A coil with 155 turns of diameter 22.0 cm rotates at 1250 rpm in Earth’s magnetic field.Calculate the maximum induced emf, if Earth’s magnetic field is 3.80 x 10-5 T. a.29.3 mV.b.2.93 mV.c.0.00293 V.d.0.293 V

To calculate the maximum induced emf, we can use Faraday's law of electromagnetic induction, which states that the induced emf in a circuit is equal to the rate of change of magnetic flux through the circuit. The formula for this is:

emf = -N * (ΔΦ/Δt)

Where: N = number of turns in the coil ΔΦ = change in magnetic flux Δt = change in time

However, in this case, we are dealing with a rotating coil in a constant magnetic field, so the change in magnetic flux is due to the change in the area vector's direction. The magnetic flux Φ through the coil at any instant is given by:

Φ = B * A * cos(θ)

Where: B = magnetic field strength A = area of the coil θ = angle between the magnetic field direction and the normal to the coil

The maximum change in flux occurs when the coil flips from being parallel to the field (θ = 0, cos(θ) = 1) to being antiparallel to the field (θ = 180°, cos(θ) = -1). So, ΔΦ = 2 * B * A.

The time it takes for the coil to flip is half the period of one rotation, which is Δt = 1/(2f), where f is the frequency of rotation.

Substituting these into Faraday's law gives:

emf = N * B * A * f

We can calculate A using the formula for the area of a circle (A = πr²), where r is the radius of the coil. The radius is half the diameter, so r = 22.0 cm / 2 = 11.0 cm = 0.11 m.

The frequency f is the number of rotations per second. We are given the number of rotations per minute (rpm), so we need to convert this to rotations per second by dividing by 60. So, f = 1250 rpm / 60 = 20.83 Hz.

Substituting these values into the formula gives:

emf = 155 turns * 3.80 x 10^-5 T * π * (0.11 m)² * 20.83 Hz = 0.00293 V

So, the maximum induced emf is 0.00293 V, which corresponds to option c.