Three identical charges each of 2 μc are placed at the vertices of a triangle A B C as shown in

step 1 Given three identical charges each of two microculum are placed at the vertices of equilator tri

Three identical charges each of 2 μc are placed at the...

Three identical charges each of $2 \mu \mathrm{c}$ are placed at the vertices of a triangle $A B C$ as shown in the figure. If $\mathrm{AB}+\mathrm{AC}=12 \mathrm{~cm}$ and $\mathrm{AB} \cdot \mathrm{AC}=32 \mathrm{~cm}^{2}$, the potential energy of the charge at $\mathrm{A}$ is $\ldots \ldots$ (A) $1.53 \mathrm{~J}$ (B) $5.31 \mathrm{~J}$ (C) $1.35 \mathrm{~J}$ (D) $3.15 \mathrm{~J}$

Three identical charges each of $2 \mu \mathrm{c}$ are placed at the vertices of a triangle $A B C$ as shown in the figure. If $\mathrm{AB}+\mathrm{AC}=12 \mathrm{~cm}$ and $\mathrm{AB} \cdot \mathrm{AC}=32 \mathrm{~cm}^{2}$, the potential energy
of the charge at $\mathrm{A}$ is $\ldots \ldots$
(A) $1.53 \mathrm{~J}$
(B) $5.31 \mathrm{~J}$
(C) $1.35 \mathrm{~J}$
(D) $3.15 \mathrm{~J}$

Key Concepts

Algebraic Relationships in Geometric Configurations

Algebraic relationships, such as the sum and product of distances (or other geometric quantities), are often used to simplify expressions in physics problems. By knowing the sum and product of two distances, one can calculate expressions involving their reciprocals or reconstruct the individual distances if needed, streamlining the solution process in problems involving geometric constraints.

Superposition Principle in Electrostatics

The superposition principle in electrostatics states that the total potential energy or force on a charge due to other charges is the sum of the individual contributions from each charge independently. This principle allows for the analysis of complex systems by breaking them down into simpler interactions between pairs of charges.

Coulomb's Law

Coulomb's Law describes the force (and, by extension, the potential energy) between two point charges. It states that the interaction between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. In the context of potential energy, the energy associated with two point charges is given by kq1q2/r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the separation distance.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored in a system of charges due to their positions relative to each other. In a system with multiple charges, the total potential energy is determined by summing the pairwise energies between all distinct pairs. This concept is essential for understanding how energy is distributed in systems of interacting charges.

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