Electric Field

Electric field is the space around an electric charge in which another electric charge feels an electrostatic force.

Intensity Of Electric Field

The strength or intensity of an electric field at a point in an electric field is defined as the electrostatic force acting on a unit positive charge kept at that point in the electric field.

If $Q_0$ is kept in electric field of $Q$ at a point then, intensity of electric field at that point will be
$E = \frac{F}{Q_0}$

Intensity of the electric field is a vector quantity and is directed along the direction of electrostatic force acting on a positive charge.

Unit = $\text{NC}^{-1}$ or Newton per Coulomb.

Dimensional Formula = $[MLT^{-2}]/[AT] = [MLT^{-3}A^{-1}]$ .

Electric field can still exist without an electric charge. But it can’t be generated from nothing. It requires either electric charge or manetic field.
Since an electric field has its own existence, it takes a definite time to propagate in space. It means that if a charge moves a distance r, then time taken by its electric field to propagate will be r/c (c = speed of light).
Generally strength or intensity of electric field is also termed as value of electric field or simply electric field.
Test Charge
Very small amount of positive charge.
Point Charge.
Very less or negligible inertia.

Direction Of Electric Field

To find the direction of an electric field at a point, put a test charge or any positive charge at that point. The direction of electric force acting on a positive charge is the direction of the electric field at that point.

Force on an Electric Charge kept in an Electric Field

An electric charge experiences electrostatic force due to another electric field.

In an electric field electric charge experiences electric force given by
$F = qE$

$F$ is the electrostatic force on $q$ due to electric field $E$ .
$F$ on $q$ depends on the value of $E$ and $q$ both.

Direction Of Forces

Consider the electric field around a positive charge $+Q$ and $E_1$ and $E_2$ be the intensities of Electric fields at point 1 and 2.

Now put a positive charge $+q$ at 1 and negative charge $-q$ at 2.

Figure II shows direction of forces acting on $+q$ and $-q$ in the electric field of $+Q$ (as per attraction and repulsion).

If we combine both figures, it is clear that $F_1$ on $+q$ is in the same direction of $E_1$ while $F_2$ on $-q$ is in the opposite direction of $E_2$ . Similarly for an Electric field due to $-Q$ .

Again $F_1$ on $+q$ is along $E_1$ at 1 and $F_2$ on $-q$ is in opposite direction of $E_2$ at 2.

Therefore, a positive charge experiences electrostatic force in an electric field in the same direction of electric field and a negative charge experiences force in electric field in the opposite direction of electric field.

Electric Field Intensity due to a Point Charge

Consider a point charge ‘P’ at a distance ‘r’ from a point charge +Q at O, where electric field intensity is required.

Take a test charge $+Q_0$ at P.
Electrostatic force on $+Q_0$ due to $+Q$
$F = \frac{1}{4\pi\epsilon} \frac{Q Q_0}{r^2}$

Electric field intensity at P↴
$E = \frac{F}{Q_0}$
$E = \frac{1}{4\pi\epsilon} \frac{Q}{r^2}$

Relation Graphs

$E \propto 1/r^2$ Intensity of electric field is greater near the charge and decreases as we move away from charge. Or as $r$ increases, $E$ decreases.

$E \propto Q$ Electric field intensity at a point in an electric field is greater for a greater charge. Or as $Q$ increases, $E$ also increases.
For a medium with dielectric constant $K$ , electric field intensity at a point due to a point charge ⟶ $E = \frac{1}{4\pi\epsilon_0 K} \frac{Q}{r^2}$

For air or vacuum $K=1$

$E_0 = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2}$

$\frac{E}{E_0} = \frac{1}{K} \quad \text{or} \quad K = \frac{E_0}{E}$

Dielectric constant of a medium affects the electric field.

Electric Lines of Forces

Also known as electric field lines. Electric lines of force are the imaginary smooth curves drawn in an electric field along which a free, isolated, positive charge would move. Electric fields can be easily visualized by electric lines of force.

Pattern of Electric Lines of Forces

Due to a Positive Point Charge

Due to a Negative Point Charge

For a pair of Equal and Opposite Charges

For a pair of Equal and Like Charges

For a uniform Electric Field

Uniform electric field in a region has the same magnitude and same direction at each point.

Properties of Electric Lines of Force

Originate from positive charge and terminate on negative charge.
Tangent drawn at any point gives direction of Electric field intensity at that point.
Electric lines of force are continuous curves, having no breaks in between.
No two Electric lines of force can intersect each other in an electric field.
Relative closeness indicates the relative strength of the electric field. It means where these lines are closer or denser, electric field is stronger and where field lines are far or less dense, electric field is weaker.

Principle Of Superposition for Electric Field

Net Electric field intensity at a point due to a number of charges around it is given by the vector sum of all the electric field intensities due to each charge individually.