Determine electrical power generated by changing B-field through a loop

[Rijad Hadzic]

Homework Statement

A circular loop of radius a and resistance R is placed in a changing magnetic field so that the field is perpendicular to the plane of the loop. The magnetic field varies with time as B(t) = B_0 * e^(-t) where B_0 is a constant. Determine the electrical power in the circuit when t = 0

Homework Equations

The Attempt at a Solution

so according to faraday-lenz law

Emf = -Nd(Mflux)/dt

I don't have to worry about N, so

Emf = -d(Mflux)/dt

M flux = BA (no cos since field is perpendicular)

B = B(t) = B_0 * e^(-t)
A = (πa^2)

A is constant, I can pull it out of the derivative, B_0 is as well, so pull that out

Emf = -πa^2 B_0 * d(e^(-t)) / dt

Emf = -πa^2 B_0 * -e^(-t)

Emf = πa^2 B_0 * e^(-t)

Since power = I V

and I = V / R

power = V^2 / R

Plug in Emf for V

power = (πa^2 B_0 * e^(-t) )^2 / R

when t = 0, e^(-t ) = 1

so power = (πa^2 B_0 )^2 / R

and that's my answer.. is this correct? Sorry I hate posting these "am I right or not!?" posts but my book doesn't have the answer to this one sadly :(

 

[CWatters]

I couldn't see a mistake.