Electrical Force

Let's start with what is a force. Force is a push, or a pull exerted on an object to change the state of motion. The thing about force is that it works differently for different particles in existence. Between solids, it is a contact force, however in case of magnets or electricity the forces are either induced or generated. The forces in those cases work very differently from general forces. The attractive electrostatic force between two charged particles is far stronger than the gravitational force being exerted between two solid particles. The electric force is one among the fundamental forces that exist in this universe. 

Electric forces are the driving forces for a lot of phenomena, maybe at a smaller scale or on a larger scale. The existence is predominant in many cases as per one can see in day to day lives but might overlook. Let's see what examples we can find nearby.

One being our hair standing up due to the cold dry air, the effect of light when a lamp is turned on and the formation of a lot of electrically significant chemical bonds.

Starting From the Basics Let’s Check the First Point in Our List:

Electric Forces and Their Types:

There are predominantly two types of electrical forces: Attractive electrical forces and repulsive electrical forces. Unlike charges exert an attractive force on one another and like charges repel each other. If a positive charge comes close to a negatively charged particle, it will be more likely for them to attract each other and come together.

Now let’s see what an electric force is and what a charged particle is. 

So as stated above, the electric force is a force exist between two charged particles. So, what are charged particles? There are minute particles present in atoms which are called protons and electrons. Protons are positively charged, and electrons are negatively charged ones. Protons and electrons are the smallest existing particles. All substances only get charged due to an imbalance between the number of existing protons and the number of electrons that are present in an atom. 

Protons are very tightly packed within a nucleus allowing little to no movement at all. On the contrary, electrons can move freely around the nucleus since they are not perpetually attracted to the nucleus. This is the reason why it is way too easy for electrons to move about from one particle to the other causing an imbalance between the number of protons and electrons being present in the particle and thereby inducing the need to bond with another particle in order to maintain equilibrium. 

In regard to the basic electrical charges, the reason behind our hair stands up in the cold dry weather after brushing it. It is because the charges from the comb are transmitted to the hair and thus causing it to stand up. Here the hair stand becomes positively charged in oppose to the negatively charged comb. 

It mainly happens in cold dry air because, in a relatively humid and hot climate, a lot of water being present in the air makes it pick up charges from the hair more easily and subsequently the hair lose charge as well way too quickly. 

So How to Calculate 

The strength of the electric force between two charged particles takes into consideration the amount of charge that each object contains and the relative distance between the two. As the amount of charge gets larger the force between the two gets larger however with the increase in distance the force of attraction between two charges gets smaller and smaller. 

So it can be told that the force of attraction between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This phenomenon is known as Coulomb's law. And can be written as:

\[F_{12} = F_{21} = k q_{1}q_{2}r^{2}\]

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In the above equation, \[q_{1}\] and \[q_{2}\] are the amounts of charge present in two particles, r represents the relative distance between the two particles. Let's explore the basic difference that is seen between an electric force and an electric field. Though thought to be similar they are actually different. The thing about technologies in the field of physics is that each section has variable differences and each word has a significant meaning. The motive is to explore each word so that the concept is clear in all sections.

In the case of electric forces and electric field, the concept it is based on is the same, but both have different actions and different significance. 

All charged particles are known to create a field of their own. The force on a charged particle is so immense that the effect causes a particular area to be affected by it. This area is called the field caused by the particle. Similarly, the created by an electric charge is called an electric field in the vicinity of the electric force. 

The electric field and in turn the electric force can change variable with time as the charge generating this effect is moving. 

If the said charged particle is static, then it is called an electrostatic field corresponding to the static electric force. 

“Electricity focuses on the movement of particle which is usually electrons since the protons are bundled in a nucleus, and thereby slower.”

Electric Force and Static Equilibrium

Let's Take two rubber balloons and let us hang them from the ceiling by two long strings such that they hang vertically. Then it is such that each balloon is given 10 average-strength rubbing from an animal fur. The balloons, that are having a greater attraction for electrons than animal fur, would acquire a negatively charged potential. The balloons will have to have the same type of charge and they would start to repel each other. The result of the phenomenon of repulsion is that the strings and balloons that were suspended would now make an angle with the vertical. The angle of the string with the vertical has to be mathematically related to the quantity of charge on the balloons. As the balloons possess a greater quantity of charge, the force of repulsion between them would increase and the angle made by the string with the vertical will have to also increase. Like any situation involving electrostatic force, this situation can be concluded using vector principles and Newton's law. 

Now let’s Jump to the Laws that Govern Electrostatic and Electric Forces of Charged Particles:

I. The electric forces are directly proportional to the product of their strengths.

II. They are seen to be inversely proportional to the square of the distance between them.

This is known as Coulomb's Law. 

What is to be said for the electric and magnetic fields is that in permittivity of free space is denoted by ε0 and magnetic permeability of free space is denoted by μ0 of free space. As mentioned about electric and magnetic constants before, these two quantities are not independent but are related to "c", the speed of light and other electromagnetic waves.

The permittivity of any medium with respect to the permittivity of free space is called relative permittivity and is denoted by εr and Absolute permittivity of any medium is given by

                           ε = εr . ε0 

An electric field is the force experienced by a charge of 1C when is placed inside an electric field. If a small charge is tested in a field, it would either move along the field lines or in the opposite direction of the field lines. If it is seen that the test charge is moving along the field lines, then it can be said that the charge is positive else it is negative.

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One is given a charge q and electric field at a distance r needs to be found. 

The electric field equation is:

|E| = \[\frac{kq}{r^{2}}\]

where:

• |E| is the magnitude of the electric field that is given in newtons-per-coulomb (N/C)

• q is the magnitude of the charge given in coulombs

• k is Coulomb's constant

• r is the distance from the charge in meters (m)

\[\overrightarrow{F_{E}} = \frac{q_{1}q_{2}}{4\pi \epsilon_{0} R^{2}}\widehat{a}(N)\]

\[\overrightarrow{E} = \frac{q_{1}}{4 \pi \epsilon_{0} R^{2}} \widehat{a} (\frac{N}{C})\]

Here the electric field is established by the source charge q1 and F is the force that has been exerted on q2 R from the q1. And E is the electric field due to q1 at a distance of R from the source charge.

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Gauss's Law states that the total electric flux in a closed surface is equal to the charge that is enclosed divided by the permittivity.

Electric flux, on the other hand, is defined as the electric field through an area of the surface projected in a plane perpendicular to the field.

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The area integral form of the electric field is given for any closed surface is equal to the net charge in a closed surface divided by the permittivity. 

This is the basic information required to start off with the topic of electric forces and fields.