Figure Q1811 shows points on several equipotential surfacces

Figure Q18.11 shows points on several equipotential surfacces, with Va > Vd

(a) A positive test charge starts at point A and moves to point C. If the test charge starts adn ends at rest, which of the following statements applies? (i) A positive amount of work must be done on the test charge by an external force. (ii) The work done on the test charge by an external force must be negative (iii) No work is done on the test charge.

Repeat this question for moving the test charge (b) from C to E (c) from B to E (d) from D to E

Solution

a)

Work done by external force + work done by the electric force = change in Kinetic energy

For the displacement from A to C, the change in Kinetic energy = 0 <---- as the start and end velocity = 0

So, work done by both forces= 0

Now, work done by Electric force = +ve (as Va > Vc, so Work done by electric force, We = q*(Va - Vc) = +ve)

So, work done by external force must be -ve so that net work done = 0

So, answer is : (ii) The work done on the test charge by an external force must be negative

b)

Now, here We = -ve (as Vc < Ve, so We = q*(Ve - Vc) = -ve)

So, work done by external force = +ve

So, answer is : (i) A positive amount of work must be done on the test charge by an external force

c)

Here :Vb = Ve, so, We = 0

So, work done by external force = 0

So, correct answer is (iii) No work is done on the test charge.

d)

Here Vd < Ve

So, We = -ve

So, work done by external force = +ve

So, answer is  (i) A positive amount of work must be done on the test charge by an external force