# Electricfield Intensity-E

### Electric field Intensity($\overrightarrow{E}$):-

Let us suppose a point charge Q is placed somewhere in space and if any other charge q is brought near to it, q experiences a force on Q and vice-versa. Thus there exists a region around a charge in which it experience a force on any other charge located in that region.

∴ The region around a charge distribution is called as Electric field produced by that charge distribution.

The electric field intensity (or) Electric field strength is defined as the force  per unit charge (test charge)

i.e, $\overrightarrow{E}&space;=&space;\frac{\overrightarrow{F}}{q}&space;Newtons/Coulomb$ —-> Equation (1)

∴ The expression for    $\overrightarrow{E_{at&space;P}}=\frac{Q}{4\pi&space;\epsilon&space;_{o}R^{2}}\widehat{a_{R}}$

q is small test charge +Q is a positive charge placed in free space. $\overrightarrow{E}$ is the electric field produced around +Q charge, then after placing a small test charge q in a field $\overrightarrow{E}$ ,$\overrightarrow{E}$ exerts some force on this test charge q , given by

$F&space;=&space;E&space;q$

and simillarly +Q and q experiences force on each other given by $F&space;=&space;\frac{Qq}{4\pi&space;\epsilon&space;r^{2}}$—>Equation(2) (magnitude)

Force (as a vector) $\overrightarrow{F}&space;=&space;\frac{Qq}{4\pi&space;\epsilon&space;r^{2}}\widehat{a_{R}}$

from equations (1) and (2)   F   =  F  (magnitudes)

$Eq&space;=&space;\frac{Qq}{4\pi&space;\epsilon&space;r^{2}}$

$E=&space;\frac{Q}{4\pi&space;\epsilon&space;r^{2}}$—> Scalar magnitude of $\overrightarrow{E}$ produced by the charge Q.

where as $\overrightarrow{E}=&space;\frac{Q}{4\pi&space;\epsilon&space;r^{2}}\widehat{a_{R}}$ which acts along the direction of Coulomb’s force $\overrightarrow{F}$.

### Types of charge distributions:-

In order to find out the electric field strength due to different types of charge distributions, first of all one must know how many types of charge distributions are there? the positive and negative charges can be distributed into 3 types of distributions.

Properties:-

1. charge is conserved , i.e, charge is neither be created nor destroyed.
2. charges are surrounded by electric and magnetic fields.

Point charge distribution:-

The name itself indicates that the charge confined to a point is known as point charge distributions. In  practical point charges my not exists and point charge does not occupy any space.

Example:- an electron with a charge of 1.6X10-19 C is a point charge.

Line charge distribution(ρL):-

If the charge is distributed along the length of the line, then it is known as line charge distribution. It may be a uniform (or) non-uniform distribution as shown in the figures.

If the charges are distributed uniformly along the line then it is a uniform charge distribution ρL is constant through out the line, otherwise it is Non-uniform type.

The line charge density $\rho&space;_{L}=\lim_{\Delta&space;l->0}\frac{\Delta&space;Q}{\Delta&space;l}$

$\rho&space;_{L}=\frac{dQ}{dl}=\frac{Q}{l}&space;Coulomb/m$—>   $Q=\int_{l}\rho&space;_{l}dl&space;Coulomb$

$\rho&space;_{L}$  is defined as the charge per unit-length.

Surface charge distribution(ρs):-

If the charge is distributed uniformly over a two dimensional surface. Then it is called uniform surface charge distribution otherwise non-uniform.

then the surface charge density $\rho&space;_{s}=&space;\lim_{\Delta&space;s->0}\frac{\Delta&space;Q}{\Delta&space;s}$

$\rho&space;_{s}=\frac{dQ}{ds}=\frac{Q}{S}&space;c/m^{2}$

$Q=\int_{s}\rho&space;_{s}ds$ Coulomb

ρs is defined as charge per unit surface area and is measured in terms of C/m2.

Volume charge distribution (ρv):-

If the charge is distributed uniformly in a volume then it is called as uniform volume distribution. Sphere represents a volume here

$\rho&space;_{v}=\lim_{\Delta&space;v->0}\frac{\Delta&space;Q}{\Delta&space;v}$

$\rho&space;_{v}=\frac{dQ}{dv}=\frac{Q}{V}&space;c/m^{3}$

$Q=\int_{v}\rho&space;_{v}dv$ Coulombs

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