A circular coil of radius 5.0 cm and resistance 0.20 Ω is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = 0.50e-20t T. What is the magnitude of the current induced in the coil at the time

Given that,

Assume number of turn is

N = 1

Radius of coil is.

r = 5cm = 0.05m

Then, Area of the surface is given as

A = πr² = π * 0.05²

A = 7.85 * 10^-3 m²

Resistance of

R = 0.20 Ω

The magnetic field is a function of time

B = 0.50exp (-20t) T

Magnitude of induce current at

t = 2s

We need to find the induced emf

This induced voltage, ε can be quantified by:

ε = - NdΦ/dt

Φ = BAcosθ, but θ = 90°, they are perpendicular

So, Φ = BA

ε = - NdΦ/dt = - N d (BA) / dt

A is a constant

ε = - NA dB/dt

Then, B = 0.50exp (-20t)

So, dB/dt = 0.5 * - 20 exp (-20t)

dB/dt = - 10exp (-20t)

So,

ε = - NA dB/dt

ε = - NA * - 10exp (-20t)

ε = 10 * NA exp (-20t)

Now from ohms law, ε = iR

So, I = ε / R

I = 10 * NA exp (-20t) / R

Substituting the values given

I = 10*1 * 7.85 * 10^-3*exp (-20*2) / 0.2

I = 1.67 * 10^-18 A