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

Let $P$ represent the point midway between the charges.

Let $r_1$ be the distance between $Q_1$ and $P$ .

Let $r_2$ be the distance between $Q_2$ and $P$ .

Let $V_p$ represent the potential at $P$ .

Let $k_e$ represent coulomb's constant.

Let $U$ represent the potential energy of the pair of charges.

$r_1=r_2=\frac{35cm}{2}=0.175m$

$\begin{aligned}\textsf{(a)} &V_p=k_e(\frac{Q_1}{r_1}+\frac{Q_2}{r_2})\\ &V_p=(8.99×10^9N.m²/C²)×(\frac{5.00×10^{-9}C}{0.175m}-\frac{3.00×10^{-9}C}{0.175m})\\ &V_p=102.74V \end{aligned}$

$\begin{aligned}\textsf{(b)}&U=k_e\frac{Q_1Q_2}{r_1+r_2}\\ &U=(8.99×10^9N.m²/C²)(\frac{(5.00×10^{-9})C×(-3.00×10^{-9})C}{0.175m+0.175m})\\ &U=-3.85×10^{-7}J\end{aligned}$