Question

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

Answer 1

Sounds like a job for integrals!  Is there any other information?  You would end up with B=Bmax(e-t^2/2T), if you do dt.  

Answer 2

The emf induced in the loop as a function of time is $A\dfrac{B_{max}e^{-t/\tau}}{\tau}.$

Explanation:

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

Induced EMF is the rate of change of magnetic flux. It is equal to work done on the charge per unit charge ($\epsilon =dWdq$) when there is no current flowing.

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

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

Where   $B_{max}$ and $\ t$ are constant

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

Therefore the emf induced in the loop as a function of time is $A\dfrac{B_{max}e^{-t/\tau}}{\tau}.$

Learn more about the emf brainly.com/question/9998037

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