A wire loop is rotated in a magnetic field such that the frequency of change of direction of the induced emf is

The correct option is "Twice per revolution".

To understand why this is correct, let's analyze the process of electromagnetic induction in a rotating loop of wire within a uniform magnetic field.

According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) is proportional to the rate of change of magnetic flux linked with the loop. The magnetic flux $\Phi$ through a loop of area $A$ in a uniform magnetic field $B$ is given by:

$\Phi =B·A·\cos \left(\theta \right)$

where $\theta$ is the angle between the magnetic field vector and the normal vector to the plane of the loop. If the loop rotates with a constant angular velocity $\omega$, we can write $\theta =\omega t$. Therefore, the magnetic flux varies as a cosine function over time:

$\Phi \left(t\right)=BA\cos \left(\omega t\right)$

The induced emf, $e$, is the negative rate of change of this flux with respect to time:

$e=-\frac{d\Phi }{dt}=BA\omega \sin \left(\omega t\right)$

This expression shows that the induced emf is a sinusoidal alternating quantity (AC). During one full revolution of the loop (which corresponds to one complete cycle of $\theta$ from 0 to 2π radians or 360 degrees), the function $\sin \left(\omega t\right)$ behaves as follows:
1. It starts at 0, increases to a positive maximum, and then decreases back to 0 (first half-cycle).
2. It then goes negative, reaching a negative maximum, and returns to 0 (second half-cycle).

The direction of the induced emf changes every time the value of the emf passes through zero and changes its sign (polar polarity).
Within one full revolution (one cycle of 360 degrees):
- The first change of direction occurs at 180 degrees (when the loop passes the position where its plane is perpendicular to the magnetic field, and the sine function transitions from positive to negative values).
- The second change of direction occurs at 360 degrees (the end of the cycle, as it starts the next revolution and transitions from negative back to positive values).

Thus, the direction of the induced emf reverses twice per revolution of the loop.