A 22-turn circular coil of radius 3.00 cm and resistance 1.00 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 0t + 0.040 0t2, where B is in teslas and t is in seconds. Calculate the induced emf in the coil at t = 4.60 s.

23.5 mV

Explanation:

number of turn coil 'N' = 22

radius 'r' = 3.00 cm=> 0.03m

resistance = 1.00 Ω

B = 0.0100t + 0.0400t²

Time 't' = 4.60s

Note that Area'A' = πr²

The magnitude of induced EMF is given by,

lƩl = ΔφB/Δt = N (dB/dt) A

=N[d/dt (0.0100t + 0.0400 t²) A

=22 (0.0100 + 0.0800 (4.60)) [π (0.03) ²]

=0.0235

=23.5 mV

Thus, the induced emf in the coil at t = 4.60 s is 23.5 mV