Module 4 Coulomb’s Law

Superposition of Forces

The superposition principle (superposition property) states that for all linear forces the total force is a vector sum of individual forces.

Learning Objectives

Apply the superposition principle to determine the net response caused by two or more stimuli

Key Takeaways

Key Points

  • The superposition principle suggests that the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.
  • Total Coulomb force on a test charge due to a group of charges is equal to the vector sum of all the Coulomb forces between the test charge and other individual charges.
  • The superposition of forces is not limited to Coulomb forces. It applies to any types (or combinations) of forces.

Key Terms

  • Lorentz force: The force exerted on a charged particle in an electromagnetic field.
  • unit vector: A vector with length 1.
  • electrostatic force: The electrostatic interaction between electrically charged particles; the amount and direction of attraction or repulsion between two charged bodies.

The superposition principle (also known as superposition property) states that: for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. For Coulomb’s law, the stimuli are forces. Therefore, the principle suggests that total force is a vector sum of individual forces.

Coulomb Force

The scalar form of Coulomb’s Law relates the magnitude and sign of the electrostatic force F, acting simultaneously on two point charges q1 and q2:

[latex]|\boldsymbol{\text{F}}|= \frac{1}{4\pi ar\epsilon_0}\frac{|\text{q}_1\text{q}_2|}{\text{r}^2}[/latex],

image

Lorentz Force on a Moving Particle: Lorentz force f on a charged particle (of charge q) in motion (instantaneous velocity v). The E field and B field vary in space and time.

where r is the separation distance and ε0 is electric permittivity. If the product q1q2 is positive, the force between them is repulsive; if q1q2 is negative, the force between them is attractive. The principle of linear superposition allows the extension of Coulomb’s law to include any number of point charges—in order to derive the force on any one point charge by a vector addition of these individual forces acting alone on that point charge. The resulting force vector happens to be parallel to the electric field vector at that point, with that point charge removed.