Two point charges are located on the x axis. The first is a...

Two point charges are located on the $x$ axis. The first is a charge $+Q$ at $x=-a$ . The second is an unknown charge located at $x=+3 a$ . The net electric field these charges produce at the origin has a magnitude of 2$k_{e} Q / a^{2}$ . What are the two possible values of the unknown charge?

Key Concepts

Directional Analysis of Electric Fields

Electric fields are vector quantities, meaning they have both magnitude and direction. Determining the correct direction of each field component requires careful analysis of the sign of the charges and their positions in space. This aspect is crucial when calculating the net electric field in a system where contributions from multiple sources may add or cancel depending on their directions.

Coulomb's Law

Coulomb's Law describes the force between two point charges, stating that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This fundamental law is the basis for calculating electric fields produced by point charges.

Electric Field from a Point Charge

The electric field from a point charge is a vector field that represents the force per unit charge experienced by a test charge placed in the field. It is calculated using Coulomb's Law and depends on both the magnitude of the source charge and the distance from the charge, decreasing as the square of the distance increases.

Superposition Principle

The superposition principle states that the net electric field created by a collection of charges is equal to the vector sum of the electric fields produced by each individual charge. This concept is essential when analyzing systems with multiple charges, as it allows the individual effects of each charge to be combined.

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