# Energy dissipated in the loop during mag. field change

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1. Oct 17, 2016

### moenste

1. The problem statement, all variables and given/known data
A closed wire loop in the form of a square of side 4.0 cm is mounted with its plane horizontal. The loop has a resistance of 2.0 * 10-3 Ω, and negligible self inductance. The loop is situated in a magnetic field of strength 0.70 T directed vertically downwards. When the field is switched off, it decreases to zero at a uniform rate in 0.80 s. What is:

(a) the current induced in the loop,
(b) the energy dissipated in the loop during the change in the magnetic field?

Show on a diagram, justifying your statement, the direction of the induced current.

Answers: (a) 0.70 A, (b) 7.8 * 10-4 J.

2. The attempt at a solution
(a) E = - N d Φ / d t, where Φ = B A = 0.7 * (0.04 * 0.04)

E = - 1 * ((0.7 * (0.04 * 0.04)) / 0.8) = 1.4 * 10-3 V.

I = V / R = 1.4 * 10-3 / 2 * 10-3 = 0.7 A.

(b) P = I2 R = V2 / R = 0.72 * 2 * 10-3 = 9.8 * 10-4 J. Why this answer is larger than the given one?

2. Oct 17, 2016

### LemmeThink

Hi again!
Glad to see you worked out the first part.
What's the second part of the question asking?

3. Oct 18, 2016

### moenste

Hi again :)!

Well, it's asking for the energy dissipated in the loop during the change in the magnetic field. When B changes from 0.7 T to 0 T in 0.80 s.

4. Oct 18, 2016

### LemmeThink

And you've found...?

5. Oct 18, 2016

### moenste

?

6. Oct 18, 2016

### LemmeThink

Do you know what P stands for? Is it the energy dissipated? If not, how are the two related?

7. Oct 18, 2016

### moenste

P is power. Indeed it's not energy dissipated.

No idea then what is the dissipated energy.

Update: I ran into a E = P t formula. So 9.8 * 10-4 * 0.8 = 7.8 * 10-4 J. So I think this should be correct.

8. Oct 18, 2016

### LemmeThink

9. Oct 18, 2016

### moenste

Thank you! I think this should be correct:
It's said in the rules to appreciate the help, and since everybody is helping here for free, that's the only way of saying "thank you" and not writing it every time :).

Maybe you could help with this post? It's stuck since Saturday : (.