Three identical point charges q are placed at each of three...

Three identical point charges $q$ are placed at each of three corners of a square of side $L .$ Find the magnitude and direction of the net force on a point charge $-3 q$ placed $(a)$ at the center of the square and (b) at the vacant corner of the square. In each case, draw a free-body diagram showing the forces exerted on the $-3 q$ charge by each of the other three charges.

Key Concepts

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. It states that the magnitude of the force is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating the forces between individual charges, taking into account whether the charge pair is attractive or repulsive based on their signs.

Superposition Principle

The superposition principle is essential for analyzing systems with multiple charges. It states that the net force acting on a charge is the vector sum of the individual forces exerted on it by all other charges. This principle allows one to compute the contributions from each charge independently and then combine them, a process that is crucial when dealing with configurations of several charges.

Symmetry in Electric Forces

Symmetry plays a significant role in simplifying the evaluation of net forces in charge distributions. When charges are arranged symmetrically, certain components of the forces can cancel out, reducing the complexity of the analysis. For instance, in symmetric configurations like a centered charge in a square, the equal and opposite force components along the same lines can lead to a net force of zero in specific directions.

Free-body Diagrams

Free-body diagrams are graphical representations used to visualize all the forces acting on a particular object. In the context of electric forces, drawing a free-body diagram helps in identifying the magnitude and direction of each force acting on a charge due to other charges. This method aids in the correct application of vector addition, ensuring that the net force is accurately determined.

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