Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity)and an electric field of $36 \hat { \mathbf { i } }$ N/C at point P.Determine the work required of an external agent to move a 3.0-$\mu$C charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle.
A)21 mJ
B)18 mJ
C)24 mJ
D)27 mJ
E)12 mJ

Question

Quizplus · Accepted Answer

The work done by an external agent to move a charge from infinity to a point in an electric field is given by the product of the charge and the electric potential at that point. Here, the potential at point P is 6.0 kV, and the charge is 3.0 μC. Thus, the work done is $ W = qV = (3.0 \times 10^{-6} \, \text{C})(6.0 \times 10^3 \, \text{V}) = 18 \, \text{mJ} $.

Several Charges in the Neighborhood of Point P Produce an Electric