Electric field Intensity (Definition) and Electric field Intensity due to point charge

Definition of Electric Field Intensity:

The force acting on the per unit test charge in electric field is called the Electric field intensity. It is represented by $'E'$.

Let us consider that a test-charged particle of $q_{0}$ Coulomb is placed at a point in the electric field and a force $F$ acting on them so the electric field intensity at that point

$ \overrightarrow{E}=\frac{\overrightarrow{F}}{q_{0}}$

SI Unit:$\quad Newton/Coulomb$ $ (N/C)$ $\quad Kg-m^{2}/sec^{3} A$

Dimension: $\left [ML^{2}T^{-3}A^{-1} \right ]$

Physical Significance of Electric Field:

The force experienced by a charge is different at different points in space. So electric field intensity also varies from point to point. In general, Electric field intensity is not a single vector quantity but it is a set of infinite vector and each point in space have a unique electric field intensity. So electric field is an example of the vector field.

Electric Field Intensity due to a Point Charge:

Let us consider that an isolated point charge of $+q$ Coulomb is placed at a point $O$ in a medium whose dielectric constant is $K$. If a test charge particle of $q_{0}$ Coulomb is placed at a point $P$ in the electric field at a distance $r$ from point $O$. So the electric field intensity (magnitude form) at point $P$
Electric field intensity due to a point charge
Electric field intensity due to a point charge
$E=\frac{F}{q_{0}}\qquad (1)$

According to Coulomb's Law:

$F=\frac{1}{4\pi \varepsilon _{0}K}\frac{qq_{0}}{r^{2}}\qquad (2)$

From equation $(1)$ and equation $(2)$, we can write

$E=\frac{1}{4\pi \varepsilon _{0}K}\frac{q}{r^{2}} \qquad (3)$

For air or vacuum $K=1$, Then from equation $(3)$

$E=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{r^{2}} \qquad (4)$

Where

$\frac{1}{4\pi \varepsilon _{0}}=9\times10^{9} N-m^{2}/C^{2}$

From equation $(4)$

$E=9\times 10^{9} \frac{q}{r^{2}}\qquad (5)$

In Vector Notation:

$\overrightarrow{E}=\frac{1}{4\pi \varepsilon _{0}K}\frac{q}{r^{2}}r\hat{}$

If a system containing $'n'$ point charge $q_{1},q_{2},q_{3},..........q_{n}$ then electric field intensity due to the system of charge particle will be equal to the vector sum of the intensities i.e.

$\overrightarrow{E}=\overrightarrow{E_{1}}+\overrightarrow{E_{2}}+\overrightarrow{E_{3}}+....+\overrightarrow{E_{n}}$

$\overrightarrow{E}=\frac{1}{4\pi \varepsilon _{0}K}\sum_{i=0}^{n}\frac{q_{i}}{r_{i}^{2}}r_{i}\hat{}$

Where $r_{i}$ is the distance from point $'P'$ to charge $q_{i}$.

Popular Posts

Study-Material













  • Classical world and Quantum world

  • Inadequacy of classical mechanics

  • Drawbacks of Old Quantum Theory

  • Bohr's Quantization Condition

  • Energy distribution spectrum of black body radiation

  • Energy distribution laws of black body radiation

  • The Compton Effect | Experiment Setup | Theory | Theoretical Expression | Limitation | Recoil Electron

  • Davisson and Germer's Experiment and Verification of the de-Broglie Relation

  • Significance of Compton's Effect

  • Assumptions of Planck’s Radiation Law

  • Derivation of Planck's Radiation Law

  • de-Broglie Concept of Matter wave

  • Definition and derivation of the phase velocity and group velocity of wave

  • Relation between group velocity and phase velocity ($V_{g}=V_{p}-\lambda \frac{dV_{p}}{d\lambda }$)

  • Group velocity is equal to particle velocity($V_{g}=v$)

  • Product of phase velocity and group velocity is equal to square of speed of light ($V_{p}.V_{g}=c^{2}$)

  • Heisenberg uncertainty principle

  • Generation of wave function for a free particle

  • Physical interpretation of the wave function

  • Derivation of time dependent Schrodinger wave equation

  • Derivation of time independent Schrodinger wave equation

  • Eigen Function, Eigen Values and Eigen Vectors

  • Postulate of wave mechanics or Quantum Mechanics

  • Quantum Mechanical Operators

  • Normalized and Orthogonal wave function

  • Particle in one dimensional box (Infinite Potential Well)

  • Minimum Energy Or Zero Point Energy of a Particle in an one dimensional potential box or Infinite Well

  • Normalization of the wave function of a particle in one dimension box or infinite potential well

  • Orthogonality of the wave functions of a particle in one dimension box or infinite potential well

  • Eigen value of the momentum of a particle in one dimension box or infinite potential well

  • Schrodinger's equation for the complex conjugate waves function

  • Probability Current Density for a free particle in Quantum Mechanics

  • Ehrenfest's Theorem and Derivation

  • Momentum wave function for a free particle

  • Wave function of a particle in free state

  • One dimensional Step Potential Barrier for a Particle

























  • Blog Archive