Question

1. An electron (charge = -e) is placed at each of the
eight corners of a cube of side a and an a-particle
(charge = + 2e) at the centre of the cube. Calculate
the potential energy of the system.
(Ans. 3.89 x 1010 e2/a joule)​

Answer 1

There are total 9 charges so total term in potential energy=N(N−1)2=9×82=36and these terms will come by this way12→edge term12→face diagonal term4→body diagonal term8→due to charge at center⎛⎝negative term⎞⎠So total potential energy of the system U=12×14πε0e2a+12×14πε0e22√a+4×14πε0e23√a−8×14πε02e23√2aU=14πε0e2a[12+122√+43√−323√]U=14πε0e2a[12+122√+−283√]