Average energy dissipated in a copper loop as magnetic field increases

[osustudent2010]

Hi, I am struggling with this physics problem:

A piece of copper wire is formed into a single circular loop of radius 11 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.50 T in a time of 0.45 s. The wire has a resistance per unit length of 3.3 10-2 /m. What is the average electrical energy (in J) dissipated in the resistance of the wire.

I really don't know where to start in this problem. I can find the circum of the loop and area of the loop. But I'm not sure how to relate resistance, magentic flux, and electrical enery- any help would be appricated!

Thanks

 

[Doc Al]

Faraday's law will allow you to calculate the induced EMF due to the changing magnetic flux through the loop of wire. Start there.

 

[osustudent2010]

I found the EMF to be -.0422
(-NA delta B)/ delta t
where N= the number of loops
A = area
B= magnetic field
t= time

 

[Doc Al]

OK. What are the units of EMF?

Now treat the wire loop as a circuit. What's the average power dissipated in the resistance of the wire?

 

[osustudent2010]

the units are V, so .0422 V

P= (V^2)/R (via P=IV and V=IR)

so I took P= (.0422^2)/.0228

The R came from the circum of the loop times the resistance per unit of length

The answer I got was 1.85 J, but this isn't the right answer-- is there something I'm missing?

 

[Doc Al]

the units are V, so .0422 V

P= (V^2)/R (via P=IV and V=IR)

so I took P= (.0422^2)/.0228

Looks OK. That's the average power. (What units?)

The R came from the circum of the loop times the resistance per unit of length

OK.

The answer I got was 1.85 J, but this isn't the right answer-- is there something I'm missing?

How did you get this answer?

 

[osustudent2010]

I got it! I made a calculation error earlier

I got the answer by using this equation:
E=Pt

where P= equals the average power
t= time

THANKS so much for helping me through this problem, you are the best!