Answer to Question #208410 in Electric Circuits for Kuina

Question

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

Answer 1

(a) We can find the work done required as follows:

$$W=kqQ(\dfrac{1}{r_2}-\dfrac{1}{r_1}),$$ $$W=9\cdot10^9\ \dfrac{N\cdot m^2}{C^2}\cdot4\cdot10^{-9}\ C\cdot60\cdot10^{-9}\ C\cdot(\dfrac{1}{0.5\ m}-\dfrac{1}{2\ m}),$$ $$W=3.24\cdot10^{-6}\ J.$$

(b) We can find the potential difference as follows:

$$W=q\Delta V,$$ $$\Delta V=\dfrac{W}{q}=\dfrac{3.24\cdot10^{-6}\ J}{4\cdot10^{-9}\ C}=810\ V.$$