Answer to Question #138556 in Electric Circuits for Kirel

Question

Two point charges Q1 = +5.00 nC and Q2 = -3.00 nC are separated by 35.0 cm (a) What is the electric potential at a point midway between the charges? (b) What is the potential energy of the pair of charges?

Answer 1

(a) The electric potential produced by a point charge can be found from the formula:

$$V=k\dfrac{Q}{r},$$

here, $k$ is the Coulomb's constant, $Q$ is the point charge, $r$ is the distance from the point charge.

So, the total electric potential produced by two point charges at the midway is the sum of the electric potential produced by 5.00 nC charge and the electric potential produced by -3.00 nC charge:

$$V=V_1+V_2=k\dfrac{Q_1}{r}+k\dfrac{Q_2}{r}=\dfrac{k}{r}(Q_1+Q_2),$$ $$V=\dfrac{8.99\cdot10^9\ N \dfrac{m^2}{C^2}}{0.175\ m}(5\cdot10^{-9}\ C+(-3\cdot10^{-9}\ C))=103\ V.$$

(b) We can find the potential energy of the pair of charges from the formula:

$$PE=\dfrac{kQ_1Q_2}{r},$$ $$PE=\dfrac{8.99\cdot10^9\ N \dfrac{m^2}{C^2}\cdot 5\cdot10^{-9}\ C\cdot (-3\cdot10^{-9}\ C)}{0.35\ m}=-3.85\cdot10^{-7}\ J.$$

Answer:

(a) $V=103\ V.$

(b) $PE=-3.85\cdot10^{-7}\ J.$