Question 775: Electrostats & Capacitance

Question

Three charges each of magnitude $3 \mu \mathrm{C}$, are placed on the vertices of an equilateral triangle of side 6 cm . The net potential energy of the system will be  nearly $\left[\frac{1}{4 \pi \epsilon_0}=9 	imes 10^9ight.$ SI unit $]$

Accepted Answer

Given: $l=6 \mathrm{~cm}=6 	imes 10^{-2} \mathrm{~m}, \mathrm{q}=3 \mu \mathrm{C}$
Potential energy of any 2 given charges will be
$$ \mathrm{U}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}_1 \mathrm{q}_2}{\mathrm{r}}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}^2}{\mathrm{r}} $$
$	herefore \quad$ Net potential energy of the system will be
$$ \begin{aligned} \mathrm{U}_{	ext {net }}=3 	imes \frac{1}{4 \pi \varepsilon_0} \frac{\left(3 	imes 10^{-6}ight)^2}{6 	imes 10^{-2}} & =3 	imes 9 	imes 10^9 	imes \frac{9 	imes 10^{-12}}{6 	imes 10^{-2}} \ & =4.05 \mathrm{~J} \approx 4.1 \mathrm{~J} \end{aligned} $$

Answer

1.4 J

Answer

2.7 J

Answer

4.1 J

Answer

8.2 J

Electrostats & Capacitance

Three charges each of magnitude 3 \mu \mathrm{C}, are placed on the vertices of an equilateral triangle of side 6 cm . The net potential energy of the system will be nearly \left[\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\right. SI unit ]

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