Question

You have two charges +4q and one charge -q.

(a) How would you place them along a line so there's no net force on any of the three?

Options:

One positive charge must be at the midpoint between the other two charges.

The negative charge must be at the midpoint between the two positive charges.    

One positive charge must be four times the distance from the negative charge as it is from the other positive charge.

There is no way to arrange the charges so that there's no net force.

(b) Is this equilibrium stable or unstable?

I believe the answer to a is the third option but I am not 100% sure, then for b I believe it is stable but again not completely sure.

Answer 1

Answer 2

the negative charge must be at mid point of two positive charges.

coz in that case force on each +ve charge will be = k(-4q^2/x^2)+k(16q^2/(2x)^2) = 0

and for -ve charge Fnet = k(-4q^2/x^2)+k(4q^2/x^2) =0

It is stable equilibrium...if you slightly shift the negative charge, then equilibrium will be restored as soon as possible...if you disturb either postive charge then also it will try to come back to its original position. Actually it will behave as a spring mass system then

Answer 3

a.) option 2.. The negative charge must be at the midpoint between the two positive charges.

b.) UNstable equilibrium