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A square loop of wire is held in a uniformB=0.24Tmagnetic field directed perpendicular to the plane of the loop. The length of each side of the square is decreasing at a constant rate of 5.0 cm/s. What emf is induced in the loop when the length is 12 cm ?

Short Answer

Expert verified

The induced in the loop is, ε=2.9×10-3V

Step by step solution

01

Given

B=0.24Tdldt=5.0cm/s=0.05m/sl=12cm=0.12m

02

Understanding the concept

By using the equation of Faraday’s law and the equation of magnetic flux related to magnetic field and area of the loop, we can find the emfinduced in the loop.

Formula:

ε=-dϕBdt

03

Calculate the emf  induced in the loop

The magnetic flux can be written as

ϕB=BA........................................................................................(1)

For the square loop the area is isA=l2. So, the rate of area is

dAdt=2ldldt

Thus, according to faradays law, theis

ε=-dϕdt

From equation (1) theis

ε=-d(BA)dt

ε=-BdAdt

As from above equation

ε=-B×2ldldt

By substituting the value we get

ε=-0.24×2×0.12×0.05

ε=-0.0029

ε=2.9×10-3V

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