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Tpy6a [65]
3 years ago
7

An emf is induced in a conducting loop of wire 1.22 m long as its shape is changed from square to circular. Find the average mag

nitude of the induced emfif the change in shape occurs in 4.25 s and the local 0.125 T magnetic field is perpendicular to the plane of the loop.
Physics
1 answer:
Afina-wow [57]3 years ago
8 0

Answer:

The induced emf in the loop is 7.35\times 10^{-4}\ V

Explanation:

Given that,

Length of the wire, L = 1.22 m

It changes its shape is changed from square to circular. Then the side of square be its circumference, 4a = L

4a = 1.22

a = 0.305 m

Area of square, A=a^2=(0.305)^2=0.0930\ m^2

Circumference of the loop,

C=2\pi r=L\\\\r=\dfrac{L}{2\pi}\\\\r=\dfrac{1.22}{2\pi}=0.194\ m

Area of circle,

A'=\pi r^2\\A'=\pi (0.194)^2\\\\A'=0.118\ m^2

The induced emf is given by :

\epsilon=\dfrac{\d\phi}{dt}\\\\\epsilon=\dfrac{\d(BA)}{dt}\\\\\epsilon=B\dfrac{A'-A}{t}\\\\\epsilon=0.125 \times \dfrac{0.118-0.0930}{4.25}\\\\\epsilon=7.35\times 10^{-4}\ V

So, the induced emf in the loop is 7.35\times 10^{-4}\ V

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Since we have two coordinates (X, Y) we use

X(t) = X0 + vx * t

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