Understanding Electrostatic Potential Energy Calculations

[chickens]

http://forum.lowyat.net/index.php?act=Attach&type=post&id=46273

Hi there, I've been trying this question quite long but I do not get the answer, could anyone help me?

For part one, i got the answer...

part (ii) ... i saw it in a book saying i suppose to choose a point to get the potential energy, let's say i choose point A, the total potential energy of the system would be, U(AB) + U (AD) + U (AC) ... but i couldn't get the answer...did i do it wrong ? do help me, thank you.

 

[dextercioby]

How many possible cases (on mutual interaction) have you identified for point b)...?

Daniel.

 

[StatusX]

The potential energy in the system is the work it would take to assemble the system. The first charge can be placed for free, but to place the second, you need to overcome the force from the first. Likewise, to place the third, you need to overcome the force from the first and second, and so on. The formula you mentioned is close, but it's missing some terms (eg, U(BC)).

 

[chickens]

oOoO, statusX, u gave me some idea :D let me try it out :)

 

[chickens]

Hi there, I think I've done part (ii)..here goes

Lets say first charge is put at A...no work is required.

Second charge put at B, U (B) = U (AB)

3rd charge put at C, U (C) = U (AC) + U (BC)

4th charge put at D, U (D) = U (AD) + U (DC) + U (DB)

U system = U (B) + U (C) + U (D)

Answer ->

 

[chickens]

I got that answer, statusX, do u get that as well, if u do..that means the answer in the book is wrong :P

 

[StatusX]

I'm not sure. I got that answer too, and it makes sense, but I don't know what your book wants. Maybe it wants the energy it takes to pull that apart, which would explain why their answer is the negative of yours. Maybe they want the energy stored in the fields, which is the integral over all space of e0|E|². If you know that formula, you could try that to see if it gives their answer, but it's a lot more work. (plus, since these are point charges, I don't know what physical meaning it would have, which is why I didn't suggest it first)

 

[chickens]

hmmm alright then, then i'll ask teacher...she'll help me confirm the answer :P I'll post the right answer after teacher has confirm it :)

 

[Doc Al]

It looks like the book missed a minus sign in the answer for (ii). The potential energy of the system is negative. When arranged in a smaller square, the PE is even more negative. Note that the net force exerted on each charge is towards the center: the system pulls itself together.

 

[chickens]

i know i suspect the same thing too, same goes to (iii)..well let me confirm with my teacher firsT :P