An electron is placed at each of the 8 cornersof a cube of side 'a' and an alpha particle at - Physics - Electrostatic Potential And Capacitance

Question

An electron is placed at each of the 8 cornersof a cube of side 'a'
and an alpha particle at the center of the cube Calculate potential
energy of the system

Vipra Mishra · Accepted Answer

Solution

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+12×14πε0e22a+4×14πε0e23a-8×14πε02e232aU=14πε0e2a12+122+43-323U=14πε0e2a12+122-283

An electron is placed at each of the 8 cornersof a cube of side 'a' and an alpha particle at the center of the cube. Calculate potential energy of the system.