Question

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12$\mathit{c}{\mathit{m}}^{\mathbf{2}}$is rotated in 0.040 s from a position where its plane is perpendicular to the earth’s magnetic field to a position where its plane is parallel to the field. The earth’s magnetic field at the lab location is$\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathit{T}$. (a) What is the total magnetic flux through the coil before it is rotated? After it is rotated? (b) What is the average emf induced in the coil?

Short answer

1. Total magnetic flux through the coil before and after rotation is
2. Average emf induced in the coil is

Step-by-step solution

Magnetic flux

Magnetic flux is expressed as;

Here, A is an area and B is the magnetic field.

Total magnetic flux before and after the rotation

a. As $A=12c{m}^2$and N=200 turns, Initially, the wire is placed perpendicularly in the earth's magnetic field. The object is then rotated from this position to one where its plane is parallel to the field and the magnetic field is, so the flux before the rotation is;

Then it is rotated, and the angle between the area and the magnetic field is

Thus, the flux after the rotation is;

Hence, the total magnetic flux through the coil before and after rotation is

Average emf induced in the coil is

b. The average magnitude of the induced emf in the coil is equal to the flux change divided by the time of change and multiplied by the number of turns;

Hence, the average emf induced in the coil is