A 26-turn circular coil of wire has radius 0.4 m. It is placed with its axis along the direction of the Earth's magnetic field of 58.0 µT and then in 0.200 seconds is flipped 180°. An average emf of what magnitude is generated in the coil? (units of V)Answer

The magnitude of the average emf generated in the coil can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf in a coil is equal to the rate of change of magnetic flux through the coil.

The formula for Faraday's law is:

emf = -N * ΔΦ/Δt

where: N = number of turns in the coil = 26 ΔΦ = change in magnetic flux = final flux - initial flux Δt = change in time = 0.200 seconds

The magnetic flux (Φ) through a coil is given by the formula:

Φ = B * A * cos(θ)

where: B = magnetic field strength = 58.0 µT = 58.0 * 10^-6 T A = area of the coil = π * r^2 = π * (0.4 m)^2 θ = angle between the normal to the coil and the magnetic field

Initially, the coil is placed with its axis along the direction of the Earth's magnetic field, so θ = 0 degrees and cos(θ) = 1. Therefore, the initial flux is:

Φ_initial = B * A * cos(0) = B * A

After the coil is flipped 180°, θ = 180 degrees and cos(θ) = -1. Therefore, the final flux is:

Φ_final = B * A * cos(180) = -B * A

The change in flux is:

ΔΦ = Φ_final - Φ_initial = -B * A - B * A = -2 * B * A

Substituting these values into Faraday's law gives:

emf = -N * ΔΦ/Δt = -N * -2 * B * A / Δt = 2 * N * B * A / Δt

Calculating this gives the magnitude of the average emf generated in the coil.