(a) Calculate the potential at a point P due to a charge of `4xx10^(-7) C` located 9 cm away.
(b) Hence obtain the work done in bringing a charge of `2xx10^(-9) C` from infinity to the point P. Does the answer depend on the path along which the charge is brought ?

Explanation

(a) `V = (1)/(4pi epsilon_(0)r)(Q)/(r) = 9 xx 10^(9) Nm^(2) C^(-2) xx (4 xx 10^(-7)C)/(0.09 m)`
`= 4 xx 10^(4)V`
(b) `W = qV = 2 xx 10^(-9)C xx 4 xx 10^(4)C`
`= 8 xx 10^(-5) J`
No, work done will be path independent. Any arbitrary infinitesimal path can be resolved into two perpendicular displacements: One along r and another perpendicular to r. The work done corresponding to the later will be zero.