In Fig. 29.8, if the $\mathbf{\omega }$angular speed of the loop is doubled, then the frequency with which the induced current changes direction doubles, and the maximum emf also doubles. Why? Does the torque required to turn the loop change? Explain

The equation of induced emf due to change in angle is given by

$$\begin{gathered} \mathrm{E}={\mathrm{E}}_0\sin \left(\mathrm{\omega t}\right) \\ =\mathrm{\omega BAsin}\left(\mathrm{\omega t}\right) \end{gathered}$$

Where, E is the induced emf and ${\mathrm{E}}_0$is the maximum emf, is the angular speed of the loop, B is applied magnetic field, t is the time and A is surface area.

Torque acting on the loop

The Torque acting on the loop is given by

$\mathrm{T}=\mathrm{NIABsin}\left(\mathrm{\omega t}\right)$

Where , N is the number of loops, l is the current in loop and T is torque.

Thus, if the angular speed is doubled then the value of the sine is doubled, which means the frequency with which the induced current changes direction doubles also maximum emf becomes double.

As, torque required to turn a loop directly proportional to the current in the loop. Therefore Torque is required to turn a loop changes when the current is changed.