Question

A 50-turn circular wire loop has a radius 3 cm and is located in a uniform magnetic field. The magnetic field lines are perpendicular to the plane of the circular loop. Suppose that the magnetic field is varied so that BBB increases from 0.1 T to 0.35 T in 1.95 ms. Part A Find the average induced emf in the coil (including sign of the emf). View Available Hint(s)

Answer 1

Average induced emf = - 18.13 V

Step-by-step explanation:

According to Faraday's law of electromagnetic induction,

Induced emf = - N (dΦ/dt)

Φ = magnetic flux = BA

(dΦ/dt) = A(dB/dt)

Emf = -NA (dB/dt)

Average induced emf = - NA (ΔB/Δt)

N = number of turns = 50 turns

A = Cross sectional Area of the circular loop = πr² = π(0.03)² = 0.00283 m²

ΔB = Change in magnetic field strength = 0.35 - 0.1 = 0.25 T

Δt = 1.95 ms = 0.00195 s

Average induced emf = - (50)(0.00283)(0.25/0.00195)

Average induced emf = - 18.13 V

The minus sign indicates that the average induced emf and the change in magnetic flux have opposite signs.