Problem 25.52


A 100-turn, 2.0-cm-diameter coil is at rest in a horizontal plane. A uniform magnetic field 60 degrees away from vertical increases from 0.50 T to 1.50 T in 0.60



Part A

What is the induced emf in the coil?

Express your answer using two significant figures.

62.8mv

To find the induced emf in the coil, we can use Faraday's Law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the coil.

The magnetic flux, denoted by Φ, is given by the product of the magnetic field (B), the area of the coil (A), and the cosine of the angle (θ) between the magnetic field and the normal to the coil:

Φ = B * A * cos(θ)

In this case, the magnetic field starts at 0.50 T and increases to 1.50 T, so the change in magnetic field, ΔB, is 1.50 T - 0.50 T = 1.00 T.

The area of the coil can be calculated using the formula for the area of a circle:

A = π * r^2

Substituting the given diameter of 2.0 cm into the formula, we find that the radius (r) is 1.0 cm or 0.01 m. Therefore, the area of the coil is:

A = π * (0.01 m)^2 = 0.000314 m^2

The angle between the magnetic field and the normal to the coil is 60 degrees. We need to convert this angle to radians by multiplying it by π/180:

θ = 60 degrees * (π/180) = 1.047 radians

Now, we can calculate the change in magnetic flux:

ΔΦ = ΔB * A * cos(θ) = 1.00 T * 0.000314 m^2 * cos(1.047) = 0.000314 T* m^2 * cos(1.047)

Finally, the induced emf is equal to the rate of change of magnetic flux with time. Since the time is not given, we can't calculate the induced emf directly.