Question

if there are two same charges (suppose Q) at a particular distance x then what should be the charge and "SIGN" of the charge which is to be kept in the middle of the two given charges?can anyone clearly explain how to find the sign of the unknown charged particle????

Answer 1

It can negative and positive. There is no definite answer.

For example, suppose the middle charge were positive. If this charge were displaced along the axis, then due to the repulsive forces, it would tend to come back to its original position. This amounts to a position of stable equilibrium along the axis.

But, if this same middle charge were displaced perpendicular to the axis, then it will never come back to its original position. This is unstable equilibrium perpendicular to the axis.

Vice-versa for negative charge in the middle.

Answer 2

So if the middle charge is negative then the force of attractin between the other two particles is also equal so either of the sign would be good!!1 but my textbook has the answer written that the charge wuold be positive,but the options also had a negative substiute of the same answer???

Answer 3

i guess the whole point of the question is for the system to be in a stable equilibrium.

Suppose the middle charge is negative. Suppose I displace this negative charge towards one of the positive charges. Then the force of attraction due to the positive charge, towards which negative charge has been displaced, will be greater than the force of attraction due to the other charge.

hence this negative charge will not come back to its equilibrium position.

But for a positive charge in the middle, a displacement in any direction would result in the charge coming back to its original position due to repulsive and not attractive forces.

I guess your book is referring to stable equilibrium along the axis. Here the answer would be positive charge placed in the middle.

Answer 4

Ahhh!!thank you so much i got it!!thank you for such a vivid explanation.you really deserve more than medals!!!