A circular loop of radius $r$, having $N$ turns of a wire, is placed in a uniform and constant magnetic field $B$. The normal of the loop makes an angle $\theta$ with the magnetic that the angle $\theta$ is constant. Choose the correct statement from the following.a. (a) emf in the loop is $Nb\omega r^2/2\cos \theta$. b. (b) emf induced in the loop is zero. c. (c ) emf must be induced as the loop crosses magnetic lines. d. (d) emf must not be induced as flux does not change with time.

Sure! Here is a step-by-step solution: We know that the emf induced in a coil is given by the equation: $emf=-N\frac{d\varphi }{dt}$ where $N$ is the number of turns in the coil and $\varphi$ is the magnetic flux passing through the coil. In this case, we have a situation where the magnetic flux passing through the coil is not changing. This means that $\frac{d\varphi }{dt}$ is equal to zero. Therefore, the emf induced in the coil is: $emf=-N\frac{d\varphi }{dt}=-N(0)=0$ Since the emf induced is zero, there is no current flowing in the coil. This is because according to Ohm's law, the current flowing in a circuit is proportional to the emf applied. Therefore, in this situation, the flux remains constant and so the emf induced is zero.