Question 857: Electrostats & Capacitance

Question

Three point charges $$+\mathrm{q},+2 \mathrm{q}$$ and $$+\mathrm{Q}$$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $$Q$$ in terms of $$q$$ is

Accepted Answer

Potential energy due to $$+\mathrm{q}$$ and $$+2 \mathrm{q}$$,
$$\mathrm{U}_1=\frac{\mathrm{K}_{\mathrm{q}}(2 \mathrm{q})}{\mathrm{r}}$$
$$	herefore \quad$$ Potential energy due to $$+\mathrm{q}$$ and $$+\mathrm{Q}$$,
$$\mathrm{U}_2=\frac{\mathrm{KqQ}}{\mathrm{r}}$$
$$	herefore \quad$$ Potential energy due to $$+Q$$ and $$+2 q$$,
$$\mathrm{U}_3=\frac{\mathrm{KQ}(2 \mathrm{q})}{\mathrm{r}}$$
Given: Potential energy of system $$=0$$
$$\begin{aligned}
	herefore \quad & \mathrm{U}_1+\mathrm{U}_2+\mathrm{U}_3=0 \
& \frac{\mathrm{Kq}(2 \mathrm{q})}{\mathrm{r}}+\frac{\mathrm{Kq} Q}{\mathrm{r}}+\frac{\mathrm{KQ}(2 \mathrm{q})}{\mathrm{r}}=0 \
& 2 \mathrm{q}+\mathrm{Q}+2 \mathrm{Q}=0 \
& 3 \mathrm{Q}=-2 \mathrm{q} \
& \mathrm{Q}=\frac{-2}{3} \mathrm{q}
\end{aligned}$$

Answer

$$\mathrm{Q}=-\frac{2 \mathrm{q}}{3}$$

Answer

$$Q=-\frac{1}{3} q$$

Answer

$$\mathrm{Q}=\frac{3 \mathrm{q}}{2}$$

Answer

$$Q=\frac{q}{2}$$

Electrostats & Capacitance

Three point charges $+\mathrm{q},+2 \mathrm{q} and +\mathrm{Q} are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q$ is

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