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Ivan
3 years ago
10

A rectangular loop of area A is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magni

tude of the field is allowed to vary in time according to B = Bmax e-t/τ , where Bmax and τ are constants. The field has the constant value Bmax for t < 0. Find the emf induced in the loop as a function of time. (Use the following as necessary: A, Bmax, t, and τ.) g
Physics
1 answer:
mina [271]3 years ago
7 0

Answer:

Induced emf, \epsilon=-A\dfrac{B_{max}e^{-t/\tau}}{\tau}

Explanation:

The varying magnetic field with time t is given by according to equation as :

B=B_{max}e^{-t/\tau}

Where

B_{max}\ and\ t are constant

Let \epsilon is the emf induced in the loop as a function of time. We know that the rate of change of magnetic flux is equal to the induced emf as:

\epsilon=-\dfrac{d\phi}{dt}

\epsilon=-\dfrac{d(BA)}{dt}

\epsilon=-A\dfrac{d(B)}{dt}

\epsilon=-A\dfrac{d(B_{max}e^{-t/\tau})}{dt}

\epsilon=A\dfrac{B_{max}e^{-t/\tau}}{\tau}

So, the induced emf in the loop as a function of time is A\dfrac{B_{max}e^{-t/\tau}}{\tau}. Hence, this is the required solution.

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