(a) Calcualte the potential at a point P due to a charge of `4 xx 10^(-7)` C located 9 cm away.
(b) Hence obtain the work done in bringing a charge of `2 xx 10^(-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/(4piepsilon_(0)). Q/r = 9 xx 10^(9)Nm^(2)C^(-2) xx (4 xx 10^(-7) C)/(0.09m)`
`=4 xx 10^(4)` V
(b) `W = qV = 2 xx 10^(-9) C xx 4 xx 10^(4)` V
`= 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.