Question

A flat coil enclosing an area of 0.10 m^2 is rotating at 60 rev/s, with its axis of rotation perpendicular to a 0.20-T magnetic field. (a) If there are 1 000 turns on the coil, what is the maximum voltage induced in the coil? (b) When the maximum induced voltage occurs, what is the orientation of the coil with respect to the magnetic field?

Answer 1

The maximum voltage induced in the coil is approximately 1200 volts when there are 1,000 turns on the coil, the coil enclosing an area of 0.10 m^2 is rotating at 60 rev/s, and the magnetic field strength is 0.20 T. The orientation of the coil with respect to the magnetic field, when the maximum induced voltage occurs, is perpendicular.

Step-by-step explanation:

(a) To calculate the maximum voltage induced in the coil, we can use the formula:

V = NABω

where V is the voltage, N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity.

Plugging in the given values:

V = (1000)(0.10 m^2)(0.20 T)(60 rev/s)

V ≈ 1200 V

Therefore, the maximum voltage induced in the coil is approximately 1200 volts.

(b) The orientation of the coil with respect to the magnetic field when the maximum induced voltage occurs is perpendicular because the maximum voltage is induced when the area vector of the coil is perpendicular to the magnetic field lines.

Answer 2

The maximum induced voltage in the coil is 1200π V, and it occurs when the coil's plane is perpendicular to the magnetic field.

Step-by-step explanation:

The student's question revolves around electromagnetic induction and Faraday's law of induction, which relates to the induced electromotive force (emf) in a rotating coil within a magnetic field. The magnetic flux through a coil is given by Φ = BAcos(θ), where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the surface of the coil. The emf induced in a coil is related to the rate of change of this magnetic flux over time, according to Faraday's law.

For part (a), using Faraday's law of induction, the maximum induced voltage (ε) in the coil is given by the equation ε = NABω, where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity in radians per second. To find ω, we convert the rotation rate from rev/s to rad/s by multiplying by 2π. The coil's rotation rate of 60 rev/s is equivalent to 60 x 2π rad/s. Therefore, the maximum induced voltage is ε = (1000 turns)(0.10 m²)(0.20 T)(60 x 2π rad/s) = 1200π V.

For part (b), the maximum induced voltage occurs when the rate of change of the magnetic flux is the greatest; this happens when the coil's plane is perpendicular to the magnetic field (orientation is 90° to the field).