The electrostatic potential due to the charge configuration at point P as shown in figure for b << a is

Options

A. `(2q)/(4piepsilon_0a)`
B. `(2qb^2)/(4piepsilon_0a^3)`
C. `(qb^2)/(4piepsilon_0a^3)`
D. zero

Answer

C

Explanation

`V_p=2(1/(4piepsilon_0)q/a)-2[1/(4piepsilon_0).q/sqrt(b^2+a^2)]`
`=q/(4piepsilon_0a)[2-2(1+b^2/a^2)^(-1//2)]`
Since `bltlta`,we can apply binoial expansion
`:. V_p=q/(4piepsilon_0a)[2-2(1-b^2/(2a^2))]`
=`(qb^2)/(4piepsilon_0a^3)`