Question

Two point charges -q and +q are located at points (0,0, -a) and (0,0,a) respectivley. What is the electric potential at point (0,0, z)? (z > a)

• A. $\frac{qa}{4\pi {ϵ}_0{z}^2}$
• B. $\frac{q}{4\pi {ϵ}_{0}a}$
• C. $\frac{2qa}{4\pi {ϵ}_0(z^2-a^2)}$
• D. $\frac{2qa}{4\pi {ϵ}_0(z^2+a^2)}$

Answer 1

The correct option is C $\frac{2qa}{4\pi {ϵ}_0(z^2-a^2)}$

Refer to Fig. 20.29. The distance of point $P_1$ from charge + q is $r_1=z-a$ and from charge -q is $r_2=z+a$

$\therefore$ Potential at $P_1=\frac{1}{4\pi {ϵ}_0}(\frac{q}{r_1}-\frac{q}{r_2})$
$=\frac{q}{4\pi {ϵ}_0}.\frac{r_2-r_1}{r_1{r}_2}=\frac{2qa}{4\pi {ϵ}_0(z^2-a^2)}$
Which is choice (c).