Energy dissipated in the loop during mag. field change

[moenste]

Homework Statement

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?

 

[LemmeThink]

Hi again!
Glad to see you worked out the first part.

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

What's the second part of the question asking?

 

[moenste]

What's the second part of the question asking?

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.

 

[LemmeThink]

And you've found...?

 

[moenste]

And you've found...?

P = I2 R = V2 / R = 0.72 * 2 * 10-3 = 9.8 * 10-4 J

?

 

[LemmeThink]

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

 

[moenste]

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

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.

 

[LemmeThink]

Here you go : https://en.m.wikipedia.org/wiki/Power_(physics)

Btw, loving the likes, but you don't need to give me a like for every post of mine;)

 

[moenste]

Here you go : https://en.m.wikipedia.org/wiki/Power_(physics)

Btw, loving the likes, but you don't need to give me a like for every post of mine;)

Thank you! I think this should be correct:

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.

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 : (.