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

Three charges $Q,+q$, and $+q$ are placed at the vertices of a right angle triangle (isosceles triangle) as shown. The net electrostatic energy of the configuration is zero, if $Q$ is equal to
(A) $\frac{-q}{1+\sqrt{2}}$
(B) $\frac{-2 q}{2+\sqrt{2}}$
(C) $-2 q$
(D) $+q$

Key Concepts

Electrostatic Potential Energy

This concept pertains to the energy stored in a system of charges due to their positions relative to each other. It involves the work done in assembling the charges from infinity to a given configuration and depends on both the magnitude and sign of the charges as well as the distances between them.

Coulomb's Law

Coulomb's Law describes the force between two point charges and is the foundational principle used to calculate the interaction energy between pairs of charges. It states that the force or potential energy between two charges is directly proportional to the product of their charges and inversely proportional to the distance between them.

Superposition Principle

The superposition principle is used in electrostatics to determine the net potential energy of a system by adding the contributions from all individual pairwise interactions. This approach allows the analysis of complex charge configurations by breaking them down into simpler two-charge interactions.

Charge Configuration

Understanding the arrangement of multiple charges and their relative positions is crucial, as the geometry influences both the distances between charges and the overall sign and magnitude of the interaction energies. Analyzing the configuration helps determine the conditions needed for specific energy outcomes, such as a net zero electrostatic energy.

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