At the centre of a fixed large circular coil of radius R , a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation. (1) $\frac { \mu _ { 0 } I } { 2 R } \omega r ^ { 2 } \sin \omega t$ (2) $\frac { \mu _ { 0 } I } { 4 R } \omega \pi r ^ { 2 } \sin \omega t$ (3) $\frac { \mu _ { 0 } I } { 2 R } \omega \pi r ^ { 2 } \sin \omega t$ (4) $\frac { \mu _ { 0 } \mathrm { I } } { 4 \mathrm { R } } \omega \mathrm { r } ^ { 2 } \sin \omega \mathrm { t }$
At the centre of a fixed large circular coil of radius R , a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation.\\
(1) $\frac { \mu _ { 0 } I } { 2 R } \omega r ^ { 2 } \sin \omega t$\\
(2) $\frac { \mu _ { 0 } I } { 4 R } \omega \pi r ^ { 2 } \sin \omega t$\\
(3) $\frac { \mu _ { 0 } I } { 2 R } \omega \pi r ^ { 2 } \sin \omega t$\\
(4) $\frac { \mu _ { 0 } \mathrm { I } } { 4 \mathrm { R } } \omega \mathrm { r } ^ { 2 } \sin \omega \mathrm { t }$