Electromagnetic Question? Check My Work!?

Question

Question: a piece of copper wire is formed into a single circular loop of radius 12 cm. a magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.60 T in time of 0.45 s. the wire has a resistance per unit length of 3.3 x 10^-2 ohms/m. what is the avg. electrical energy dissipated in the resistance of the wire?

My Approach: I found the area using the radius...A = .0144 m^2 and then found L using the radius....L = .75 m

Then, I used this equation to determine emf... Emf = (BA - initial BA)/ change(time)

Emf = (.60)(.0144) - 0/ 0.45 = .0192 V

Next, I found resistance by multiplying the L to ohms/L value:

R = 3.3 x 10-2 ohms/m (.75m) = .025 ohms

Then I found current using V = IR:

I = .0192V/.025 ohm = .768A

Then I plugged to P = IV (to find power):

P = IV = (.768)(.0192) = .0147 J/s

Then I multipilied by time to get the energy:

.0147 J/s (.45 s) = .0066J ---- THAT'S THE ANSWER!

Again, just rectify my approach and correct what is wrong!

Answer 1

the only problem with your set is that you are using the wrong formula to find the area. You are forgetting the most important ingredient, pi!!!

instead of (.0144 m^2) you should use (.04524 m^2)

check me if I'm wrong :P

Answer 2

FWIW, It looks good to me. I wouldn't have bothered to calculate the current after the resistance (since P = V²/R) but it's probably a good exercise for you ☺

Good job ☺


Doug