Answer to Question #28828 in Electricity and Magnetism for Sai Mahidhar

Question

charges 5uC , -2uC ,3uC and -9uC are placed at the corners A,B,C and D of a square ABCD of side 1m . the net electric potential at the centre of the square is A) -27 KV B) -27ROOT2 KV C) -90 KV D) ZERO

Answer 1

Distance from any charge to the center of the square is r =1/sqrt(2) m = 0.7071 m.
Electric potential of one charge in the center is phi1 = q / (4*pi*eps0*r).
Since potential is a scalar, contributions from differentcharges will simply add up.
Thus, the net
phi = (q1+q2+q3+q4) /(4*pi*eps0*r) = (5-2+3-9) microC / (4*3.14*8.85*10^(-12) F/m * 1/sqrt(2) m) =
approximately - 27*sqrt(2) *10^3 V = - 38149 V.
Answer: B) -27ROOT2 KV