Question

# A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero area, find the charge flowing through the galvanometer.

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Solution

## Step 1: GivenMagnetic induction= $B$Area = $A$Resistance = $R$ Step 2: Formula used and calculationMagnetic flux is given by$\Phi =BA\phantom{\rule{0ex}{0ex}}∆\Phi =B∆A=BA$Induced EMF is given by$E=\frac{∆\Phi }{∆t}=\frac{BA}{∆t}$Current is given by$i=\frac{E}{R}=\frac{BA}{R∆t}\phantom{\rule{0ex}{0ex}}⇒\frac{Q}{∆t}=\frac{BA}{R∆t}\phantom{\rule{0ex}{0ex}}⇒Q=\frac{BA}{R}$

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