Four pointtlike charges are placed as shown in the figure th

Four pointt-like charges are placed as shown in the figure, three of them are at the corners and one at the center of a square, 36.0 cm on cach side. What is the electric potential energy of the entire system of charges? Let q_1 = +29.0 mu C, q_2 = -25.0 mu C, q_3 = +22.0 mu C, and q_4 = -45.0 mu C. J

Solution

Utot = k*q1*q2/r12 + k*q1*q3/r13 + k*q1*q4/r14 + k*q2*q3/r23 + k*q2*q4/r24+k*q3*q4/r34

r13 = sqrt2*a = 51 cm

r14 = r24 = r34 = r13/2 = 25.5 cm

Utot = (9*10^9)*( -(29*25/0.36) +(29*22/0.51) - (29*45/0.255) - (25*22/0.255) + (25*45/0.255) - (22*45/0.255) )*10^-12

Utot = -65.57 J