Question 835: Electrostats & Capacitance

Question

Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ' $Q$ ', the electrostatic potential energy of the system is zero?

Accepted Answer

Potential energy $U=\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{a}$
$	herefore \quad$ Potential energy at $A$ due to $B=\frac{\mathrm{q}^2}{4 \pi \varepsilon_0 \mathrm{a}}$
Potential energy at $B$ due to $C=\frac{Q q}{4 \pi \varepsilon_0 a}$
Potential energy at C due to $\mathrm{A}=\frac{\mathrm{Qq}}{4 \pi \varepsilon_0 \mathrm{a}}$
$$\begin{array}{ll}
	herefore & 	ext { Total P.E }=\frac{q}{4 \pi \varepsilon_0 a}(q+Q+Q)=0 \
	herefore & 2 Q+q=0 \quad \Rightarrow Q=-\frac{q}{2}
\end{array}$$

Answer

$-q$

Answer

$\frac{\mathrm{q}}{2}$

Answer

$-2 q$

Answer

$-\frac{\mathrm{q}}{2}$

Electrostats & Capacitance

Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ' Q ', the electrostatic potential energy of the system is zero?

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