Question

How much is required to move a charge of 4 nC from a point 2 m away to point 0.5 m away from a point charge of 60 nC? What is the potential difference between these points?

Answer 1

Find the potentials at points 2 and 0.5 m away from the 60nC-charge respectively:

$$\phi_1=\frac{kQ}{r_1}=269.6\text{ V},\\\space\\ \phi_2=\frac{kQ}{r_2}=1079\text{ V}.$$

Find how much energy is required to move the charge from a position of 2 to 0.5 m away from the larger charge:

$$W=q(\phi_2-\phi_1)=3.238\space\mu\text{J}.$$