Six point charges Qi i 16 each equal to Q are equally space

Six point charges Q_i (i = 1,...,6). each equal to +Q, are equally spaced on a circle of radius a as shown in the figure below. A seventh charge Q_tau, equal to +q, is placed at the center of the circle. 1. (a) Find the total electrostatic potential energy of the system. Solution: (b) Find a relationship between q and Q for which the total electrostatic potential energy of the system i. vanishes, Solution: ii. is minimized. Solution:

Solution

your part a seems correct.

for b) i for potential energy to be zero 3kq/r(2q+2Q+2Q/root3+Q/2) =0

so Q=-2q/(2+2/root3+.5).

so Q should be of opposite charge and value is given above.

ii) for minimum du/dQ=0 so

Du/DQ =3K/R(2q+4Q+4/root3 Q+Q) =0

so Q=-2q/(5+4/root3) for potential to be minimum