EMF and induced current question

[StephenDoty]

The rectangular loop in the figure has 1.7×10^−2 ohm resistance. What is the induced at this instant? See picture below. Answer is in terms of I, like 5*I.

emf = Bvl
I= emf/R

B= [$$\mu$$_0 / 2*pi] *I * ln(.03/.02) since the magnetic field goes through the loop from 2cm to 3cm

then I used this magnitude in emf=B*10*.04 and then used the emf to find the induced current:

I = emf/ (1.7*10^-2)

However, the answer I got using these calculations was incorrect. What did I do wrong?

Thanks.
Stephen

 

[jbsteele]

You forgot to include the factor of 4π in your equation for B. The correct equation should be:B = [\mu_0 / (4*pi)] *I * ln(.03/.02) Once you include this factor, you should get the correct answer.

 

[thomate1]

Your calculations seem to be correct, but there may be a small mistake in converting the units. The units for magnetic field are Tesla (T), and the units for length are meters (m). So when you calculate B = μ0/2π * I * ln(0.03/0.02), the result should be in units of T*m, not just T. This may be the reason why your final answer is incorrect. To get the correct answer in terms of I, you can simply multiply the result by the length of the loop (0.04m). So the final equation would be I = (B * 0.04) / (1.7 * 10^-2). This should give you the correct answer of 5I.