Consider a system of four point charges as shown in the figu

Consider a system of four point charges as shown in the figure below. The four point charges have the values q_1 = 1.00 mu C, q_2 = 2.00 mu C, q_3 = -3.00 mu C, and q_4 = 4.00 mu C. The charges are placed with a = 6.00 in and b = 4.00 in. What is the electric potential energy of this system of four point charges?

Solution

PE of two point charge system :

PE = kq1q2 / d  

where d is the distance between q1 and q2.

there 6 sets: (q1,q2) (q2,q4) (q4,q3) (q3,q1) (q2,q3) (q1, q4)

PE = [ k(q1)(kq2) / a ] + [ k(q4)(kq2) / b ] + [ k(q4)(kq3) / a ] + [ k(q1)(kq3) / b ] + [ k(q3)(kq2) / sqrt(a^2 + b^2) ]

   + [ k(q1)(kq4) / sqrt(a^2 + b^2) ]

putting values,

k = 9 x 10^9, q1 = 1 x 10^-6 C, q2 = 2 x 10^-6 C , q3 = - 3 x 10^-6 C, q4 = 4 x 10^-6 C

a = 6m, b = 4 m

PE = - 6.25 x 10^-3 J Or - 6.25 m J