coulomb's law
the mathematical equation calculating the electrostatic force vector between two charged particles
Examples of coulomb's law in the following topics:

Solving Problems with Vectors and Coulomb's Law
 Coulomb's Law, which calculates the electric force between charged particles, can be written in vector notation as $F(E) = \frac{kq_1q_2}{r^2}$ r+.
 Applying Coulomb's Law three times and summing the results gives us:
 In a simple example, the vector notation of Coulomb's Law can be used when there are two point charges and only one of which is a source charge.
 Coulomb's Law applied to more than one point source charges providing forces on a field charge.
 Explain when the vector notation of Coulomb's Law can be used

Gauss's Law
 Gauss's law can be used to derive Coulomb's law, and vice versa.
 Note that since Coulomb's law only applies to stationary charges, there is no reason to expect Gauss's law to hold for moving charges based on this derivation alone.
 In fact, Gauss's law does hold for moving charges, and in this respect Gauss's law is more general than Coulomb's law.
 Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.
 In fact, any "inversesquare law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inversesquare Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inversesquare Newton's law of gravity.

Spherical Distribution of Charge
 The mathematical formula for the electrostatic force is called Coulomb's law after the French physicist Charles Coulomb (1736–1806), who performed experiments and first proposed a formula to calculate it.
 Coulomb's law holds even within the atoms, correctly describing the force between the positively charged nucleus and each of the negatively charged electrons.
 This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids.
 An electric field is a vector field which associates to each point of the space the Coulomb force that will experience a test unity charge.
 Describe shape of a Coulomb force from a spherical distribution of charge

Superposition of Forces
 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:
 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.
 Express the scalar form of Coulomb's Law in an equation form

Properties of Electric Charges
 Its SI unit is known as the Coulomb (C), which represents 6.242×1018e, where e is the charge of a proton.
 The formula for gravitational force has exactly the same form as Coulomb's Law, but relates the product of two masses (rather than the charges) and uses a different constant.
 The forces (F1 and F2) sum to produce the total force, which is calculated by Coulomb's Law and is proportional to the product of the charges q1 and q2, and inversely proportional to the square of the distance (r21) between them.

Electric Field from a Point Charge
 A point charge creates an electric field that can be calculated using Coulomb's law.
 The above mathematical description of the electric field of a point charge is known as Coulomb's law.
 Identify law that can be used to calculate an electric field created by a point charge

Stress and Strain
 A point charge creates an electric field that can be calculated using Coulomb's Law.
 The above mathematical description of the electric field of a point charge is known as Coulomb's Law.

B.2 Chapter 2
 For example, suppose we have a conducting medium so that the current density j is related to the electric field E by Ohm's law: ${\vec j} = \sigma {\vec E}$ where $\sigma$ is the conductivity (cgs unit = sec$^{1}$.
 Derive the equations describing the dynamics of the electric and vector potentials in the Coulomb gauge
 How does the expression for the scalar potential in the Coulomb gauge differ from that in the Lorenz gauge?

Introduction to Simple Harmonic Motion
 is the electric field of the ith point charge (Coulomb's law).
 The restoring force is the component of the gravitational force acting perpendicular to the wire supporting the mass.This is $mgsin(\theta)$ .Assuming the wire support is rigid, the acceleration of the mass is in the $\theta$ direction, so $ma=m\ell\ddot\theta$ and we have from Newton's second law: $\ddot{\theta} + \frac{g}{\ell} \sin(\theta) = 0$ .This is a nonlinear equation except for small $\theta$ , in which case $\theta$ .

The Junction Rule
 Kirchhoff's junction rule, also known as Kirchhoff's current law (KCL), Kirchoff's first law, Kirchhoff's point rule, and Kirchhoff's nodal rule, is an application of the principle of conservation of electric charge.
 This law is founded on the conservation of charge (measured in coulombs), which is the product of current (amperes) and time (seconds).
 Practically, this is always true so long as the law is applied for a specific point.
 This flow would be a current, thus violating Kirchhoff's junction law.
 Kirchhoff's Junction Law illustrated as currents flowing into and out of a junction.