#### Table of Contents:

- Electric Charge
- Gauss Law
- Coulombs law
- Electric Field Intensity
- Equipotential Surface
- Electric Potential Energy

## What isÂ Electrostatics?

Study of stationary electric charges at rest is known as **electrostatics**. An **electroscope** is used to detect the charge on a body.Â **Pith ball electroscope** is used to detect a charge and to know the nature of the charge.Â **Gold leaf electroscope** which was invented by Bennet detects a charge and the nature of the charge and determines the quantity of the charge.

### Conductors, Insulators, and Semiconductors

- A body in which electric charge can easily flow through is called
**conductor**(e.g. metals). - A body in which electric charge cannot flow is called
**insulator**or**dielectric**. (e.g. glass, wool, rubber, plastic, etc.) - Substances which are intermediate between conductors and insulators are called
**semiconductors**. (e.g. silicon, germanium, etc)

**Dielectric Strength: ** It is the minimum field intensity that should be applied to break down the insulating property of insulator.

- Dielectric strength of air = 3 Â 10
^{6}V/m - Dielectric strength of Teflon = 60Â Ã— 10
^{6}Vm^{â€“1}

The maximum charge a sphere can hold depends on the size and dielectric strength of the medium in which sphere is placed.

- The maximum charge a sphere of radius â€˜râ€™ can hold in air = 4
**Îµ**_{0}r^{2}dielectric strength of air. - When the electric field in air exceeds its dielectric strength air molecules become ionized and are accelerated by fields and the air becomes conducting.

### Watch this Video for More Reference

### Surface Charge Density (\(\sigma\))

The charge per unit area of a conductor is defined as surface charge density. \(\sigma\) = \(\frac{q}{A}=\frac{total\,\,charge}{area}\) . When A=1 m^{2} then \(\sigma\) = q.

Its unit is coulomb/ meter and its dimensions are ATL^{â€“2}. It is used in the formula for the charged disc, charged conductor and an infinite sheet of charge etc.Â Â Surface Charge Density depends on the shape of the conductor and presence of other conductors and insulators in the vicinity of the conductor.

- \(\sigma\alpha \frac{1}{r^{2}}\;i.e.\frac{\sigma_1}{\sigma_2} = \frac{r_{2}^{2}}{r_{1}^{2}}\)
- \(\sigma\) is maximum at pointed surfaces and for plane surfaces it is minimum.
- Surface Charge Density is maximum at the corners of rectangular laminas and at the vertex of the conical conductor.

## Electric Flux

The number of electric lines of force crossing a surface normal to the area gives electric flux \(\phi _E\).

Electric flux through an elementary area ds is defined as the scalar product of area and field.

d\(\phi _E\) = Eds \(\cos \theta\)

Or, \(\phi _E = \int \vec{E}.\vec{ds}\)

- Electric Flux will be maximum when electric field is normal to the area (\((d\phi = Eds)\))
- Electric Flux will be minimum when field is parallel to area (\((d\phi = t0)\))
- For a closed surface, outward flux is positive and inward flux is negative.

## Electric potential (V)

The electric potential at a point in a field is the amount of work done in bringing a unit +ve charge from infinity to the point. It is equal to the Electric potential energy of unit + ve charge at that point.

- It is a scalar
- S.I unit is volt

Electric Potential at a distance â€˜dâ€™ due to a point charge q in air or vacuum is V = \(\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{d}\)

**Electric Potential (V)** = â€“ \(\int{\vec{E}.\vec{d}x}\)

\(\vec{E}=-\frac{dv}{dx}\) (or) V = Ed

A positive charge in a field moves from high potential to low potential whereas electron moves from low potential to high potential when left free. Work done in moving a charge q through a potential difference V is W = q V joule

**Gain in the Kinetic energy:**\(\frac{1}{2}m{{v}^{2}}=qV\)**Gain in the velocity:**\(v\,\,=\sqrt{\frac{2qV}{m}}\)

## Equipotential Surface

A surface on which all points are at the same potential.

- Electric field is perpendicular to the equipotential surface
- Work done in moving a charge on the equipotential surface is zero.

### In the Case of a Hollow Charged Sphere.

- Intensity at any point inside the sphere is zero.
- Intensity at any point on the surface is same and it is maximum \(\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{r}^{2}}}\)
- Outside the sphere \(\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{d}^{2}}}\) i.e.d = distance from the centre. It behaves as if the whole charge is at its centre.

Electric field Intensity in vector form \(\vec{E}=\,\,\;\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{d}^{3}}}\vec{d} \;or\; \vec{E}\,\,=\,\,\;\;\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{{{d}^{2}}}\hat{d}\)

The resultant electric field intensity obeyâ€™s the principle of superposition.

\(\vec{E}\,\,=\,\,{{\vec{E}}_{1\,\,}}+{{\vec{E}}_{2}}+{{\vec{E}}_{3}}+……………\)### In the Case of Solid Charged Sphere

The potential at any point inside the sphere is the same as that at any point on its surface

V = \(\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{r}\)

It is an equipotential surface. Outside the sphere, the potential varies inversely as the distance of the point from the center.

V = \(\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{d}\)

** Note: **Inside a non conducting charged sphere electric field is present.

**Electric intensity inside the sphere**

E = \(\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{{{R}^{3}}}d\)

Here, d is the distance from the centre of sphere and E\(\propto\)d

## Electron volt

This is the unit of energy in particle physics and is represented as eV.

- 1 eV = 1.602×10
^{â€‘19}J.

### Charged Particle in Electric Field

When a positive test charge is fired in the direction of an electric field

- It accelerates,
- Its kinetic energy increases and hence
- Its potential energy decreases.

A charged particle of mass m carrying a charge q and falling through a potential V acquires a speed of \(\sqrt{2Vq/m}\).

## Electric Dipole

Two equal and opposite charges separated by a constant distance is called electric dipole.

\(\vec{P}=q.2\bar{l}\)

### Dipole Moment

ItÂ is the product of one of the charges and distance between the charges. It is a vector directed from negative charge towards the positive charge along the line joining the two charges.

The torque acting on an electric dipole placed in a uniform electric field is given by the relation

\(\vec{\tau }=\vec{P}\text{ }x\text{ }\vec{E}\ \text{ }i.e.,\ \tau =PE\sin \theta\) , where \(\theta\) is the angle between \(\vec{P} \;and\; \vec{E}\).â‡’ The electric intensity (E) on the axial line at a distanceâ€™dâ€™ from the center of an electric dipole is \(E=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2Pd}{{{({{d}^{2}}-{{l}^{2}})}^{2}}}\) and on equatorial line, the electric intensity (E) =\(\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{P}{{{({{d}^{2}}+{{l}^{2}})}^{3/2}}}\).

â‡’ For a short dipole i.e., if l^{2 }<< d^{2}, then the electric intensity on equatorial line is given by

E = \(\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{P}{{{d}^{3}}}\).

â‡’ The potential due to an electric dipole on the axial line is V =\(\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{P}{({{d}^{2}}-{{l}^{2}})}\) and at any point on the equatorial line it is zero.

**When two unlike equal charges +Q and â€“Q are separated by a distance**

- The net electric potential is zero on the perpendicular bisector of the line joining the charges.
- The bisector is equipotential and zero potential line.
- Work done in moving a charge on this line is zero.
- Electric intensity at any point on the bisector is perpendicular to the bisector.
- Electric intensity at any point on the bisector parallel to the bisector is zero.

### Combined field due to two Point Charges

#### Due to two Similar Charges

If charges q_{1} and q_{2} are separated by a distance â€˜râ€™, null point ( where resulting field intensity is zero) is formed on the line joining those two charges.

- Null point is formed within the charges.
- Null point is located nearer to weak charge.

If x is distance of null point from q_{1},

(weak charge) then \(\frac{{{\text{q}}_{\text{1}}}}{{{\text{x}}^{\text{2}}}}\,\,=\,\,\frac{{{q}_{2}}}{{{(r-x)}^{2}}}\)

** \(\Rightarrow \,\,x\,\,=\,\,\frac{r}{\sqrt{{{q}_{2}}/{{q}_{1}}\,}\,\,+1}\) **Here q_{1} and q_{2} are like charges

#### Due to two Dissimilar Charges

- If q
_{1}and q_{2 }are unlike charges then null point is formed on the line joining two charges. - Null point is formed outside the charges.
- Null point is from nearer weak charge.
- x is the distance of null point from q
_{1}(weak charge) then\(\frac{{{\text{q}}_{\text{1}}}}{{{\text{x}}^{\text{2}}}}\,\,=\,\,\frac{{{q}_{2}}}{{{(r+x)}^{2}}}\)Â**\(\Rightarrow \,\,x\,\,=\,\,\frac{r}{\sqrt{{{q}_{2}}/{{q}_{1}}\,}\,\,-1}\)**

In the above formulae \({{q}_{2}}/{{q}_{1}}\)is numerical ratio of charges

#### Zero Potential point due to two Charges

- If two unlike charges q
_{1}and q_{2}are separated by a distance â€˜râ€™, the net potential is zero at two points on the line joining them. - One in between them and the other outside the charges.
- Both the points are nearer to weak charge (q
_{1}).

_{2}is numerical value of strong charge \(\Rightarrow \,\,x\,\,=\,\,\frac{r}{\frac{{{q}_{2}}}{{{q}_{1}}}+1}\;\; ; y\,\,=\,\,\frac{r}{\frac{{{q}_{2}}}{{{q}_{1}}}-1}\)

**Due to two similar charges zero potential point is not formed. **

## Electric Lines of Force

The line of force is the path along which a unit +ve charge, accelerates in the electric field.Â The tangent at any point to the line of force gives the direction of the field at that point.

### Properties ofÂ Electric Lines of Force

- Two lines of force never intersect.
- The number of lines of force passing normally through a unit area around a point is numerically equal to E, the strength of the field at the point.
- Lines of force always leave or end normally on a charged conductor.
- Electric lines of force can never be closed loops.
- Lines of force have a tendency to contract
**longitudinally**and exert a force of repulsion on one another laterally. - If in a region of space there is no electric field, there will be no lines of force. Inside a conductor, there cannot be any line of force.

The number of lines of force passing normally through a unit area around a point is numerically equal to E.

In a uniform field, lines of force are parallel to one another.

**Difference between electric lines of force and magnetic lines of force**

- Electric lines of force never form closed loops while magnetic lines are always closed loops.
- Electric lines of force do not exist inside a conductor but magnetic lines of force may exist inside a magnetic material.