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A uniform magnetic field is restricted within a region of radius $r$ . The magnetic field changes with time at a rate $\frac{d \to B}{d t}$ . Loop $1$ of radius $R > r$ enclose the region $r$ and loop $2$ of radius $R$ is outside the region of magnetic field as shown in the figure below. Then the $e . m . f$ . generated is :

$- \frac{d \to B}{d t} π r^{2}$ in loop $1$ and zero in loop $2$
Zero in loop $1$ and zero in loop $2$
$- \frac{d \to B}{d t} π r^{2}$ in loop $1$ and $- \frac{d \to B}{d t} π r^{2}$ in loop $2$
$- \frac{d \to B}{d t} π R^{2}$ in loop $1$ and zero in loop $2$

A

- \frac{d \to B}{d t} π r^{2}

in loop

1

and zero in loop

2

B

Zero in loop

1

and zero in loop

2

C

- \frac{d \to B}{d t} π R^{2}

in loop

1

and zero in loop

2

D

- \frac{d \to B}{d t} π r^{2}

in loop

1

and

- \frac{d \to B}{d t} π r^{2}

in loop

2

Open in App

Solution

Verified by Toppr

Emf is induced in a coil due to change of flux through it.

In the loop 1, the flux passing through it is $B π r^{2}$

Hence emf induced= $- \frac{d ϕ}{d t} = - \frac{d \to B}{d t} π r^{2}$

Since the magnetic field does not change inside loop 2, no emf is induced in it.

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