Answer to Question #21866 in Electricity and Magnetism for divya rawal

Question

four charges each equal to Q are placed at the four corners of a square q and a charge q is placed ct the centre of the square. if the system is in equilibrium then what is the value of q ?

Answer 1

System is in equilibrium when resultant of all forcesis 0.
That means: forces from charges Q must be balanced by forcefrom charge q.
So, we will find q from this condition.
Forces from Q-s are:
k Q^2/(2a^2) + 2 k Q^2/a^2 = 2.5 kQ^2/a^2
where a is a side of a square
Force from q is
kQq / (a^2/2) = 2kQq/a^2

So we find
2kQq/a^2 = -2.5 kQ^2/a^2
2q =- 2.5Q
q= -2.5/2 Q = -1.25 Q
answer is q=-1.25*Q