Three charges Q,+q and +q are placed at the vertices of an...

Three charges $\mathrm{Q},+\mathrm{q}$ and $+\mathrm{q}$ are placed at the vertices of an equilateral triangle of side $\ell$ as shown in the figure. It the net electrostatic energy of the system is zero, then $Q$ is equal
(A) $-\mathrm{q}$
(B) $+q$
(C) Zero
(D) $-(q / 2)$

Key Concepts

Coulomb's Law

Coulomb's Law describes the force and potential energy between two point charges. It tells us that the magnitude of the force (and by extension the potential energy) between charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them, establishing the foundation for understanding interactions in electrostatics.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored in a system of charges due to their positions relative to one another. It is calculated by summing the pairwise potential energies, where the interaction between any two point charges is given by a constant multiplied by the product of the charges divided by the distance between them.

Pairwise Interaction

In systems with multiple charges, the total electrostatic energy is determined by considering the energy contributions from each unique pair of charges. This pairwise approach simplifies the process by allowing us to calculate the interaction for each pair independently and then sum these contributions to obtain the overall energy of the system.

Superposition Principle in Electrostatics

The superposition principle in electrostatics states that the net potential or energy in a system of charges is the algebraic sum of the potentials or energies due to individual pairs or sources. This principle enables the analysis of complex systems by breaking them down into simpler, more manageable interactions.

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