Question

Three-point charges Q, q and -q are kept at the vertices of an equilateral triangle of side L as shown in the figure. What is 

1. the electrostatic potential energy of the arrangement? and
2. the potential at point D?

Answer 1

1. The electrostatic potential energy of the arrangement.
   U = `1/(4piepsi_0)[((Q) xx (-q))/L + ((-q)(q))/L + ((q)(Q))/L]`
   = `1/(4piepsi_0.L)[-qQ - q^2 + qQ]`
   U = `-q^2/(4piepsi_0.L)`
2. 
   
   The potential at point D.
   `V_D = 1/(4piepsi_0)[((-q))/(L"/"2) + q/((L"/"2)) + Q/(Lsqrt3"/"2)]`
   `V_D = 1/(4piepsi_0) . (2Q)/(sqrt(3)L)`
   ⇒ `V_D = Q/(2sqrt3piepsi_0L)`