∙∙Three point charges are arranged along the x axis. Charge q1=-4.50 nC is located at x=0.200 m,

step 1 Problem number 65, in this problem it is given that there are three charges on the x -axis. The

∙∙Three point charges are arranged along the x axis. Charge...

$\bullet$$\bullet$ Three point charges are arranged along the $x$ axis. Charge $q_{1}=-4.50 \mathrm{nC}$ is located at $x=0.200 \mathrm{m},$ and charge $q_{2}=+2.50 \mathrm{nC}$ is at $x=-0.300 \mathrm{m} .$ A positive point charge $q_{3}$ is located at the origin. (a) What must the value of $q_{3}$ be for the net force on this point charge to have magnitude 4.00$\mu \mathrm{N} ?$ (b) What is the direction of the net force on $q_{3} ?$ (c) Where along the $x$ axis can $q_{3}$ be placed and the net force on it be zero, other than the trivial answers of $x=+\infty$ and $x=-\infty$ ?

$\bullet$$\bullet$ Three point charges are arranged along the $x$ axis. Charge
$q_{1}=-4.50 \mathrm{nC}$ is located at $x=0.200 \mathrm{m},$ and charge
$q_{2}=+2.50 \mathrm{nC}$ is at $x=-0.300 \mathrm{m} .$ A positive point charge $q_{3}$
is located at the origin. (a) What must the value of $q_{3}$ be for the
net force on this point charge to have magnitude 4.00$\mu \mathrm{N} ?$
(b) What is the direction of the net force on $q_{3} ?$ (c) Where
along the $x$ axis can $q_{3}$ be placed and the net force on it be
zero, other than the trivial answers of $x=+\infty$ and $x=-\infty$ ?

Key Concepts

Charge Sign and Interaction

The interaction between charges depends on their signs: like charges repel while opposite charges attract. Understanding this principle is essential in determining the direction of each force when using Coulomb's Law and the Superposition Principle, as the sign of each charge influences whether the force will be attractive or repulsive.

Vector Nature of Electric Forces

Electric forces are vector quantities, meaning they have both magnitude and direction. When solving problems involving multiple charges, it is crucial to consider the direction in which each force acts and use vector addition to determine the overall net force on a charge.

Superposition Principle

The Superposition Principle states that when multiple charges exert forces on a given charge, the net force is the vector sum of the individual forces produced by each of the other charges. This concept allows for the separate calculation of forces which can then be combined to understand the overall effect in a multi-charge system.

Coulomb's Law

Coulomb's Law establishes that the electric force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental for calculating the magnitude and direction of forces in systems involving multiple point charges.

Equilibrium Conditions

The condition for equilibrium in electrostatics occurs when the net force acting on a charge is zero. Achieving equilibrium involves ensuring that the sum of forces from surrounding charges cancels out, which may require analyzing the contributions of both magnitude and direction of each individual force.

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