Several charges in the neighbourhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of 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.

Question

Quizplus · Accepted Answer

The potential at point P is given as 6.0 kV, which means that the electric potential energy of a 3.0 µC charge at infinity is 6.0 kJ. 
Now, using the formula for electric potential energy, we can find the work done to move the charge from infinity to point P:

$W=-\Delta U=q\Delta V=3.0	imes 10^{-6}	ext{ C} 	imes(6.0	imes 10^3	ext{ V})=-18	ext{ mJ}$

Note that the negative sign indicates that the external agent must do work on the charge to move it against the electric field. Therefore, the correct answer is (B) 18 mJ.

Several Charges in the Neighbourhood of Point P Produce an Electric