Question 325: Electromagnetic Induction

Question

Two conducting circular loops of radii R
1
and R
2
are placed in the same plane with their centres coinciding. If R
1
>> R
2
, the mutual inductance M between them will be directly proportional to :

Accepted Answer

Two concentric coils are of radius R
1
and R
2
as
shown
Let current in outer loop be i
Magnetic field at center = B = $${{{\mu _0}i} \over {2{R_1}}}$$
Magnetic flux through inner coil = B $$ 	imes $$ $$\pi R_2^2$$
$$ \Rightarrow $$ $$\phi $$ = $${{{\mu _0}i} \over {2{R_1}}} 	imes \pi R_2^2$$
As per definition, $$\phi $$ = Mi
$$ \Rightarrow $$ M = $$\left( {{{{\mu _0}\pi } \over 2}} ight){{R_2^2} \over {{R_1}}}$$
$$ 	herefore $$ M $$ \propto $$ $${{R_2^2} \over {{R_1}}}$$

Answer

$${{R_2^2} \over {{R_1}}}$$

Answer

$${{{R_1}} \over {{R_2}}}$$

Answer

$${{{R_2}} \over {{R_1}}}$$

Answer

$${{R_1^2} \over {{R_2}}}$$

Electromagnetic Induction

Two conducting circular loops of radii R 1 and R 2 are placed in the same plane with their centres coinciding. If R 1 >> R 2 , the mutual inductance M between them will be directly proportional to :

Choose the correct answer: