Question

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

Answer 1

a)

$$V=k\frac{Q_1}{0.5d}+k\frac{Q_1}{0.5d}=2k\frac{Q_1+Q_2}{d}$$

$$V=2(8.99\cdot10^{9})\frac{5\cdot10^{-9}-3\cdot10^{-9}}{0.35}=103\ V$$

b)

$$E_p=k\frac{Q_1Q_2}{d}$$

$$E_p=(8.99\cdot10^{9})\frac{(5\cdot10^{-9})(-3\cdot10^{-9})}{0.35}=-3.85\cdot10^{-7}\ J$$

Negative sign means that positive work must be done to separate the charges (bring them up to a state of zero potential energy).