Figures (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

As `V prop (1)/( r) :. V_(p) gt v_(Q) or (V_(P) - V_(Q))` is positive
Also `V_(B)` is less negative than `V_(A)`
(`:'` distance fo B is more than distance of A)
Thus, `V_(B) gt V_(A) :. (V_(B) - V_(A))` is positive.
(b) A negative charge held at Q would move towards P. As charge moves from higher potential energy to lower potential energy `:.(P.E)_(Q) gt (P.E)_(P)`
Therefore, sign of potential energy difference of a small negative charge between Q and P is positive. Similarly , `(P.E)_(A) gt (P.E)_(B)`
Sign of potential energy difference is positive.
(c) In moving a small positive charge from Q to P, work has to be done by us against the electric filed. Therefore, work has to be done by the field is negative.
(d) In moving a small negative charge from B to A, work done by external agency is positive.
(e) Due to force of repulsion on the negative charge, velocity decreases and hence K.E. decreases in going from B to A.