Two charges are placed on the x -axis: one, of 2.50 μC, at the origin and the other, of -3.50 μC

Two charges are placed on the x -axis: one, of 2.50 μC, at...

Two charges are placed on the $x$ -axis: one, of $2.50 \mu \mathrm{C}$, at the origin and the other, of $-3.50 \mu \mathrm{C},$ at $x=0.600 \mathrm{~m}$ (Fig. $\mathrm{P} 21.58$ ). Find the position on the $x$ -axis where the net force on a small charge $+q$ would be zero.

Key Concepts

Coulomb's Law

Coulomb's Law describes the electric force between two point charges. It states that the magnitude of the force is directly proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance between them. This law provides the mathematical foundation to calculate forces when charges are placed in space.

Superposition Principle

The superposition principle in electrostatics states that the net force acting on a charge is the vector sum of the individual forces exerted by each of the other charges. This means that when multiple charges are present, each exerts its own force independently, and these forces can be added together to find the total force acting on any given charge.

Equilibrium in Electrostatics

Equilibrium in electrostatics exists at a point where the net force on a charge is zero. At this point, the individual forces from surrounding charges cancel each other out completely. Finding such a point often involves setting the magnitudes of the forces from the different charges equal and solving for the position, taking into account the distances and the nature (attractive or repulsive) of the interactions.

Effects of Charge Sign

The sign of a charge determines whether the interaction between two charges is attractive or repulsive. Like charges repel and opposite charges attract. Understanding the influence of charge sign is crucial when determining the direction of forces acting on a test charge and consequently finding the point of equilibrium.