An elastic conducting material is stretched into a circular loop of 10.7 cm radius. It is placed with its plane perpendicular to a uniform 0.803 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 81.0 cm/s. What emf is induced in volts in the loop at that instant?

0.44 V

Explanation:

Parameters given:

Radius of loop, r = 10.7 cm = 0.107 m

Magnetic field strength, B = 0.803 T

Rate of shrinkage of Radius, dr/dt = 81 cm/s = 0.81m/s

EMF induced is given in terms of magnetic Flux, Φ, as:

EMF = dΦ/dt

Magnetic Flux, Φ, is given as:

Φ = B * A (where A is area of loop)

Therefore, EMF is:

EMF = d(B*A)/dt

The area of the loop is given as A = πr²

EMF = d(Bπr²) / dt = Bπ*d(r²)/dt

=> EMF = Bπ*2r*(dr/dt)

EMF = 0.803 * π * 2 * 0.107 * 0.81

EMF = 0.44 V

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