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How many colls must a loop have with a cross-sectional area of 0.5m ^ 2 that is pulled through a magnetic field of 0.25T in 1.0s in order for there to be an induced emf of 4 ?

User Joe Benton
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1 Answer

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We can use Faraday's Law of Induction to solve this problem:

EMF = -N * d(phi)/dt

where EMF is the induced electromotive force, N is the number of turns in the loop, and d(phi)/dt is the rate of change of the magnetic flux through the loop.

In this problem, we are given that the induced EMF is 4 V, the magnetic field is 0.25 T, and the time taken is 1.0 s. The magnetic flux through the loop is given by:

phi = B * A

where B is the magnetic field and A is the cross-sectional area of the loop.

Substituting these values into Faraday's Law, we get:

4 = -N * d(phi)/dt

4 = -N * (d/dt)(B * A)

4 = -N * (A * dB/dt)

4 = -N * (0.5 * 0.25)

N = -32

Since we cannot have a negative number of turns, we must take the absolute value of N:

N = |-32| = 32

Therefore, the loop must have 32 turns in order for there to be an induced EMF of 4 V.

User Carolin
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