91Ó°ÊÓ

Magnetic flux is given by

$\mathit{ϕ}\mathbf{=}\stackrel{\mathbf{→}}{\mathbf{B}}\mathbf{.}\stackrel{\mathbf{→}}{\mathbf{A}}$

Where is the magnetic field andis the area vector

Faraday’s law states that The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.

$\mathit{e}\mathit{m}\mathit{f}\mathbf{=}\mathbf{-}\mathit{N}\frac{\mathbf{∆}\mathbf{ϕ}}{\mathbf{∆}\mathbf{t}}$

Replacing the change of flux into faraday’s law we get

$emf=-N\frac{∆\left(BA\right)}{∆t}$

The area does not change and only magnetic field changes

$emf=A\frac{dB}{dt}$

Applying Ohm’s law

$I=\frac{\mathrm{Î\mu }}{R}=\frac{A}{R}\frac{dB}{dt}$

Thus, the induced current is proportional to the slope of the curve.

From part (b) graph at the beginning of this set of passage problems, we can see that the magnetic field increases rapidly where the slope of the curve is positive. Then, it slows down but still positive as it comes close to its peak at t = 0.15ms. At the peak, the slope is zero. After the peak, the magnetic field gradually decreases to zero as the slope is negative. Since the current is proportional to the slope of the curve, it is initially positive, increasing in the first part then it decreases to zero when the curve in B-t graph is at its maximum. Then, it becomes negative as the slope becomes negative, and it then gradually approaches zero as the slope approaches zero.

Therefore, the right choice is c