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
 Explain when the vector notation of Coulomb's Law can be used
Express Coulomb's Law using vectors
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+.  The vector notation of Coulomb's Law can be used in the simple example of two point charges where only one of which is a source of charge.
 Coulomb's Law can be further simplified and applied to a fixed number of charge points.
 Coulomb's Law applied to more than one point source charges providing forces on a field charge.
 The total force on the field charge q is due to applications of the force described in the vector notation of Coulomb's Law from each of the source charges.
 coulomb's law (noun) the mathematical equation calculating the electrostatic force vector between two charged particles
 Explain when the vector notation of Coulomb's Law can be used
Express Coulomb's Law using vectors
Coulomb's Law, which calculates the electric force between charged particles, can be written in vector notation as

Gauss's Law
 Provide word formulation of the Gauss's law Describe relationship between the Gauss's law and the Coulomb's law Gauss's law is a law relating the distribution of electric charge to the resulting electric field.
 Gauss's law can be used to derive Coulomb's law, and vice versa.
 Carl Friedrich Gauss (1777–1855), painted by Christian Albrecht Jensen 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.

Superposition of Forces
 Apply the superposition principle to determine the net response caused by two or more stimuli Express the scalar form of Coulomb's Law in an equation form The superposition principle (superposition property) states that for all linear forces the total force is a vector sum of individual forces.
 The superposition of forces is not limited to Coulomb forces.
 For Coulomb's law, the stimuli are forces.
 The scalar form of Coulomb's Law relates the magnitude and sign of the electrostatic force F, acting simultaneously on two point charges q_{1} and q_{2}:
$\boldsymbol{F}= \frac{1}{4\pi ar\epsilon_0}\frac{q_1q_2}{r^2}$ , where r is the separation distance and ε_{0} is electric permittivity.  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.

Spherical Distribution of Charge
 Express Coulomb’s law in a form of the mathematical formula Describe shape of a Coulomb force from a spherical distribution of charge The charge distribution around a molecule is spherical in nature, and creates a sort of electrostatic "cloud" around the molecule.
 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.
 Modern experiments have verified Coulomb's law to great precision.
 Coulomb's law holds even within the atoms, correctly describing the force between the positively charged nucleus and each of the negatively charged electrons.
 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.

Properties of Electric Charges
 Charge is measured in Coulombs (C), which represent 6.242×10^{18} e, where e is the charge of a proton.
 Its SI unit is known as the Coulomb (C), which represents 6.242×10^{18}e, where e is the charge of a proton.
 This is known as Coulomb's Law.
 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.
 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.
 coulomb (noun) In the International System of Units, the derived unit of electric charge; the amount of electric charge carried by a current of 1 ampere flowing for 1 second. Symbol: C

Electric Field from a Point Charge
 Identify law that can be used to calculate an electric field created by a point charge Describe relationship between the sign of the charge and the direction of the field lines 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.
 coulomb's law (proper noun) the mathematical equation calculating the electrostatic force vector between two charged particles

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.
 coulomb's law (noun) the mathematical equation calculating the electrostatic force vector between two charged particles

B.2 Chapter 2
 Derive Coulomb's law from Maxwell's Equations
The first of Maxwell's equations is
$\displaystyle \nabla \cdot {\vec E} = 4 \pi \rho$ Let's assume that there is a single charge q located at r=0 and integrate over a spherical region centered on the origin we get$\displaystyle \int_V dV \nabla \cdot {\vec E} = \int dV 4 \pi \rho = 4 \pi q$ However the integral of the lefthand side is a integral of a divergence over a volume so we have$\displaystyle \int_{\partial V} dV \nabla \cdot {\vec E} = \int {\vec E} \cdot d A = {\vec E} 4 \pi R^2 = 4 \pi q$ $\displaystyle {\vec E} = \frac{q}{R^2} {\hat r}$ In certain cases the process of absorption of radiation can be treated by means of the macroscopic Maxwell equations.  Why is this called the Coulomb gauge?
 How does the expression for the scalar potential in the Coulomb gauge differ from that in the Lorenz gauge?
 Show that the RHS can be expressed as
$\displaystyle \frac{4\pi}{c} \left ( {\bf J}  {\bf J}_\text{long} \right )$ $\displaystyle {\bf J}_\text{long} = \frac{1}{4\pi} \nabla \int \frac{\nabla' \cdot {\bf J}}{{\bf x}{\bf x}'} d^3 x$ Answer: In the Coulomb gauge the scalar potential follows Coulomb's law$\displaystyle \nabla^2 \phi = 4\pi \rho.  $ That is why it is called the Coulomb gauge.
 Derive Coulomb's law from Maxwell's Equations
The first of Maxwell's equations is

Introduction to Simple Harmonic Motion
 The ith term in the sum on the right hand side,
$\mathbf{r}$ $\displaystyle\mathbf{E}(q_i) = q_i \frac{ (\mathbf{r}  \mathbf{r_i})} {\mathbf{r}  \mathbf{r_i}^3},$ (Eq. 1.0.2) 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$\theta$ .  Then Newton's second law is
$m\ddot{x} = F(x)$ .
 The ith term in the sum on the right hand side,

What is Potential Energy?
 For example, the work of an elastic force is called elastic potential energy ; work done by the gravitational force is called gravitational potential energy; and work done by the Coulomb force is called electric potential energy.
 Coulomb force (proper noun) the electrostatic force between two charges, as described by Coulomb's law