Help me with this homework

Question

A circular loop of wire with a radius of 0.2 m is placed in a uniform magnetic field of 0.5 T. The magnetic field is perpendicular to the plane of the loop and is reduced to zero in 0.1 seconds.

Calculate the magnitude of the induced EMF in the loop.

If the resistance of the loop is 2 Ω, determine the induced current.

Explain how Lenz’s Law applies to this scenario.

Retro Bowl

Answer 1

Let

r = 0.2 m be the radius of the loop,

S = πr² be the area of the loop,

B = 0.5 T be the magnetic field,

Φ = B•S be the magnetic flux,

Δt = 0.1 s be the time period for the magnetic field to reduce to 0,

R = 2 Ω be the resistance,

ε (to be calculated) be the induced EMF,

I (to be calculated) be the induced current.

You want to use the law

ε = -dΦ/dt

The "dΦ/dt" portion of the law is attributed to Faraday, while

the negative sign is attributed to Lenz.

It indicates that the induced current in turn induces magnetic field

working against the change in the magnetic flux.

Since the magnetic field is perpendicular to the plane of the loop,

Φ = B•S = BS

Assuming that the change in the magnetic field is constant,

dΦ/dt = ΔΦ/Δt

Assuming that the loop does no change

ΔΦ = (ΔB)S

So putting everything together

ε = -dΦ/dt = -ΔΦ/Δt = -(ΔB/Δt)S = -(0.5/0.1)×2π×(0.2)² ≈ -1.2 V

By Ohm's Law

I = ε/R = -1.2/2 = -0.6 A