Induced current from changing magnetic field

[iharuyuki]

Homework Statement

Homework Equations

emf = i (induced) R
emf = - d(Ф)/dt
Ф = B (dot) A
B = μi/(4piR)

The Attempt at a Solution

emf = - d(Ф)/dt
emf = - d( B (dot) A )/dt
emf = - d[ (μi/(4piR) * A ]/dt, A and B are perpendicular

Really not sure how to proceed from here as there are multiple derivatives (di/dt dR/dt and dA/dt) that I don't quite get.

Thank you very much.

 

[phyzguy]

You have to calculate the total flux φ through the loop. Since B is a function of R, you have to integrate to find the total flux, which will be a function of i. In terms of your question about time derivatives, the only thing changing with time is i. A and R are constant in time.

 

[iharuyuki]

Got it! Thank you very much.