Question

Three point charges $q,2q$ and $8q$ are to be placed on a $9cm$ long straight line. Find the positions between the charges should be placed such that the potential energy of this system is minimum. In this situation what is the electric field at the position of the charge ${}^{\prime }{q}^{\prime }$ due to the other two charges.

Answer 1

For the potential energy to be minimum, bigger charges should be at most separation. Hence 2q and 8q are put at ends. The position of q is assumed to be at r distance from 2q. By minimising the expression for potential energy, r comes out to be 3 cm.

After that, Electric field at q is $\frac{4}{9}K{q}^2.$