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.

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 can be calculated using the formula:

Φ = B * A * cos(θ)

Where:
Φ is the magnetic flux
B is the magnetic field
A is the area of the coil
θ is the angle between the magnetic field and the normal to the coil's surface

In this case, the coil is at rest in a horizontal plane, so the angle between the magnetic field and the normal to the coil's surface is 90 degrees minus 60 degrees, which is 30 degrees.

The diameter of the coil is given as 2.0 cm, so the radius (r) of the coil is half of that, which is 1.0 cm or 0.01 m. Using the formula for the area of a circle, we can calculate the area of the coil:

A = π * r^2

Plugging in the values:
A = π * (0.01 m)^2 = 0.000314 m^2

The change in magnetic field is given as 1.50 T - 0.50 T = 1.00 T.

Now we can calculate the induced emf using the formula:

emf = -N * ΔΦ/Δt

Where:
emf is the induced emf
N is the number of turns in the coil
ΔΦ is the change in magnetic flux
Δt is the time interval over which the magnetic field changes

The number of turns in the coil is given as 100.

Plugging in the values:
emf = -100 * (1.00 T * 0.000314 m^2 * cos(30 degrees))/0.60 s

Evaluating the expression:
emf = -0.053 V

Therefore, the induced emf in the coil is -0.053 V.