Question

I have question about Faraday law.

the question is about problem 7:
http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/faradays-law-1/faradays-law/MIT8_02SC_challenge_sol21.pdf

In c part, I was asked to find the force on the rod,
I tried to find it by equalize the power in the circle
and the power of the movement of the rod.

the equalization is P = I^2*R -> THE POWER IN THE CIRCLE
P = F*v = F *omega* a -> POWER FROM THE FORCE

but I found that the force is not the right answer
and is small in factor 2.

what was the problem?!

Answer 1

remark: In similar question when the rod moves in rectangle, the equalization of the power led to the correct answer of the force.

Answer 2

I think that I understood what the problem was.In the second equation I wrote that
v = omega*a but the problem is that the force is from the middle of the rod so
v = omega*a/2 and this explain why i got the same reult by factor 2.

Thank you anyway