need help with this problem :/

A circular coil (980 turns, radius = 0.078 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.027 s, the normal makes an angle of 45o with the field because the coil has made one-eighth of a revolution. An average emf of magnitude 0.058 V is induced in the coil. Find the magnitude of the magnetic field at the location of the coil.

To find the magnitude of the magnetic field at the location of the coil, we can make use of Faraday's law of electromagnetic induction, which states that the magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through the coil.

The formula for the induced emf is given by:

emf = N * ΔΦ / Δt

Where:
emf is the induced electromotive force (0.058 V in this case)
N is the number of turns in the coil (980 turns in this case)
ΔΦ is the change in magnetic flux through the coil
Δt is the change in time (0.027 s in this case)

Since we are given that the coil has rotated one-eighth of a revolution, we know that the change in angle is 45 degrees.

To calculate the change in magnetic flux, we can use the formula:

ΔΦ = B * A * cos θ

Where:
B is the magnitude of the magnetic field
A is the area of the coil
θ is the angle between the normal to the coil and the magnetic field (45 degrees in this case)

The area of a circular coil is given by the formula:

A = π * r^2

Where:
r is the radius of the coil (0.078 m in this case)

Substituting these values into the equations, we have:

emf = N * ΔΦ / Δt
0.058 V = 980 * (B * A * cos θ) / 0.027 s

Now, we can plug in the values we know:

0.058 V = 980 * (B * (π * 0.078^2) * cos 45) / 0.027 s

Simplifying and solving for B:

B = (0.058 V * 0.027 s) / (980 * (π * 0.078^2) * cos 45)
B ≈ 1.36 T

Therefore, the magnitude of the magnetic field at the location of the coil is approximately 1.36 Tesla.