In a uniform magnetic field of induction $B$ a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is (1) $\frac { B \pi r ^ { 2 } \omega } { 2 R }$ (2) $\frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 2 R }$ (3) $\frac { ( \mathrm { B } \pi \mathrm { r } \omega ) ^ { 2 } } { 2 \mathrm { R } }$ (4) $\frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 8 R }$
In a uniform magnetic field of induction $B$ a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is\\
(1) $\frac { B \pi r ^ { 2 } \omega } { 2 R }$\\
(2) $\frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 2 R }$\\
(3) $\frac { ( \mathrm { B } \pi \mathrm { r } \omega ) ^ { 2 } } { 2 \mathrm { R } }$\\
(4) $\frac { \left( B \pi r ^ { 2 } \omega \right) ^ { 2 } } { 8 R }$