A coil is rotated at frequency $f$ in a uniform magnetic field - AQA - A-Level Physics - Question 23 - 2022 - Paper 2

To determine the smallest value of $t_1 - t_2$, we need to consider the relationship between the magnetic flux and induced emf in the context of rotational motion.

When the coil is rotated in a magnetic field, the magnetic flux $abla$ through the coil is given by:

$$ext{Flux} = B imes A imes ext{cos}( heta)$$

Where:

• $B$ is the magnetic field strength,
• $A$ is the area of the coil,
• $heta$ is the angle between the magnetic field and the normal to the coil's surface.

The conditions provided indicate that the magnetic flux is maximum at time $t_1$. This occurs when $heta = 0$, or at the moment where the plane of the coil is perpendicular to the magnetic field. The emf induced in the coil is maximum at time $t_2$ when the rate of change of magnetic flux is at its peak. A maximum emf occurs when the magnetic flux is changing the fastest, which corresponds to when $heta = 90$ degrees (the plane of the coil is parallel to the magnetic field).

Therefore, the time period of $t_1$ to $t_2$ reflects a quarter of the full rotation. Given the frequency $f$, the period $T$ of the rotation can be expressed as:

T = rac{1}{f}

Consequently, the time difference $t_1 - t_2$ will be:

t_1 - t_2 = rac{T}{4} = rac{1}{4f}

Thus, the smallest value of $t_1 - t_2$ is:

Answer: $\frac{1}{4f}$