How much net work must be done by an external force to move a –1 μC point charge

Question

The diagram above shows equipotential lines produced by an unknown charge distribution. A, B, C, D, and E are points in the plane.

How much net work must be done by an external force to move a –1 μC point charge from rest at point C to rest at point E ?

(A) –20 μJ 

(B) –10 μJ 

(C) 10 μJ 

(D) 20 μJ 

(E) 30 μJ

Answer 1

The correct option is: (B) –10 μJ 

Explanation:

ΔV_CE = V_E – V_C = 10 V. The amount of work, W = qΔV = 1 μC × 10 V = 10 μC. Since the external force must push against the negative charge to keep it from accelerating and bring it to rest at point E, the work done by the external force must be negative.