# CBSE Physics for Class 12 | Electrostatics | Electrical Field

## Electrical Field

A positive charge or a negative charge is said to create its field around itself.

If a charge $\displaystyle {{Q}_{1}}$ exerts a force on charge $\displaystyle {{Q}_{2}}$placed near it, it may be stated that since $\displaystyle {{Q}_{2}}$ is in the field of $\displaystyle {{Q}_{1}}$, it experiences some force, or it may also be said that since charge $\displaystyle {{Q}_{1}}$is inside the field of $\displaystyle {{Q}_{2}}$, it experience some force.

Thus space around a charge in which another charged particle experiences a force is said to have electrical field in it.

### (1) Electric field intensity $\displaystyle (\vec{E})$:

The electric field intensity at any point is defined as the force experienced by a unit positive charge placed at that point. $\displaystyle \vec{E}= \frac{{\vec{F}}}{{{q}_{0}}}$

Where $\displaystyle {{q}_{0}}\to 0$so that presence of this charge may not affect the source charge Q and its electric field is not changed, therefore expression for electric field intensity can be better written as $\displaystyle \vec{E}=\underset{{{q}_{0}}\to 0}{\mathop{Lim}}\,\,\,\,\frac{{\vec{F}}}{{{q}_{0}}}$

### (2) Unit and Dimensional formula of Electrical Field :

It’s S.I. unit –$\displaystyle \frac{Newton}{coulomb}=\frac{volt}{meter}=\frac{Joule}{coulomb\times meter}$ and

C.G.S. unit – Dyne/stat coulomb.

Dimension :
[$\displaystyle E$] =[$\displaystyle ML{{T}^{-3}}{{A}^{-1}}$]

### (3) Direction of electric field :

Electric field (intensity) $\displaystyle \vec{E}$ is a vector quantity. Electric field due to a positive charge is always away from the charge and that due to a negative charge is always towards the charge

### (4) Relation between electric force and electric field :

In an electric field $\displaystyle \vec{E}$ a charge (Q) experiences a force $\displaystyle F=QE$. If charge is positive then force is directed in the direction of field while if charge is negative force acts on it in the opposite direction of field

### (5) Superposition of electric field (electric field at a point due to various charges) :

The resultant electric field at any point is equal to the vector sum of electric fields at that point due to various charges.

$\displaystyle \vec{E}={{\vec{E}}_{1}}+{{\vec{E}}_{2}}+{{\vec{E}}_{3}}+...$

The magnitude of the resultant of two electric fields is given by

$\displaystyle E=\sqrt{E_{1}^{2}+E_{2}^{2}+2{{E}_{1}}{{E}_{2}}\cos \theta }$ and the direction is given by $\displaystyle \tan \alpha =\frac{{{E}_{2}}\sin \theta }{{{E}_{1}}+{{E}_{2}}\cos \theta }$

### (6) Electric field due to continuous distribution of charge :

A system of closely spaced electric charges forms a continuous charge distribution

#### Linear charge distribution

In this distribution charge distributed on a line.

For example : charge on a wire, charge on a ring etc. Relevant parameter is $\displaystyle \lambda$ which is called linear charge density i.e.,

$\displaystyle \lambda =\frac{\text{charge}}{\text{length}}$

$\displaystyle \lambda =\frac{Q}{2\pi R}$

#### Surface charge distribution

In this distribution charge distributed on the surface.

For example : Charge on a conducting sphere, charge on a sheet etc. Relevant parameter is $\displaystyle \sigma$which is called surface charge density i.e.,

$\displaystyle \sigma =\frac{\text{charge}}{\text{area}}$

$\displaystyle \sigma =\frac{Q}{4\pi {{R}^{2}}}$

#### Volume charge distribution

In this distribution charge distributed in the whole volume of the body.

For example : Non conducting charged sphere. Relevant parameter is $\displaystyle \rho$ which is called volume charge density i.e.

$\displaystyle \rho =\frac{\text{charge}}{\text{volume}}$

$\displaystyle \rho =\frac{Q}{\frac{4}{3}\pi {{R}^{3}}}$

To find the field of a continuous charge distribution, we divide the charge into infinitesimal charge elements.

Each infinitesimal charge element is then considered, as a point charge and electric field $\displaystyle \overrightarrow{dE}$ is determined due to this charge at given point.

The Net field at the given point is the summation of fields of all the elements. i.e., $\displaystyle \overrightarrow{E\,}=\int{\overrightarrow{dE}}$

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