Question

A circular coil of 40 turns and radius 9.0 cm is placed with its plane oriented at 90 degrees to a uniform magnetic field of 0.10 T. The field is now increased at a steady rate, reaching a value of 0.60 T after 7.0 seconds. What emf is induced in the coil?

A. 0.17 V
B. 0.096 V
C. 0.073 V
D. 0.12 V
E. 0.14 V

Answer 1

By using Faraday's law of electromagnetic induction, the induced emf in a coil is calculated based on the change in magnetic field and the coil's parameters. After performing the calculations, the induced emf in the coil is found to be 0.073 V.

Step-by-step explanation:

To calculate the induced emf in a circular coil due to a changing magnetic field, we can use Faraday's law of electromagnetic induction. Faraday's law states that the induced emf in a coil is equal to the negative change in magnetic flux (Φ) through the coil divided by the change in time (t), and is given by the formula ε = -N * dΦ/dt.

In this scenario, the magnetic field is changing from 0.10 T to 0.60 T over 7.0 seconds. The area (A) through which the field lines pass is given by πr^2, where r is the radius of the coil. So,

• A = π * (0.09 m)^2

We calculate the change in magnetic flux (Φ) as the product of the change in magnetic field (ΔB) and the area (A).

• Φ = ΔB * A = (0.60 T - 0.10 T) * A

The induced emf (ε) can then be calculated as:

• ε = -N * (Φ / Δt)

Where:

• N is the number of turns in the coil (40)
• Δt is the change in time (7.0 s)

Substituting the values we have:

• ε = -40 * ((0.60 T - 0.10 T) * π * (0.09 m)^2) / 7.0 s

After calculating, we get:

• ε = 0.073 V

Hence, the correct answer is 0.073 V, which is option C.