3 identical charged spheres each having charge 'q' and mass m are suspended from same point through a 3 equal strings of length 'l' . if they are in equilibrium at the vertices of an equilateral triangle of side length 'a'. find 'a'.

Consider three indentical charged spheres each having charge q and mass m are suspended through a three equal strings of length l.

Let they are in equilibrium at the vertices of an equilateral triangle.

Total height of the triangle 'h' is  and centroid of an equilateral triangle is 

 

Consider the right angle traingle AEC

From the pythagoras theorem side AE is

From the figure,

 

Since, the three charges are identical possesing repulsive force outwards as shown in diagram

from the equillibrium system.

From (i) and (ii)