Understanding Forces Between Stationary Point Charges

The question asks to identify the law that provides the mathematical expression for the force experienced between two stationary point charges when they are placed in a vacuum or free space. This topic falls under the domain of electrostatics, which studies electric charges at rest.

Analyzing the Options for Electrostatic Force

Let's examine each option provided:

• Lenz’s Law: This law relates to electromagnetic induction. It states that the direction of the induced electromotive force (EMF) and hence the induced current is such that it opposes the change in magnetic flux that produces it. This law is relevant for changing magnetic fields and induced currents, not for the force between stationary charges.
• Coulomb’s Law: This fundamental law describes the electrostatic interaction between two point charges. It specifically gives the expression for the magnitude and direction of the force between two stationary point charges. The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• Gauss' Law: Gauss's Law is another important law in electrostatics. It relates the electric flux through a closed surface to the net electric charge enclosed within that surface. While Gauss's Law is derived from Coulomb's Law and is useful for calculating electric fields (and subsequently forces) for symmetrical charge distributions, it does not directly provide the fundamental expression for the force between any two arbitrary point charges in the way Coulomb's Law does.
• Ohm’s Law: This law applies to electric circuits and relates the voltage (\(V\)) across a conductor to the current (\(I\)) flowing through it and the resistance (\(R\)). It is given by the formula \(V = IR\). This law is about the flow of charge (current) in a conductor and is not related to the force between stationary charges.

Coulomb's Law: The Law for Electrostatic Force

Based on the analysis, Coulomb's Law is the law that precisely describes the force between two stationary point charges. The mathematical expression for the magnitude of the electrostatic force (\(F\)) between two point charges, \(q_1\) and \(q_2\), separated by a distance \(r\) in vacuum or free space is given by:

\(F = k \frac{|q_1 q_2|}{r^2}\)

Here, \(k\) is Coulomb's constant, which is approximately \(8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2\). In vacuum, \(k\) is often expressed in terms of the permittivity of free space, \(\epsilon_0\), as \(k = \frac{1}{4\pi\epsilon_0}\).

The force is attractive if the charges have opposite signs and repulsive if they have the same sign. This force acts along the line joining the two charges.

Conclusion on the Law for Stationary Charges

The law that provides the expression for the force between two stationary point charges in vacuum or free space is Coulomb's Law.

Revision Table: Laws in Physics

Additional Information on Coulomb's Law and Electrostatics

Coulomb's Law is a fundamental principle in electrostatics. Key aspects include:

• Inverse Square Law: The force is inversely proportional to the square of the distance between the charges, similar to Newton's Law of Universal Gravitation.
• Permittivity of Free Space (\(\epsilon_0\)): This constant represents the ability of a vacuum to permit electric fields. Its value is approximately \(8.854 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2\). The force expression in vacuum is often written as \(F = \frac{1}{4\pi\epsilon_0} \frac{|q_1 q_2|}{r^2}\).
• Medium Dependence: If the charges are placed in a medium other than vacuum, the force between them is reduced. The force in a medium is given by \(F_{\text{medium}} = \frac{1}{4\pi\epsilon} \frac{|q_1 q_2|}{r^2}\), where \(\epsilon\) is the permittivity of the medium (\(\epsilon = \epsilon_r \epsilon_0\), with \(\epsilon_r\) being the relative permittivity or dielectric constant of the medium).
• Vector Form: Coulomb's Law can also be expressed in vector form to show the direction of the force. The force on charge \(q_2\) due to \(q_1\) is \(\vec{F}_{12} = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \hat{r}_{12}\), where \(\hat{r}_{12}\) is the unit vector pointing from \(q_1\) to \(q_2\).

Understanding Coulomb's Law is crucial for studying electric fields, electric potential, and the behavior of charges in various configurations.