Question

A circular coil of 4 turns with a radius of 0.03m., and it is subjected to a varying magnetic field that changes uniformly from 0.4 T to 3.4 T in an interval of 27s. The axis of the solenoid makes an angle of 35° to the magnetic field. Find the induced EMF. (A = π r2)ε = - N (ΔΦ / Δt)= N (A cos!) (Bf – Bi)

Answer 1

Let’s use the Faraday’s law and find the induced emf: 

$$\Epsilon=-N\dfrac{\Delta\Phi }{\Delta t},$$ $$\Epsilon=N\dfrac{Acos\theta(B_f-B_i)}{\Delta t},$$ $$\Epsilon=N\dfrac{\pi r^2cos\theta(B_f-B_i)}{\Delta t},$$ $$\Epsilon=4\cdot\dfrac{\pi(0.03\ m)^2\cdot cos35^{\circ}\cdot(3.4\ T-0.4\ T)}{27\ s}=1.03\cdot10^{-3}\ V.$$