A uniform held decreases at a constant rate dB/dt = K, where K is a positive con

Question

A uniform held decreases at a constant rate dB/dt = K, where K is a positive constant. A circular loop of wire of radius a containing a resistance R and a capacitance C is placed with its plane normal to the ficeld. (a) Find the chargeQ on the capacitor when it is fully charged. b) Which plate, upper or lower is at the higher potential ·e, is the upper plate positively or negatively charged? (For maximum points, clearly label and indicate the direction of the induced magnetic field and the current in the loop while charging.)

Explanation / Answer

When the capacitor is fully charged no current flows through it.

We know that EMF generated is given as

EMF = A * dB/dt = Ak

Hence the current across the capacitor will be

I = Ak/R e (-t/RC)

Hence the total charge will be time intergral from 0 to infintire time.

Q = AK*C

where A is the area of the loop.

b. As the current generated is anti clockwise. hence the upper plate will be positvely charged.

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