Question 351: Electromagnetic Induction

Question

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s$$-$$1. The induced emf when the radius is 2 cm, is

Accepted Answer

Constant rate at which radius of the loop shrinks
$${{dr} \over {dt}} = 1 	imes {10^{-3}}$$ m s
-1
Magnetic flux linked with the loop is
$$\phi $$ = BAcos$$\phi $$ = B($$\pi $$r
2
)cos0
o
= B$$\pi $$r
2
The magnitude of the induced emf is
|e| = $${{d\phi } \over {dt}} = {d \over {dt}}\left( {B\pi {r^2}} ight) = B\pi 2r{{dr} \over {dt}}$$
= 0.025 $$ 	imes $$ $$\pi $$ $$ 	imes $$ 2 $$ 	imes $$ 2 $$ 	imes $$ 10
-2
$$ 	imes $$ 1 $$ 	imes $$ 10
-3
= $$\pi $$ $$ 	imes $$ 10
-6
V
= $$\pi \mu V$$

Answer

$$2\pi \mu V$$

Answer

$$\pi \mu V$$

Answer

$${\pi  \over 2}\mu V$$

Answer

2$$\mu $$$$V$$

Electromagnetic Induction

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s$-$1. The induced emf when the radius is 2 cm, is

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