.7)^2=1.539\ m^2[/tex]
For the area of square,
The circumference of wire, [tex]C=2\pi r=2\pi \times 0.7=4.39\ m[/tex]
Side of square, [tex]l=\dfrac{4.39}{4}=1.09\ m[/tex]
Area of square, [tex]A_2=1.09^2=1.188\ m^2[/tex]
An emf is induced in the loop due to change in its area. The induced emf is given by :
[tex]\epsilon=-B\dfrac{dA}{dt}[/tex]
[tex]\epsilon=-B\dfrac{A_2-A_1}{t}[/tex]
[tex]\epsilon=-0.44\times \dfrac{1.188-1.539}{0.14}[/tex]
[tex]\epsilon=1.10\ V[/tex]
So, the magnitude of the average induced emf is 1.10 volts. Hence, this is the required solution.
