# Classical Electromagnetism

Come friends today we will know about classical electromagnetism. Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interaction between electric charges and currents using an extension of the classical Newtonian model . The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are so large that quantum mechanical effects are negligible. For short distances and low field strengths, such interactions are better described by quantum electrodynamics .

Fundamental physical aspects of classical electrodynamics are presented in several treatises, such as those by Feynman , Leighton and Sands ,  Griffiths ,  Panofsky and Phillips, and Jackson .

## History

The physical phenomena described by electromagnetism have been studied as separate fields since ancient times. For example , many advances were made in the field of optics centuries before light was understood as an electromagnetic wave . However, the theory of electromagnetism , as it is currently understood, grew out of Michael Faraday ‘s experiments suggesting the existence of an electromagnetic field and James Clerk Maxwell ‘s use of differential equations to describe it in his A Treatise on Electricity and Magnetism (1873). For a detailed historical account, see Paulie,  Whitaker,  Pace, And consult Hunt.

## Lorentz force

The electromagnetic field exerts the following force (often called the Lorentz force) on charged particles:

\mathbf{F} = q\mathbf{E} + q\mathbf{v} \times \mathbf{B}


where all boldfaced quantities are vectors : F is the force that a particle with charge q experiences, E is the electric field at the location of the particle, V is the velocity of the particle, B is the magnetic field at the location of the particle.

The above equation shows that Lorentz force is the sum of two vectors. A is the cross product of velocity and magnetic field vectors . Based on the properties of the cross product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors. The second vector is in the same direction as the electric field. The sum of these two vectors is the Lorentz force.

Although the equation suggests that the electric and magnetic fields are independent, the equation can be rewritten in terms of a four-current (rather than charge) and a single electromagnetic tensor representing the combined field

(F^{\mu \nu }) \\
f_{\alpha} = F_{\alpha\beta}J^{\beta} .\!

## Electric field

The electric field E is defined such that, on a stationary charge:

\mathbf{F} = q_0 \mathbf{E}


where qo is what is known as the test charge and F is the force acting on that charge . The size of the charge doesn’t really matter, as long as it is small enough that it doesn’t affect the electric field by its mere presence. However, what is clear from this definition is that the unit of E is N/C ( Newton per Coulomb ). This unit is equal to V/m ( Volts per meter); Look down

In electrostatics, where charges are not in motion, around the distribution of point charges, the forces determined by Coulomb’s law can be summed up. The result obtained by dividing qo by is:

\mathbf{E(r)} = \frac{1}{4 \pi \varepsilon_0 } \sum_{i=1}^{n} \frac{q_i \left( \mathbf{r} - \mathbf{r}_i \right)} {\left| \mathbf{r} - \mathbf{r}_i \right|^3}

where n is the number of charges, q is the sum of charges associated with the i th charge, r is the position of the i th charge, r is the position where the electric field is being determined, and 0 is the electrical constant .

If the field is instead produced by a continuous distribution of charge, then the sum becomes an integral:

\mathbf{E(r)} = \frac{1}{ 4 \pi \varepsilon_0 } \int \frac{\rho(\mathbf{r'}) \left( \mathbf{r} - \mathbf{r'} \right)} {\left| \mathbf{r} - \mathbf{r'} \right|^3} \mathrm{d^3}\mathbf{r'}

where is the charge density and is the vector that indicates from the volume element to the point in space where e is being determined.

\rho(\mathbf{r'})\mathbf{r}-\mathbf{r'}\mathrm{d^3}\mathbf{r'}

Both of the above equations are cumbersome, especially if one wishes to determine E as a function of position. A scalar function called electric potential can help. Electric potential, also called voltage (the units for which volts are), is defined by the line integral

\varphi \mathbf{(r)} = - \int_C \mathbf{E} \cdot \mathrm{d}\mathbf{l}


where (r) is the electric potential, and C is the path on which the integration is being taken.

Unfortunately, this definition has a caveat. From Maxwell’s equations, it is clear that × E is not always zero, and therefore the scalar potential alone is insufficient to truly define the electric field. Consequently, one has to add a correction factor, which is usually done by subtracting the time derivative of the A vector potential, as described below. However, whenever the charges are quasi-static, this condition must be satisfied.

From the definition of charge, one can easily show that the electric potential of a point charge as a function of position is:

\varphi \mathbf{(r)} = \frac{1}{4 \pi \varepsilon_0 }
\sum_{i=1}^{n} \frac{q_i} {\left| \mathbf{r} - \mathbf{r}_i \right|}


where q is the charge of the point charge, r is the position at which the potential is being determined, and i is the position of each point charge. The probability of a continuous distribution of charge is:

\varphi \mathbf{(r)} = \frac{1}{4 \pi \varepsilon_0}
\int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}\, \mathrm{d^3}\mathbf{r'}


where is charge density, and volume is the distance from the element in space to the extent is being determined.

\rho(\mathbf{r'})\mathbf{r}-\mathbf{r'}\mathrm{d^3}\mathbf{r'}

The scalar will add up to the other potentials as a scalar . This makes it relatively easy to break down complex problems into simpler parts and sum up their potentials. Taking the definition of backwards , we see that the electric field has just negative gradient (the del operator of the potential). either:

\mathbf{E(r)} = -\nabla \varphi \mathbf{(r)} .

It is clear from this formula that E can be expressed in e V/m (Volts per metre).

## Electromagnetic waves

A changing electromagnetic field propagates away from its origin as a wave. These waves travel in zero at the speed of light and exist in a broad spectrum of wavelengths. Examples of dynamic fields of electromagnetic radiation (in order of increasing frequency): radio waves, microwaves, light (infrared, visible light and ultraviolet), X-rays and gamma rays. In the field of particle physics, this electromagnetic radiation is a manifestation of the electromagnetic interaction between charged particles.

## Normal area equation

As simple and satisfying as Coulomb’s equation may be, it is not entirely accurate in the context of classical electromagnetism. Problems arise because the change in charge distribution requires a non-zero time that is “felt” elsewhere (needed by special relativity).

For regions of normal charge distribution, the retarding potential can be calculated and differentiated accordingly to obtain Jefimenko’s equations.

Dim potentials can also be obtained for point charges, and the equations are known as the Leonard–Weichert potential. The possible scalar is:

{\displaystyle \varphi ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q}{\left|\mathbf {r} -\mathbf {r} _{q}(t_{\rm {ret}})\right|-{\frac {\mathbf {v} _{q}(t_{\rm {ret}})}{c}}\cdot (\mathbf {r} -\mathbf {r} _{q}(t_{\rm {ret}}))}}}

where q is the charge of the point charge and r is the position. q and q are the position and velocity of charge respectively as a function of slow time. The vector potential is the same:

{\displaystyle \mathbf {A} ={\frac {\mu _{0}}{4\pi }}{\frac {q\mathbf {v} _{q}(t_{\rm {ret}})}{\left|\mathbf {r} -\mathbf {r} _{q}(t_{\rm {ret}})\right|-{\frac {\mathbf {v} _{q}(t_{\rm {ret}})}{c}}\cdot (\mathbf {r} -\mathbf {r} _{q}(t_{\rm {ret}}))}}.}

These can then be differentiated accordingly to obtain the complete field equation for a moving point particle.

## Model

Branches of classical electromagnetism such as optics, electrical and electronic engineering contain a collection of relevant mathematical models of varying degrees of simplification and idealization to enhance the understanding of specific electrodynamics phenomena, cf.  An electrodynamics phenomenon is determined by particular fields, specific densities of electric charges and currents, and the particular transmission medium. Since there are infinite many of them, modeling requires some specific, representative(a) electric charges and currents, such as moving points such as charges and electric and magnetic dipoles, electric currents in a conductor, etc.;(b) electromagnetic fields, such as voltage, Leinard-Weichert potential, monochromatic plane waves, optical rays; Radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, gamma rays etc.;(c) transmission media, for example electronic components, antennas, electromagnetic wave guides, flat mirrors, mirrors with curved surfaces, convex lenses, concave lenses; resistors, inductors, capacitors, switches; Wires, power and optical cables, transmission lines, integrated circuits etc.;

All of which have only a few variable characteristics. It is noteworthy that the electromagnetic field is accurately represented in the analysis and design of antennas. 658017