A 30-Turn, 10-Cm-Diameter Coil Is Oriented in a Vertical Plane with Its Axis Aligned East-West

A 30-turn, 10-cm-diameter coil is oriented in a vertical plane with its axis aligned east-west. A magnetic field pointing to the northeast decreases from 0.82 T to 0.18 T in 2.3 s. What is the emf induced in the coil?

Here it is given that,

Number of turns, N = 30

Diameter of the coil, d = 10cm = 0.10 m

Radius of the coil, r = d/2 = 0.05 m

Initial magnetic field, B1 = 0.82T

Final magnetic field, B2 = 0.18T

Change in the magnetic field ΔB = B2-B1= -0.64T

Time Δt = 2.30s

Now,

∆Φ = ∆BA cos θ

= - 0.64T *(π * (0.05 m)²) * Cos(45°)

= - 0.64T *(3.14 * (0.05 m)²) * 0.7071

= - 0.00355431 Wb

By Faraday's law of the induction the induced EMF is calculated as

ε = -N(ΔΦ/Δt)

= -30*(- 0.00355431 Wb/2.30s)

= 0.0463604 Volt