Question

A metallic rod of length l is rotated with a frequency v with one end hinged at the centre and the other at circumference of circular metallic ring, about an axis passing through the centre and perpendicular ti plane of ring. A constant and uniform mag. field B parallel to axis is present everywhere. express emf induced between centre and ring. resistance is R how much power will be generated?

Answer 1

$$\begin{gathered} Theradiusofthemetallicringr=l \\ andthelengthoftherod=l \\ Thespeedofrod=\frac{2\pi l}{\nu }. \\ Theinducedemfgenerated=e=B\times \frac{2\pi l}{\nu }\times l=B\times \frac{2\pi l^2}{\nu } \\ Thecurrentflowingthroughtherodandringsystem=i=\frac{e}{R}=B\times \frac{2\pi l^2}{R\times \nu } \\ Thereforepowergenerated=P=e\times i=B\times \frac{2\pi l^2}{\nu }\times B\times \frac{2\pi l^2}{R\times \nu }=\frac{4{\pi }^2{B}^2{l}^4}{R\times {\nu }^2} \end{gathered}$$