Electric field | Electromagnetics

Electric field

Electric field

The space around a charged particle in which another charge experience a force.

Here red circles shows the electric field. In this figure q is source charge and q₀ is test charge.
The source of electric field is either a charge or a time varying magnetic field.
If electric field (E) does not change with time, then it is said to be uniform electric field, otherwise it is non-uniform electric field.

Electric field intensity

The electrostatic force per unit test charge is electric field intensity.

$https://latex.codecogs.com/svg.image?\overrightarrow{E}=\frac{\overrightarrow{F}}{q_{0}}$

Since test charge q₀ should be infinitesimally small.

$https://latex.codecogs.com/svg.image?\therefore \overrightarrow{E}=\displaystyle \lim_{q_{0} \to 0}\frac{\overrightarrow{F}}{q_{0}}$

Unit of electric field

Unit of electric field is N / C or V / m
Since force on q₀ due to q

$https://latex.codecogs.com/svg.image?\overrightarrow{F}=\frac{kqq_{0}}{r^{2}}\hat{r}$

Therefore electric field

$https://latex.codecogs.com/svg.image?\overrightarrow{E}=\frac{kq}{r^{2}}\hat{r}$

Direction of unit charge is from q to q₀.

Electric field intensity due to many charges

If q₁, q₂, q₃, ... are the points charges at the distance r₁, r₂, r₃, ... from the observation point respectively, then the total electric field at observation point will be

Electric field due to different charge distribution

Electric field due to line charge

Linear charge density, λ = dq / dl
Unit of λ is C / m

Electric field due to surface charge

Surface charge density, σ = dq / ds
Unit of σ is C / m²

Electric field due to volume charge

Volume charge density, ρ = dq / dv
Unit of ρ is C / m³

To know more about this lecture please click on the link https://youtu.be/sm7IpZXKULc or https://youtu.be/9bR1LfbVrGw

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