First slide

Magnetic flux and induced emf

Question

A horizontal ring of radius r = 1/2 m is kept in a vertical constant magnetic field 1 T. The ring is collapsed from maximum area to zero area in 1 s. Then the emf induced in the ring is

Easy

A

1 V
B

$(π / 4) V$
C

$(π / 2) V$
D

$π V$

Solution

$\begin{array}{l} | ε | = B \frac{d A}{d t} \\ \Rightarrow | ε | = B \frac{(A_{2} - A_{1})}{(t_{2} - t_{1})} \\ \Rightarrow | ε | = \frac{1 (\frac{π}{4} - 0)}{(1 - 0)} \\ \Rightarrow ε = \frac{π}{4} V \end{array}$

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