Complete Guide to Electrostatics for Science Students

Question

Electrostatics as the name suggest - Electro and Statics is the science that studies of electricity at rest. The fundamental concept in electrostatics is electrical charge.  As we know, atoms are electrically neutral, because the total charge is balanced as the charges of protons equates that of the electrons.

An addition or removal of an electron in an atom can influence the overall charge as addition of electron introduces more negative charge, making the atom to have an overall negative charge. On the contrary, the removal of an electron will mean that more proton charge exist than the electron, making the atom to be electrically positive.

Thus, we can say that positive electrification of an atom results from the deficiency of electrons while negative electrification results from an excess of electron in the atom.

We all know that rubbing two materials together &mdash; like a rubber comb against hair fur &mdash; creates a static charge. This phenomenon is called charging by friction. Although the detailed physics behind how friction causes this charging is not fully understood. What we know is that charge transfer occurs when the two materials make and break contact.

Key concepts in electrostatics:

Charge: the fundamental property that causes matter to experience a force when placed in an electric or magnetic field. It comes in two types: positive and negative.

Electric Permittivity(&epsilon;) is a measure of how much electric field is reduced (or allowed) inside a material when the material is placed in an external electric field. It quantifies a material&rsquo;s ability to permit electric field lines to pass through it. Permittivity can be relative or absolute.

Absolute Permittivity (&epsilon;0):  It is the actual measure of how much electric field a material can allow or oppose.

It depends on the material. Unit:
	Farads per meter (F/m).
	For a vacuum (free space), the absolute permittivity is: &epsilon;0 =8.854&times;10-12&thinsp;F/m

Relative Permittivity(&epsilon;) The ratio of the absolute permittivity of a material (&epsilon;) to the permittivity of free space (&epsilon;0). Relative permittivity of free space, &epsilon;r = 1. It has no unit since it is a ratio of two similar quantities

Example

Given the relative permittivity of mica is 5, then find it&rsquo;s absolute permittivity. 
&epsilon; = &epsilon;0 &epsilon;r = 8.854 &times; 10&minus;12 &times; 5 = 44.27 &times; 10&minus;12 F/m

Laws of Electrostatics

There are basically two laws in electrostatics; the first and second laws.

First Law

Like charges of electricity repel each other, whereas unlike charges attract each other.

Second Law

Also called Coulomb's law, it states that the force of attraction or repulsion between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

F&#8733;   q 1   q 2     d 2

k= 1  4&#960; &#949; 0

= 1  4&#8727;3.142&#8727;8.85&#8727;  10  &#8722;12

k=8.9918* 10 9      =9.0* 10 9

Example 
Calculate the electrostatic force of repulsion between two &alpha;-particles when at a distance of 10&minus;13 m from each other. Charge of an &alpha;-particles is 3.2 &times; 10&minus;12 C.

Here Q1 = Q2 = 3.2 &times; 10&minus;19 C, d = 10&minus;13 m

F=9&#8727; 10 9        3.2&#8727;  10  &#8722;2    2          10  &#8722;13    2    =9.2&#8727; 10  &#8722;2  N

Most objects we encounter are electrically neutral, they are made up of atoms, each consisting of negatively charged electrons moving in orbits around a positively charged nucleus. The total negative charge of the electrons balances the total positive charge of the nucleus, resulting in neutrality in electrical charge for the atom &mdash; and therefore for the object as a whole.

When a material is charged by friction, some electrons are transferred from one material to another, disrupting this balance. Metals conducts electricity because their atoms have free electrons orbiting the outer shell ready to migrate free. This freedom to move cause it to conduct electricity (movement of electric charge from one point to another).

Conversely, insulators do not conduct because their electrons are tightly bound and not free to move, meaning that charge can accumulate on an insulator as it does not flow through it.

When a negatively charged rod is brought near an isolated, neutral insulator, the electrons in the insulator&rsquo;s atoms are pushed slightly away from the rod, while the positive nuclei shift slightly toward it. This creates a small separation of charge within the insulator, even though its overall charge remains zero.

Electric Field Intensity

An electric field is a region of space around a charged object where another charged object experiences a force. It is a vector field that represents the force per unit charge exerted on a small positive test charge placed at any point in the field.

The electric field is represented by imaginary lines of force as shown above. These lines of force emanate from the positive charge to the negative charge when unlike charges are place together.

Mathematically, the strength of an electric field E at a point is defined as:

E &#8594;  =  F &#8594;  q

where:

E is the electric field (in newtons per coulomb, N/C),
	F is the force experienced by the test charge (in newtons),
	q is the magnitude of the test charge (in coulombs).

Substituting into the electric field equation we have:

F= 1  4&#960; &#949; 0       q 1   q 2     d 2         E &#8594;  = 1  4&#960; &#949; 0       q 1   q 2     d 2    &#8727; 1 q       q 1  = q 2  =q      E &#8594;  = 1  4&#960; &#949; 0     q   d 2      N/C       E &#8594;  =9.0&#8727; 10 9   q   d 2         E &#8594;  = D   &#949; 0      N/C

In terms of flux density, we can define electric field strength as the lines of force passing through a cross-sectional area at that point.

Mathematically,

E &#8594;  = D   &#949; 0      N/C       E &#8594;  = D   &#949; 0   &#949; r      N/C

Where D is flux density q/A and A is the area of the electric force field.

We can also define Electric field strength in terms of voltage gradient. As Electric intensity at any point in an electric field is equal to the potential gradient at that point.

E &#8594;  = V d    &#160;v/m

Example

Point charges in air are located as follows: +5 &times; 10&minus;8 C at (0, 0) m, +4 &times; 10&minus;8 C at (3, 0) m and &minus;6 &times; 10&minus;8 C at (0, 4) m.
Find electric field intensity at (3, 4) m.

First, we represent the charges in accordance with their respective coordinates:

A(0,0)m, B(3,0)m, C(0,4)m, D(3,4)m.

Let EA, EB, EC to denote the Electric field strength due to point charge A, B, and C respectively. And E to denote the combined electric field strength of these three-point charge.

AD=  A B 2  +B D 2    =   3 2  + 4 2    =5 
Field strength at D due to point charge A:
      E A  &#8196;=&#8196;9&#8196;* 10 9  *   q A     d 2         E A  =9&#8727; 10 9  &#8727;  5&#8727;  10  &#8722;8     5 2    =18  N/C     
Field strength at D due to point charge B:
     E B  &#8196;=&#8196;9&#8196;* 10 9  *   q B     d 2         E B  =9&#8727; 10 9  &#8727;  4&#8727;  10  &#8722;8     4 2    =22.5  N/C     
Field strength at D due to point charge C:
     E C  =9&#8727; 10 9  &#8727;   q C     d 2         E C  =9&#8727; 10 9  &#8727;  6&#8727;  10  &#8722;8     3 2    =60  N/C      &#952;= tan  &#8722;1     5 4   = 53.1301 o

Resolving these intensities into the respective horizontal and vertical components

x-components of Electric Field intensity:

Ex = EA cos (53.13) + EB cos (90) - EC cos (0)
Ex = 18 cos (53.13) + 22.5 cos (90) &ndash; 60 cos (0)
Ex = 10.8 + 0 &ndash; 60 = &ndash; 49.2 (N/C)

y-components of Electric Field intensity:

Ey = EA sin (53.13) + EB sin (90) - EC sin (0)
Ey = 18 sin (53.13) + 22.5 sin (90) &ndash; 60 sin (0)
Ey = 14.40 + 22.5 &ndash; 0 = 36.90 (N/C)
​​​​    E=   E x    2  + E y    2        =      &#8722;49.2  2  +    36.90  2        =61.5(N/C)     &#934;= tan  &#8722;1      36.9  &#8722;49.2   =&#8722; 36.87 o

Electrostatic Induction

Electrostatic induction is the process by which an uncharged body becomes electrically polarized (develops opposite charges at opposite ends) when a charged object is brought near it without direct contact.

A                                             B

In the diagram, a positively-charged body A is brought close to a perfectly-insulated uncharged body B. It is found that the end of B nearer to A gets negatively charged whereas further end becomes positively charged. The negative and positive charges of B are known as induced charges.

We therefore conclude that:

A positive charge induces a negative charge and vice-versa.

Each of the induced charges is equal to the inducing charge.

Electric Potential and Potential difference

Electric Potential is the work done in moving a unit positive charge from one point to another in an electric field.

Mathematically;
For air
​​​​​​ W= q  4&#960; &#949; 0  d

For medium,

W= q  4&#960; &#949; 0   &#949; r  d

This work done is also called the potential difference V.

Thus W = V = volts.

Conductors

Conductors are materials that allow the easy flow of electric current due to the presence of free-moving charged particles, typically electrons.

Characteristics of a conductor

High electrical conductivity: They permit the movement of electrons with minimal resistance.
	Low resistivity: They offer little opposition to current flow.
	Contain free electrons: These electrons are not bound to atoms and move freely through the material.

Examples of conductors

Metals: Copper, aluminum, gold, and silver are excellent conductors.
	Graphite: A non-metal that can conduct electricity due to delocalized electrons.
	Saltwater: Due to dissolved ions, it can conduct electricity.

Insulators

Insulators are materials that do not allow the free flow of electric current because they lack free-moving charged particles like electrons.

Characteristics of Insulators:

High resistivity: They strongly oppose the flow of electric current.
	No free electrons: Electrons are tightly bound to their atoms.
	Poor heat and electricity conductors

Examples:

Rubber
	Plastic
	Glass
	Dry wood
	Ceramics
	Pure water

Applications of Insulators:

Coating for electrical wires (e.g., plastic insulation)
	Handles of electrical tools (to protect users from electric shock)
	Circuit boards (to separate conductive paths)
	Power line supports (porcelain insulators)

Semiconductors

Semiconductors are materials whose electrical conductivity lies between that of conductors and insulators. They can behave as insulators at low temperatures but conduct electricity under certain conditions (e.g., heat, light, voltage, or doping).

Characteristics of Semiconductors

Moderate conductivity: Neither very good nor very poor conductors.
	Conductivity increases with temperature (opposite of metals).
	Can be modified by doping (adding small amounts of impurities).
	Essential in modern electronics.

Common Semiconductor Materials:

Silicon (Si) &ndash; the most widely used.
	Germanium (Ge)
	Gallium arsenide (GaAs)

Types of Semiconductors:

Intrinsic Semiconductors:

Pure semiconductors (e.g., pure silicon or germanium).

Extrinsic Semiconductors:

Doped to increase conductivity:

N-type: More electrons (negative charge carriers).
P-type: More holes (positive charge carriers).

Applications of Semiconductors:

Diodes
	Transistors
	Solar cells
	Integrated circuits (ICs)
	Light-emitting diodes (LEDs)