22.5
Coulomb's Law
Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitu…
Electrical experiments lead to a mathematical law that quantifies observations. Coulomb's law formulates the force of attraction or repulsion between two point charges.
Consider two electrically charged point masses, with charges q-1 and q-2. They experience the same magnitude of force, called the Coulomb force. It is directly proportional to the product q-1-q-2 and inversely proportional to the square of the distance between them. It acts along the imaginary line joining them.
In the SI units, the proportionality constant is approximately 8.988 times 109. For theoretical reasons, it is described via another constant, epsilon-naught, known as the permittivity of vacuum. Its value is 8.854 times 10-12 in SI.
If both the charges are positive, or both are negative, they experience equal and opposite force away from each other. If one charge is positive and the other is negative, the force is attractive and equal.
The inverse square nature of the force implies that it is effective only at small distances. Friction is an example of a Coulomb force.
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Q1: What is Coulomb's law and how does it describe the force between charged objects?
Coulomb's law quantifies the force between two point charges. The force magnitude is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them. The force acts along the line joining the charges and can be attractive or repulsive depending on charge signs.
Q2: How do the signs of electric charges affect the direction of the Coulomb force?
When both charges are positive or both negative, they experience repulsive forces pushing them apart. When one charge is positive and the other negative, the force is attractive, pulling them together. In both cases, Newton's third law applies: the forces on each charge are equal in magnitude but opposite in direction.
Q3: What is the permittivity of vacuum and why is it important in Coulomb's law?
The permittivity of vacuum, epsilon-naught, is a fundamental constant approximately 8.854 × 10⁻¹² in SI units. It appears in Coulomb's law as the proportionality constant and has significant physical meaning related to the speed of light in vacuum. This constant enables quantitative prediction of electric forces between charges.
Q4: Why is Coulomb's force described as an inverse square law?
The Coulomb force is inversely proportional to the square of the distance between charges, meaning it decreases rapidly as charges move apart. This inverse square relationship implies the force is effective only at small distances. If separation distance changes, the force magnitude changes accordingly, making direct application of Newton's laws mathematically complex.
Q5: How does the Coulomb force compare to gravitational force?
Both forces follow inverse square laws and depend on fundamental constants. However, the comparison between electrical and gravitational forces reveals key differences: gravitational force is always attractive, while Coulomb force can be attractive or repulsive. Additionally, Coulomb force does not depend on object mass, unlike gravitational force.
Q6: Does the Coulomb force depend on the mass of charged objects?
No, the Coulomb force is independent of object mass. The force depends only on the magnitudes of the charges and the distance between them. This fundamental difference distinguishes electric forces from gravitational forces, which directly depend on the masses of interacting objects.
Q7: What happens to the Coulomb force when the distance between charges changes?
The Coulomb force is not constant; it changes as the separation distance between charges changes. If either charge moves, the distance changes and the force magnitude changes accordingly. This distance-dependent behavior makes solving problems with moving charges more complex than static situations.