Finding the charge at center of a square for equilibrium

[mirzaicpc]

four charges each equal -Q placed at the four edges of a square and a charge q is placed at the centre. if system is in equilibrium the value of q is,

the answer is q = Q/4 * ( 1 + 2(√2)

can anyone please solve this, would be great

 

[rumborak]

That sounds like a homework question, you should probably take it there. Also, I don't understand the setup; you say a charge "q" is placed in the middle. So, isn't the value of q ... q?

 

[ArmanCham]

Are you sure about the answer ? It should be zero I guess net force will be zero any case so we can't tell anything about q and Q

 

[mirzaicpc]

ya i am sure abt it,

 

[rumborak]

But the problem as you describe it make no sense. You already know the value of q, why do you need to calculate it again?

Also, please spend more time writing your responses.

 

[ArmanCham]

Q's are stable or unstable ?

 

[mirzaicpc]

this was one of the replies i got, but couldn't understand it, hope it will help

 

[ArmanCham]

I solved it.I will send a picture I hope it will be not a problem cause its not in homework section

 

[mirzaicpc]

thank you so much,,, waiting for the pic

 

[ArmanCham]

Who moved this in homework section I will be banned now. This post first opened general physics forum.For that I send picture.I don't take any responsibility to share this picture.I don't break the rules.

 

[mirzaicpc]

thank u so much people

 

[Evo]

Who moved this in homework section I will be banned now. This post first opened general physics forum.For that I send picture.I don't take any responsibility to share this picture.I don't break the rules.

Post number 2 stated it was homework, and in the post you edited, you knew it was homework, you won't be banned, don't worry, just make sure to follow the homework rules for helpers.

 

[jbriggs444]

Who moved this in homework section I will be banned now

Don't panic. You're not getting banned. The moderators are just working to help you out by moving your post into the forum where it should have been placed to start with. We're not evil overlords around here. [Though I hear that the ban stick is a fun thing to wield]

It is clear by inspection that the center charge will be in equilibrium regardless of the value of q.

So the original problem is surely intended to find the value of q for which the four equal charges at the corners are each in an equilibrium. Whether that equilibrium would be stable is a separate question that we need not delve into here.

One should be able to calculate the repulsion on each corner charge from its peers. And one should be able to calculate the attraction of the corner charge from the center charge in terms of the known value Q and the unknown value q. Find q such that the net force on a corner charge is zero and the problem is solved. I believe that is the approach that was taken in the posted answer.