Question 855: Electrostats & Capacitance

Question

Two charges of equal magnitude '$$q$$' are placed in air at a distance '$$2 r$$' apart and third charge '$$-2 \mathrm{q}$$' is placed at mid point. The potential energy of the system is $$\left(\varepsilon_0=\right.$$ permittivity of free space)

Accepted Answer

Potential energy of '$$n$$' point charges,
$$\mathrm{U}=\frac{1}{4 \pi \varepsilon_0} \sum_\limits{	ext {all pairs }} \frac{\mathrm{q}_{\mathrm{j}} \mathrm{q}_{\mathrm{k}}}{\mathrm{r}_{\mathrm{jk}}}$$
For 3 point charges,
$$\begin{aligned}
	herefore \quad U & =-\frac{q(2 q)}{4 \pi \varepsilon_0 r}-\frac{q(2 q)}{4 \pi \varepsilon_0 r}+\frac{q(q)}{4 \pi \varepsilon_0(2 r)} \
U & =-\frac{2 q^2}{4 \pi \varepsilon_0 r}-\frac{2 q^2}{4 \pi \varepsilon_0 r}+\frac{q^2}{4 \pi \varepsilon_0(2 r)} \
U & =-\frac{4 q^2}{8 \pi \varepsilon_0 r}-\frac{4 q^2}{8 \pi \varepsilon_0 r}+\frac{q^2}{8 \pi \varepsilon_0 r} \
U & =-\frac{7 q^2}{8 \pi \varepsilon_0 r}
\end{aligned}$$

Answer

$$-\frac{q^2}{8 \pi \varepsilon_0 r}$$

Answer

$$-\frac{3 \mathrm{q}^2}{8 \pi \varepsilon_0 \mathrm{r}}$$

Answer

$$-\frac{5 q^2}{8 \pi \varepsilon_0 r}$$

Answer

$$-\frac{7 q^2}{8 \pi \varepsilon_0 r}$$

Electrostats & Capacitance

Two charges of equal magnitude '$q' are placed in air at a distance '2 r' apart and third charge '-2 \mathrm{q}' is placed at mid point. The potential energy of the system is \left(\varepsilon_0=\right.$ permittivity of free space)

Choose the correct answer: