Three point charges lie in a straight line along the y...

Three point charges lie in a straight line along the $y$ -axis. A charge of $q_{l}=-9.0 \mu \mathrm{C}$ is at $y=6.0 \mathrm{m}$ and a charge of $q_{2}=-8.0 \mu \mathrm{C}$ is at $y=-4.0 \mathrm{m} .$ The net electric force on the third point charge is zero. Where is this charge located? (See Sample Problem 17C.)

Key Concepts

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges as being 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 in electromagnetism serves as the basis for calculating forces in systems involving multiple charges.

Superposition Principle

The Superposition Principle states that the net electric force acting on a charge is the vector sum of all individual forces exerted by other charges. This principle allows for complex charge configurations to be analyzed by considering the contribution of each pairwise interaction independently and then summing them.

Equilibrium in Electric Fields

Equilibrium in the context of electric fields refers to a situation where the net force acting on a charge is zero, meaning that all the individual forces cancel each other out. This concept is crucial for understanding stable configurations in electrostatics and for determining positions where a charge can remain at rest in the presence of other charges.

Distance Dependence of Electric Forces

Since the electric force varies inversely with the square of the distance between charges, even small changes in separation can lead to significant changes in the force magnitude. This distance dependence is a key consideration when analyzing interactions in multi-charge systems, as it affects how forces balance in order to achieve equilibrium.

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