A circular loop of wire with radius 2.00 cm and resistance 0.600 Ω is in a region of a spatially uniform magnetic field B⃗ that is perpendicular to the plane of the loop. At t = 0 the magnetic field has magnitude B0=3.00T. The magnetic field then decreases according to the equation B (t) = B0e-t/τ, where τ=0.500s.

Incomplete questions

Let assume we are asked to find

Calculate the induced emf in the coil at any time, let say t=2

And induced current

Explanation:

Flux is given as

Φ=NAB

Where

N is number of turn, N=1

A=area=πr²

Since r=2cm=0.02

A=π (0.02) ²=0.001257m²

B=magnetic field

B (t) = Bo•e-t/τ,

Where Bo=3T

τ=0.5s

B (t) = 3e (-t/0.5)

B (t) = 3exp (-2t)

Therefore

Φ=NAB

Φ=0.001257*3•exp (-2t)

Φ=0.00377exp (-2t)

Now,

Induce emf is given as

E = - dΦ/dt

E = - 0.00377*-2 exp (-2t)

E=0.00754exp (-2t)

At t=2

E=0.00754exp (-4)

E=0.000138V

E=0.138mV

b. Induce current

From ohms laws

V=iR

Given that R=0.6Ω

i=V/R

i=0.000138/0.6

i=0.00023A

i=0.23mA