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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
- the electrostatic potential energy of the arrangement? and
- the potential at point D?
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Solution
- 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)` 
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)`
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