Question

When will the induced current be highest based on the coil motion?

Answer 1

Step 1: Induced current

1. Due to a changing magnetic field, the generated current in the wire is called induced current. The induced current would be proportional to the rate of change of the magnetic flux.
2. The induced current is the highest when the direction of motion of the coil is at right angles to the magnetic field.

Step 2: Explanation

1. When there has been a shift throughout flux, an emf, as well as current, are generated throughout the coil, and even this current creates one's own magnetic field, as per Faraday's law of electromagnetic.
2. The direction of the current can be determined by considering Lenz’s law, which says that an induced electric current will flow in such a way that it generates a magnetic field that opposes the change in the field that generated it.
3. If the applied magnetic field increases, the current in the wire will flow so that the magnetic field that it generates around the wire will decrease the applied magnetic field.
4. The induced current is found to be highest when the direction of motion of the coil is at right angles to the magnetic field. The induced current is proportional to the time rate of change in magnetic flux.

Step 3: Mathematical interpretation

Let, the induced current be $\mathrm{I}$, magnetic flux be $\mathrm{\varphi }$, $\mathrm{B}$ is the magnetic flux density,$\mathrm{\omega }$ is the angle between the direction of motion of the coil and the magnetic field, and, $\mathrm{A}$ is the area. Therefore, the induced current is proportional to the rate of change in magnetic flux.

$$\begin{gathered} \mathrm{I}\propto \frac{\mathrm{d\varphi }}{\mathrm{dt}}=\mathrm{A}\frac{\mathrm{d}\overrightarrow{\mathrm{B}}\overrightarrow{\mathrm{n}}}{\mathrm{dt}} \\ =\frac{\mathrm{d}}{\mathrm{dt}}\mathrm{ABcos\omega t} \\ =-\mathrm{ABsin\omega t} \end{gathered}$$

When $\mathrm{\omega }$ is $90°$, $\mathrm{sin\omega }$ is maximum.

Therefore, when the direction of motion of the coil is at right angles to the magnetic field, the induced current is the highest.