Three charges, each of value Q, are placed at the vertex of...

Three charges, each of value $Q$, are placed at the vertex of an equilateral triangle. A fourth charge $q$ is placed at the centre of the triangle. If the charges remains stationery then, $q=\ldots \ldots \ldots$ (A) $(\mathrm{Q} / \sqrt{2})$ (B) $-(\mathrm{Q} / \sqrt{3})$ (C) $-(Q / \sqrt{2})$ (D) $(\mathrm{Q} / \sqrt{3})$

Three charges, each of value $Q$, are placed at the vertex of an equilateral triangle. A fourth charge $q$ is placed at the centre of the triangle. If the charges remains stationery then, $q=\ldots \ldots \ldots$
(A) $(\mathrm{Q} / \sqrt{2})$
(B) $-(\mathrm{Q} / \sqrt{3})$
(C) $-(Q / \sqrt{2})$
(D) $(\mathrm{Q} / \sqrt{3})$

Key Concepts

Symmetry in Electrostatics

Symmetry in electrostatic configurations, such as equal charges arranged at the vertices of a regular shape, can greatly simplify analysis. When a system's geometry is symmetric, the forces or fields from different charges can cancel out or add in predictable ways, making it easier to apply equilibrium conditions and solve for unknowns.

Superposition Principle

The superposition principle asserts that the total electric force or field at a particular point is the vector sum of the contributions from each individual charge. This principle is essential when analyzing systems with multiple charges as it allows for the independent calculation of each charge's effect before combining them to find the overall effect.

Coulomb's Law

Coulomb's Law describes how the electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them. It provides the fundamental framework for calculating the forces acting in systems with multiple charges.

Electrostatic Equilibrium

Electrostatic equilibrium is the condition in which all charges in a system experience zero net force, meaning that the contributions from all other charges balance each other precisely. This concept is crucial for determining unknown quantities in charge configurations where the system remains stationary.

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