Question:
At each of the 4 cornors of a square of side a, a charge q is placed freely.What charge should be placed at the centre of the square so that the whole system be in equilibrium
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
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