Three identical charges q 40 mu Clie along a circle of radi

Three identical charges (q = -4.0 mu C)lie along a circle of radius 2.0 m at angles of 30 degree, 150 degree, and 270 degree, as shown in the figure. What is the resultant electric field at the center of the circle (magnitude and orientation ? What is the electric potential at the center of the circle? What is the force acting on a test charge of +1.0 mu C is placed at the center of the circle?

Solution

a) magnitude of field due to each charge will be same a center
(but directions will be different )

|E| = kq/r^2 = (9 x 10^9 x 4.8 x 10^-6) / (2^2)

   = 10800 N/C

and E1 = 10800(cos30i + sin30j)

E2 = 10800(cos150i + sin150j)

E3 = 10800(cos270i + sin270j)

Enet = E1 + E2 + E3 = 0i + 0j

fiels is zero at centre.

b) V = 3 [ kq/r]

   = 3 [ (9 x 10^9 x -4.8 x 10^-6) / 2 ]

   = - 64800 Volt

c) F = qE

E = 0 at cntre hence

F = 0