## What is an electric field?

A physical field present around an electrically charged particle that exerts a force on all other charged particles is called an electric field. The charged particles present in the field either repel or attract. From electric charges or time-varying magnetic fields, the electric field originates. One of the manifestations of electromagnetic force which is one of the four fundamental forces present in nature are the electric fields and magnetic fields.

Electric fields are exploited practically in electrical technology and are important in many areas of physics. The electric field is the force in the case of atomic physics and chemistry where the electric field is the force that holds the nucleus of atom and electrons together. The chemical bonding between atoms is also due to the electric field force that results in molecules.

The total electric field is defined as the force per unit source charge in Coulomb which is exerted on an infinitesimal positive test charge at rest at that point. The SI unit of the electric field is volt/m (V/m) which is exactly equivalent to newton per coulomb (N/C). The electric charge density is defined as the electric charge per unit area of surface or unit volume of a field or body. Separated by regions containing no charge the charge distribution consists of individual charged particles.

## Description of an electric field

If a source charge is held at a point then the force experienced by that vanishingly small positive test charge is defined as an electric field at each point in space. Force is a vector quantity that has both magnitude and direction, so we can say that the electric field is also a vector field. These types of vector fields are also called electric force fields. Similar to the way the gravitational field acts between two masses, the electric force field acts between two electric charge particles as they both obey an inverse square law with distance. Therefore according to Coulomb's law for the stationary electric charges, the electric field varies directly with the agnitude of source charge and varies inversely as the square of the distance. It means that if the source charge is doubled then the electric field will also get doubled and if we move far away as twice from the source field then the electric field at that point would be one fourth of its original electric field strength.

According to the concept of Faraday, the electric field can be visualized with a set of lines whose direction at each point is the same as the electric field's direction. The electric field strength depends on the density of these electric field lines. The term lines of force are used very often. The electric field strength is proportional to the density of lines and this is the useful property according to this illustration. Similar to the trajectories that masses follow with the gravitational field, the field lines are the paths that a point positive charge would follow as within the field it is forced to move. Several important properties are for field lines due to stationary charges which include that a field line always starts from a positive charge and terminates on a negative charge.

A positive charge is written with a positive sign-magnitude and a negative charge is written with a negative sign-magnitude. The electric field vector lines always enter good conductors at right angles and they never cross each other. The relationship between a time-varying magnetic field and an electric field is described by Faraday's law. The negative time derivative of the magnetic field is equal to the curl of the electric field according to one way of Faraday's law. The electric field is called conservative in the absence of the time-varying magnetic field. Therefore there are two kinds of electric field, one is an electrostatic force field and the other is a field arising from the time-varying magnetic field. Time-varying fields are usually treated as a component of a unified electromagnetic field so the curl-free nature of the static electric field allows for a simpler treatment.

## Mathematical formulation

According to Gauss's law the divergence of total electric field flux which comes out of a surface which is closed is equal to the charge enclosed in that region divided by the permittivity that is, $\nabla .E=\frac{\rho}{{\epsilon}_{o}}$

where

E = Electric field,

$\rho $= charge enclosed

and ${\epsilon}_{o}$ = permittivity of free space

And according to Faraday's law the curl of electric field is zero that is, $\nabla \times E=0$

Where E = Electric field and if these two are taken together then we get Coulomb's law that states that a particle with electric point charge ${q}_{1}$ at position ${x}_{1}$ exerts a force on a point charge ${q}_{o}$ which is at position ${x}_{o}$ of :

$F=\frac{1}{4\pi {\epsilon}_{o}}\frac{{q}_{1}{q}_{o}}{{({x}_{1}-{x}_{o})}^{2}}{\hat{r}}_{1,0}$

where F = Force, ${\hat{r}}_{1,0}$is the unit vector in the direction from point ${x}_{1}$ to ${x}_{o}$ and ${\epsilon}_{o}$ = electric constant.

The electric field is termed as force per unit charge which is as follows:

$E\left({x}_{o}\right)=\frac{F}{{q}_{o}}=\frac{1}{4\pi {\epsilon}_{o}}\frac{{q}_{1}}{{({x}_{1}-{x}_{2})}^{2}}{\hat{r}}_{1,0}$

## Electric potential

Electric potential E stands for the total amount of work done in moving a charged particle from one place to another in an electric field. If the system is static and the magnetic field is not time-varying then electric field is curl-free by Faraday's law. Therefore electric potential can be defined as a function of ϕ such that:

$E=-\nabla \varphi $

It is the same as the gravitational field. The potential difference is the difference between the electric potential at two points in space. An equipotential surface is the kind of surface where the locus of all points is at the same potential.

## Energy in the electric field

The total energy per unit volume stored by the electromagnetic field is given as :

${u}_{EM}=\frac{\epsilon}{2}|E{|}^{2}+\frac{1}{2\mu}|B{|}^{2}$

where ε=permittivity of the medium, μ = magnetic permeability and E and B are the respective electric and magnetic field vectors. It would be misleading if we split this expression into "magnetic" and "electric" because E and B fields are coupled. The electrostatic field in any given frame of reference can be transformed into a field with a magnetic component that has a relatively moving frame. The total energy stored in the electromagnetic field in volume V is given by the following equation:

${U}_{EM}=\frac{1}{2}{\int}_{V}\left(\epsilon \right|E{|}^{2}+\frac{1}{\mu}\left|B{|}^{2}\right)dV$

## Context and Applications

This topic is significant in the following courses;

- Bachelors of Science in Electrical Engineering
- Masters of Science in Electrical Engineering

## Practice Problems

**Q1. **What is the SI unit of electric field?

- Newton per coulomb
- Newton per meter
- Coulomb per meter
- None of these

**Answer**- a

**Explanation: **The SI unit of electric field is volt/m (V/m) which is exactly equivalent to newton per coulomb (N/C).

**Q2.** What among the following electric field has in it?

- Magnitude
- Direction
- Both a and b
- None of the above

**Answer:** c

**Explanation: **Electric field is a vector quantity which has both magnitude and direction.

**Q3**. How does an electric field vary with point charge?

- Directly
- Inversely
- Does not depend on point charge
- None of the above

**Answer**- a

**Explanation:** According to Coulomb's law, the electric field varies directly with the point charge.

**Q4. **How does an electric field varies with distance?

- Directly
- Inversely
- Inversely to the square of it
- None of the above

**Answer**- c

**Explanation: **The electric field varies inversely to the square of distance in accordance with the Coulomb's law.

**Q5. **What is direction of an electric field in an electric dipole?

- From positive to negative charge
- From negative to positive charge
- Both a and b
- None of the above

**Answer**- a

**Explanation:** The electric field always arises from a positive charge and terminates into a negative charge.

## Related conceptS

- Classical electromagnetism
- Electricity
- Magnetism
- Optical field

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