A +8.75-point charge is glued down on a horizontal...

A $+$8.75-$\mu$C point charge is glued down on a horizontal frictionless table. It is tied to a -6.50-$\mu$C point charge by a light, nonconducting 2.50-cm wire. A uniform electric field of magnitude 1.85 $\times 10^8$ N$/$C is directed parallel to the wire, as shown in $\textbf{Fig. E21.34.}$ (a) Find the tension in the wire. (b) What would the tension be if both charges were negative?

Key Concepts

Vector Addition of Forces

When forces act in different directions, they must be combined using vector addition. This process involves breaking each force into components and summing the components along each axis. It is pivotal in determining the net force acting on an object when the forces do not align along a single direction.

Equilibrium of Forces

The principle of equilibrium of forces involves the condition where the net force acting on an object is zero, leading to no acceleration. In problems involving multiple forces—such as those due to electric fields and inter-charge interactions—this concept allows one to set up equations balancing these forces to solve for unknowns like tension.

Tension Force

Tension is the force transmitted through a string, rope, or wire when it is pulled tight by forces acting from opposite ends. In the context of electrostatic problems, tension acts as a reactive force that balances the net force on a charged particle tied to a wire, ensuring that the system remains in equilibrium.

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges. It states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is essential in determining the interaction between charged objects in electrostatics.

Electric Field

An electric field represents the force per unit charge exerted on any charges placed in the field. A uniform electric field has the same magnitude and direction at every point in space, making it useful for analyzing how charged particles experience consistent forces.

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