Fig shows the electric field lines due to a point positive charge. P and Q are two point in the electric field.

i) What is the sign pf `V_(P)-V_(Q)`?
ii) What is the sign of the potential energy difference of a small negative charge between Q and P?
iii) What is the sign of work done by the field in moving a small positive charge from Q to P?
iv)What is the sign of work done by external agent in moving a positive charge from Q to P?

Explanation

(i) Potential at point `V prop 1//r`. Therefore, `V_(P) gt V_(Q)`.
Hence sign of `V_(P)-V_(Q)` is positive.
(ii) If a negative charge is placed at Q, it will move towards P.
Since, a charge moves from higher potential energy to lower potential energy, `U_(Q) gt U_(P)`. Therefore, `U_(Q)-U_(P)` is positive.
(iii) If a small positive charge is placed at P, work done by the field in moving it to Q is positive. Hence, work done by the field in moving small positive charge from Q to P is negative.
(iv) Since in moving the positive charge from Q to P, external agent should do work against the field, the work done is positive.