Question 105: Electromagnetic Induction

Question

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of
a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field
changes with time at a steady rate $${{dB} \over {dt}}$$ = 0.032 Ts–1. The induced current in the loop is close to
(Resistivity of the metal wire is 1.23 $$ 	imes $$ 10–8 $$\Omega $$m)

Accepted Answer

We know, $$\phi  = BA$$
Also, $$E = {{d\phi } \over {dt}} = {{AdB} \over {dt}}$$
$$E = {l^2}{{dB} \over {dt}}$$
$$i = {E \over R} $$
= $${{{l^2}{{dB} \over {dt}}} \over {{{ho l} \over A}}}$$
$$= {{{l^2}} \over {pl}}{{dB} \over {dt}}A$$
= $${{{{l^2}\pi {R^2}} \over {ho l}}{{dB} \over {dt}}}$$
$$ 	herefore $$ $$i = {{30} \over 4} 	imes {{30} \over 4} 	imes {{{{10}^{ - 4}} 	imes 0.032 	imes 4 	imes {{10}^{ - 6}} 	imes \pi } \over {1.23 	imes {{10}^{ - 8}} 	imes 30 	imes {{10}^{ - 2}} 	imes {{10}^3}}}$$
$$ \Rightarrow $$ $$i = {{240 	imes \pi  	imes {{10}^{ - 10}}} \over {1.23 	imes {{10}^{ - 7}}}}$$
$$ \Rightarrow $$ $$i = {{240 	imes 3.14 	imes {{10}^{ - 3}}} \over {1.23}}$$
$$ = {{753.6} \over {1.23}} 	imes {10^{ - 3}}$$
$$ \Rightarrow $$ $$i = 612.68 	imes {10^{ - 3}} = 0.61A$$

Answer

0.53 A

Answer

0.43 A

Answer

0.34 A

Answer

0.61 A

Electromagnetic Induction

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