Figures 2.8 (a) and (b) show the field lines of a positive and negative point charge respectively.

(a) Give the signs of the potential difference `V_(P)-V_(Q): V_(B)-V_(A)`.
(b) Give the sign of the potential energy difference of a small negative charge between the points Q and P, A and B.
(c) Give the sign of the work done by the field in moving a small positive charge from Q to P.
(d) Give the sign of the work done by the external agency in moving a small negative charge from B to A.
(e) Does the kinetic energy of a small negative charge increase or decrease in going from B to A?

Explanation

(a) As `V prop 1/r, V_(P) gt V_(Q)`, Thus, `(V_(P)-V_(Q))` is positive. Also `V_(B)` is less negative than `V_(A)`. Thus `V_(B) gt V_(A)` or `(V_(B)-V_(A))` is positive.
(b) A small negative charge will be attracted towards positive charge. The negative charge moves from higher potential energy to lower potential energy. Therefore the sign of potential energy difference of a small negative charge between Q and P is positive.
Similarly, `(P.E)_(A) gt (P.E)_(B)` and hence sign of potential energy differences is positive.
(c) In moving a small positive charge from Q to P, work has to be done by an external agency against the electric field. Therefore, work done by the field is negative.
(d) In moving a small negative charge from B to A work has to be done by the external agency. It is positive.
(e) Due to force of repulsion on the negative charge, velocity decreases and hence the kinetic energy decreases in going from B to A.