# Answer to Question #21866 in Electromagnetism for divya rawal

Question #21866

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 ?

Expert's answer

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

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

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