## What do you Mean by Electrostatics?

An electrostatic force is a force caused by stationary electric charges /fields. The electrostatic force is caused by the transfer of electrons in conducting materials. Coulomb’s law determines the amount of force between two stationary, charged particles. The electric force is the force which acts between two stationary charges. It is also called Coulomb force.

Electric charge is the property by virtue of which a particle feels a force when placed in an electric field region. Charge can be said to be the property of matter that exhibit electrostatic attraction/repulsion in the presence of other matter.

There are two types of electric charge, namely positive and negative (commonly carried by protons and electrons respectively).

Static electricity is generated when certain materials rub against each other, like wool on plastic or the rubber on carpet. This process causes electrons (static charge) to be pulled from the surface of one material onto the surface of the other.

The electrostatic force is an attractive and repulsive force between particles .It is caused due to their electric charge. The electric force between stationary charged body is known as the electrostatic force.

## Electric Charges

Electric charge is a characteristic property of many subatomic particles like electrons and protons. The SI derived unit of quantity of electric charge is the Coulomb (symbol is C). One coulomb of charge is defined as quantity of charge that passes through a cross section area of an electrical conductor carrying current one ampere for one second.

The amount of charge in a single electron (elementary charge) is defined as a fundamental constant in the SI system of units of electric charge (Coulomb), value being equal to 1.602176634×10−19 C.

Electric potential and capacitance starts from the concept of charge.

## Coulomb's Law

Coulomb's law states that electrical force on two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between them.

There are three conditions for Coulomb's law to be valid:

1. The electric charges must have spherically symmetric distribution (e.g. be point charges, or charged metal sphere).
2. The electric charges must not overlap (e.g. distinct point charges).
3. The electric charges must be stationary with respect to each other.

Coulomb force acting on two (stationary) charges is a conservative force. Thus, we can define electrostatic potential energy of a charge in an electrostatic field.

In the above equation ke is the proportionality constant. It is called the Coulomb's constant.

The value of ke is dependent upon the medium that the charged objects are immersed in.

In an air medium, the value of ke is approximately 9.0 x 109 N • m/ C2.

## Electric Field

An electric field is a vector field that is defined to each point in space, the Coulomb force experienced by a unit test charge.

## Electric Potential

We define electric potential of a test charge q as work done on a unit charge q. The work  done depends on q. This is because of the equation of force on a charge in electric field, E.

F=qE

It is convenient to divide the work by the amount of charge q, so that W is independent of q. Therefore, work done per unit test charge is characteristic of the electric field associated with the charge configuration.

## Potential Energy

It is the energy that is stored within an object, when not in motion.

### Potential of charge

Let us consider a unit charge of magnitude q, placed in an external electric field of magnitude E.

The charge q under consideration is very minute. The potential (V) of the charge q in the electric field is equal to the work done in bringing the charge from infinity to the nearest point.

V=W/q

Since both electric field and electric potential is dependent on the position of charge, it would vary at different points.

The potential at infinity is always taken to be zero; hence the work done in bringing a charge from infinity to the nearest point is given as qV.

### Electromotive Force

The electromotive force (emf, denoted by {displaystyle {mathcal {E}}}E) is the electrical action force that drives the charges produced by an electrical /non electrical source.

### Potential difference

The electrical potential difference is defined as the amount of work done to carry a unit charge from one point to another within an electric field. The SI unit is given as Volt (V).

## Equipotential Surface

A surface having same electrostatic potential at every point on it, is known as equipotential surface.

The shape of equipotential surface due to
(i) line charge distribution is cylindrical.
(ii) point charge is spherical distribution as shown in figure below

The properties include:
(a) Equipotential surfaces do not  intersect each other as it shows two directions of electric field E at intersecting points.
(b) In strong electric field regions, the equipotential surfaces are cluttered.
(c) Work done in moving a test charge from one point of equipotential surface to another is zero.

## Relationship between Electric Field and Potential Gradient

The negative sign indicates that the direction of electric field is from higher potential to lower potential, i.e. in the direction of decreasing potential.
NOTE:

• Electric field points in the direction of decreasing potential.
• Electric field magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point.

## Electrostatic Potential Energy

The work done against the electrostatic force in moving charges gets stored as potential energy. This is called electrostatic potential energy.

∆U = UB-UA =WAB

If the test charge is moved over a closed path, the work done is zero. Thus, electrostatic forces are conservative in nature. The electric potential for a system of two charges is given below

## Capacitor

Capacitor is also known as Condenser. It is a two terminal electric component which has ability to store energy in the form of electric charge.

### Capacitance

The ability of a capacitor to store the energy in form of electric charge is known as Capacitance.

In other words, capacitancecan be described as the storing ability of an capacitor and it is measured in Farads.

Q=CV

For e.g., if we connected a capacitor to a 9 volt battery and measure that it stored 9 coulombs of charge, its capacitance would be 1 farad.

### Electrical Capacitance

Electrical conductance of a conductor is defined as the capacity of chargestored in it. Whenever charge is applied to an insulator its potential is raised to a voltage level. The electric charge on a conductor and its electric potential is directly proportional to each other. If we increase the charge, electric potential also increases.

Q = C V

C is the proportionality constant

### Effect of Dielectric on Capacitance of Capacitor

Michael Faraday developed this theory, that the space between two electrodes are filled with dielectric the capacitance of the capacitor will be increased.

If the whole space is filled by a dielectric till there is no place left, the capacitance of a capacitor will be increased by k.

k is known as Dielectric Constant.

### Energy Stored on a Capacitor

Energy Stored on a Capacitor is calculated through following expression:

$\begin{array}{c}U=\frac{1}{2}\frac{{Q}^{2}}{C}\\ =\frac{1}{2}QV\\ =\frac{1}{2}C{V}^{2}\end{array}$

## Numerical Problem

A particle having a charge of 30 electrons on it falls through a potential difference of 100 volts. Calculate the energy acquired by it in electron volts (eV)

Given Data: Charge = q = 30 electrons

e = 30× 1.6× 10-19 C = 48 × 10-19 C

Potential difference = ΔV = 100 V

To determine: Energy required in (eV) = E =?

Calculations:

We know that:

Energy E = qΔV

E = (48 × 10-19)(100) J

E = 4800 × 10-19 Joules

Since 1eV = 1.6 × 10-19 C

E = 3000 eV

## Common Mistakes

1) Students sometimes do not identify and calculate capacitance in series & parallel correctly.

2) Students may get confused between potential and potential energy, they are not the same.

## Formulae

• $F=\frac{{q}_{1}{q}_{2}}{4\pi {\epsilon }_{0}{r}^{2}}$
• Q=CV
• F=qE
• E = qΔV
• $\begin{array}{c}U=\frac{1}{2}\frac{{Q}^{2}}{C}\\ =\frac{1}{2}QV\\ =\frac{1}{2}C{V}^{2}\end{array}$
• ∆U = UB-UA =WAB
• $U=\frac{1}{2}{\epsilon }_{0}{E}^{2}$

## Context and Application

• Electrical Engineering
• High school and AP Physics
• Electric Field
• Energy Density
• Coulomb's law
• Equipotential Surface
• Capacitance
• Xerography
• Electrostatic Potential

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