Question 353: Electromagnetic Induction

Question

A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is

Accepted Answer

Constant rate at which radius of the loop shrinks
$${{dr} \over {dt}} = 2 	imes {10^{-3}}$$ 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| = $${{d\phi } \over {dt}} = {d \over {dt}}\left( {B\pi {r^2}} ight) = B\pi 2r{{dr} \over {dt}}$$
= 0.04 $$ 	imes $$ $$\pi $$ $$ 	imes $$ 2 $$ 	imes $$ 2 $$ 	imes $$ 10
-2
$$ 	imes $$ 2 $$ 	imes $$ 10
-3
= 3.2$$\pi $$ $$ 	imes $$ 10
-6
V
= 3.2$$\pi \mu V$$

Answer

4.8$$\pi $$$$\mu $$V

Answer

0.8$$\pi $$$$\mu $$V

Answer

1.6$$\pi $$$$\mu $$V

Answer

3.2$$\pi $$$$\mu $$V

Electromagnetic Induction

A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is

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