Question

(i) Can two equpotential surfaces intersect each other ? Give reason.
(ii) Two charges `+ q and -q` are located at points A `(0, 0, -2) and B(0, 0, 2)` respectively. How much work will be done in moving a test charge from point P`(4, 0, 0) " to " (-5, 0,0)` ?

Answer 1

(ii) Potential at P (4, 0, 0) is
`V_(1) = (-q)/(4 pi epsi_(0)).(1)/(sqrt((4 -0)^(2) + (0 + 2)^(2))) + (q)/(4 pi epsi_(0)).(1)/(sqrt((4 -0)^(2) + (0 -2)^(2)))`
`= (-q)/(4 pi epsi_(0)).(1)/(sqrt(16 + 4)) + (q)/(4 pi epsi_(0)) .(1)/(sqrt(16 + 4)) = 0`
Potential at `q(-5, 0, 0)` is
`V_(2) = (-q)/(4 pi epsi_(0)).(1)/(sqrt((-5 -0)^(2) + (0 + 2)^(2))) + (q)/(4pi epsi_(0)).(1)/(sqrt((-5-0)^(2) + (0-2)^(2)))`
`= (-q)/(4pi epsi_(0)).(1)/(sqrt(25 + 4)) + (q)/(4pi epsi_(0)).(1)/(sqrt(25 + 4)) = 0`
`:.` Work done `= q (V_(2) - V_(1)) = q (0 -0) = 0`
Hence, `w = 0`