If 3 charges are placed at the vertices of equilateral...

If 3 charges are placed at the vertices of equilateral triangle of charge ' $q$ ' each. What is the net potential energy, if the side of equilateral triangle is $\ell \mathrm{cm}$. (A) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(3 q^{2} / \ell\right)$ (B) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(2 q^{2} / \ell\right)$ (C) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(q^{2} / \ell\right)$ (D) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(4 q^{2} / \ell\right)$

If 3 charges are placed at the vertices of equilateral triangle of charge ' $q$ ' each. What is the net potential energy, if the side of equilateral triangle is $\ell \mathrm{cm}$.
(A) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(3 q^{2} / \ell\right)$
(B) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(2 q^{2} / \ell\right)$
(C) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(q^{2} / \ell\right)$
(D) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(4 q^{2} / \ell\right)$

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Key Concepts

Superposition Principle

The superposition principle allows for the total electric potential energy of a multi-charge system to be determined by the algebraic sum of the energies from each pair. This principle is essential in electrostatics as it permits the analysis of complex systems by breaking them down into simpler, two-charge interactions.

Electric Potential Energy

Electric potential energy is the energy stored in a system of charges due to their positions relative to each other. When dealing with point charges, this energy arises from the work done to assemble the configuration by bringing each charge from infinity to its position in the presence of the other charges.

Coulomb's Law

Coulomb's law describes the force between two point charges, stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is foundational for calculating the energy associated with pairs of charges based on their separation.

Pairwise Interactions

In a system with multiple charges, the total potential energy is calculated by summing the potential energy contributed by each unique pair of charges. This approach recognizes that each pair contributes an interaction energy, and the overall energy is the aggregate of these individual interactions.

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