A point charge q1=+5.0 μC is fixed in place at x=0 and a point charge q2=-3.0 μC is fixed at x=-

step 1 Let's write down the given data. Q1 is equal to 5 micropoleum. Q2 is equal to minus 3 micropoleu

A point charge q1=+5.0 μC is fixed in place at x=0 and a...

A point charge $q_{1}=+5.0 \mu \mathrm{C}$ is fixed in place at $x=0$ and a point charge $q_{2}=-3.0 \mu \mathrm{C}$ is fixed at $x=-20.0 \mathrm{cm}$ Where can we place a point charge $q_{3}=-8.0 \mu \mathrm{C}$ so that the net electric force on $q_{1}$ due to $q_{2}$ and $q_{3}$ is zero?

Key Concepts

Algebraic Analysis for Equilibrium Position

Determining the position where the net force on a charge is zero involves setting up an equality where the magnitudes of the contributing forces, as calculated by Coulomb's Law, are balanced. This often leads to solving an algebraic equation that relates distance and charge values, ensuring that all vector components of the forces cancel each other.

Direction of Electric Forces

The direction of the electric force depends on the sign of the interacting charges. Like charges repel while opposite charges attract. Understanding how charge signs influence force directions is crucial in setting up the correct equations for the net force, ensuring that vector directions are properly accounted for.

Coulomb's Law

Coulomb's Law is the fundamental principle that describes the electric 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 essential for calculating the forces between charges in any electrostatic problem.

Superposition Principle

The superposition principle in electrostatics asserts that the net force on any charge is the vector sum of the forces exerted by all other individual charges. This means that when multiple charges are present, one must calculate each force separately using Coulomb’s Law, and then add them together, component by component, to find the overall force on a charge.

Electrostatic Equilibrium

Electrostatic equilibrium occurs when a charged particle experiences zero net force due to the cancellation of forces from surrounding charges. In solving for equilibrium, one sets the sum of all the individual electric forces acting on the charge to zero and solves for the unknown variables, typically involving distances between charges.

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