An electric force is an interaction between two charged bodies, either attractive or repulsive. Similar to other forces, this force effects and impacts a particular object and can easily be demonstrated by Newton’s law of motion. The electric force is one of the forces which is exerted over other bodies.

Newton’s law can also be used to analyze the effects of motion when this kind of force is present. An analysis begins by constructing a free body image in which the direction of that image and the individual force types are seen by a vector which can help calculate the total. The net force applied to a body in order to calculate acceleration is known as the net force.

**What Is Electric Force?**

It is the electric force that is responsible for attracting or repelling any two charged objects. In the same way as any force, its effects on objects are described by Newton’s laws of motion. With Felect, the electric force can act on objects in addition to a wide range of other forces. Newton’s laws are used to analyze the motion (or lack of motion) of objects under such a force or combination of forces.

Analyses usually begin with the construction of a free-body diagram where the type and direction of forces are represented by vector arrows and labeled according to the type. As a result, the magnitudes of the forces are added as vectors to determine the resultant sum, also known as the net force. The net force can then be used to calculate the acceleration of the object.

The goal of the analysis may not always be to determine the acceleration of the object. The free-body diagram is instead used to determine the distance or charge between two objects that are at static equilibrium. In this case, a free-body diagram is used in conjunction with vector concepts in order to solve a puzzle involving geometry, trigonometry, and Coulomb’s law. This article will explore both types of applications of Newton’s laws to static electricity.

**Definition**

The repulsive or attractive interaction between any two charged bodies is called an electric force. Similar to any force, its impact and effects on the given body are described by Newton’s laws of motion. The electric force is among the list of other forces that exert over objects.

Newton’s laws are applicable to analyze the motion under the influence of that kind of force or combination of forces. The analysis begins with the construction of a free body image wherein the direction and type of the individual forces are shown by the vector to calculate the resultant sum which is called the net force that can be applied to determine the body’s acceleration.

**Charge**

How do we know there is such a thing as charge? The concept of charge arises from an observation of nature: We observe forces between objects. Electric charge is the property of objects that gives rise to this observed force. Like gravity, electric force “acts at a distance”. The idea that a force can “act at a distance” is pretty mind-blowing, but it’s what nature really does.

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Electric forces are very large, far greater than the force of gravity. Unlike gravity, there are two types of electric charge, (whereas there is only one type of gravity; gravity only attracts).

**Types Of Electric Force**

The electric force consists of two different types of charges. They are positive electric charge and negative electric charge. The interaction of both of these charges is easily predictable. Unlike electric charges, they attract each other, while the like charges repel one another. This basically means that if the two charges are positive then there exists a repulsive force between both the charges.

The same thing happens if two negative charges come in contact, they both will repel each other too. In contrast, if one positive charge and one negative charge come into contact, then there is generated an attractive force, in which both the charges will be attracted towards one another. The given below is the diagrammatic representation of the same.

**Electric Force And Charged Particles**

Electric force can happen among all the charged particles irrespective of the type of charge. These are seen as tiny particles and can be found inside atoms. They are termed protons and electrons. Protons are made up of positively charged particles whereas electrons are built by negatively charged ones. The other objects which are produced from atoms become charged due to an imbalance of the number of electrons and protons contained inside the atoms.

In an atom, protons are present inside the nucleus and are very tightly bound. They cannot move or travel across the atoms or nucleus. Meanwhile, electrons can be seen away from the atoms in their own orbitals. They can move around the atom.

**What is Coulomb’s Law For Electric Force?**

Coloumb’s law is an experimental law that quantifies the amount of force between two stationary electrically charged particles. The electric force between stationary charged bodies is conventionally known as the electrostatic force or Coloumb’s force. Coulomb’s law describes the amount of electrostatic force between stationary charges.

**Electric Field Between Two Plates: Magnitude, Direction, Examples & More**

Coulomb’s law states that:

The value of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the charges and inversely proportional to the square of the distance among them.

**Formula Of Coulomb’s Law For Electric Force Between Point Charges**

Coulomb’s Law very nicely describes this natural phenomenon. The law has this form,

$$\vec F = K\frac{q_0.q_1}{r^2}\hat{r}$$

Where

- \(\vec{F}\) is the electric force, directed on a line between the two charged bodies.
- \(K\) is a constant of proportionality that relates the left side of the equation (newtons) to the right side (coulombs and meters). It is needed to make the answer come out right when we do a real experiment.
- \(q_0\) and \(q_1\) represent the amount of charge on each body, in units of coulombs (the SI unit for a charge).
- \(r\) is the distance between the charged bodies.
- \(\hat{r}\) is a variable unit vector that reminds us of the force points along the line between the two charges. If the charges are alike, the force is repulsive; if the charges are unlike, the force is attractive.

**The Electric Constant, \(\epsilon_0\), The Permittivity Of Free Space**

\(K\), the constant of proportionality, frequently appears in this form,

$$K = \frac{1}{4\pi \epsilon_0}$$

and Coulomb’s Law is written in this form,

$$\vec{F} = \frac{1}{4\pi\epsilon_0}\frac{q_0. q_1}{r^2}\hat{r}$$

The Greek letter \(\epsilon_0\) is the electric constant, also known as the permittivity of free space, (free space is a vacuum). Coulomb’s Law describes something that happens in nature. The electric constant, \(\epsilon_0\), describes the experimental setup and the system of units.

“Experimental conditions” refers to measuring \(\vec F\), with, vector, on top of point charges (or something that acts like a point charge, like charged spheres). In the SI system of units, \(\epsilon_0\) is experimentally measured to be,

$$\epsilon_0 = 8.854 187 817 \times 10^{−12}\frac{coulomb^2}{newton-meter^2}$$

This value of \(\epsilon_0\) makes,

$$K = \frac{1}{4\pi \epsilon_0} = \frac{1}{4\pi \times 8.854 \times 10^{−12} } = 8.987 \times 10^{9}$$

or for engineering purposes, we round \(K\) to something easier to remember,

$$K = \frac{1}{4\pi \epsilon_0} = 9 \times 10^{9}$$

The dimensions of \(K\) are: \(\frac{newton-meter^2}{coulomb^2}\).

### Electric Force Between Line Of Charge With A Point Charge Off The End

A line of charge \(L\) meters long has a total charge of \(Q\). Assume the total charge, \(Q\), is uniformly spread out on the line. A point charge \(q\) is positioned \(a\) meters away from one end of the line.

#### Find the total force on a charge \(q\) positioned off the end of a line of charge.

The line contains a total charge \(Q\) coulombs. We can approach this problem by thinking of the line as a bunch of individual point charges sitting shoulder to shoulder. To compute the total force on \(q\) from the line, we sum up (integrate) the individual forces from each point charge in the line.

We define the **charge density** in the line as \(\frac{Q}{L} \frac{coulombs}{meter}\).

The idea of charge density lets us express the amount of charge, \(dQ\), in a little piece of the line, \(dx\), as,

\(Q\) is close enough to be a point charge to allow us to apply Coulomb’s Law. We can figure out the direction of the force right away: The force on \(q\) from every \(Q\) is directed straight between \(q\) and \(dQ\). Direction solved, now the magnitude of the force,

$$dF = \frac{1}{4\pi\epsilon_0}\frac{q.dQ}{x^2}$$

The numerator multiples the two charges, \(Q\) and \(dQ\); the denominator \(x\) is the distance between the two charges.

To find the total force, add up all the forces from each little \(dQ\)’s by integrating from the near end of the line \(a\), to the far end \(a+L\).

$$F = \int_{a}^{a+L}d\vec{F}=\int_{a}^{a+L}\frac{1}{4\pi\epsilon_0}\frac{q.dQ}{x^2}$$

This equation includes both \(x\) and \(dQ\) as variables. To get down to a single independent variable, eliminate \(dQ\) by replacing it with the expression \(\frac{Q}{L}dx\) from above,

$$F =\int_{a}^{a+L}\frac{1}{4\pi\epsilon_0}\frac{q.Q}{L.x^2}dx$$

Move everything that does not depend on \(x\) outside the integral.

$$F =\frac{1}{4\pi\epsilon_0}\frac{q.Q}{L}\int_{a}^{a+L}\frac{1}{x^2}dx$$

And solve the integral,

$$\large F = \frac{1}{4\pi\epsilon_0} \frac{qQ}{a(a+L)}$$

**Some things to notice about the solution:**

- The numerator is the product of the test charge and the total charge on the line, which makes sense.
- The denominator has the form , created by a combination of distance to the near end and far end of the line. The \(a(a+L)\) form of the denominator emerges from the particular geometry of this example.
- If the point charge \(q\) moves very far away from the line, \(L\) becomes insignificant compared to \(a\), and the denominator approaches \(a^2\). So at a great distance, the line starts to resemble a far-off point charge, and as one would hope, the equation approaches Coulomb’s Law for two-point charges.

We’ll do a few more electrostatics problems with simple charge geometries. After that, the math gets really involved, so the common strategy with complex geometries becomes: break down the geometry into simpler versions we already know how to do, then merge the answers.

## Strategies for applying Coulomb’s Law

Coulomb’s Law is a good choice for situations with point charges and/or simple symmetric geometries like lines or spheres of charge.

Since Coulomb’s Law is based on pairwise forces between charges, when faced with multiple (more than two) point charges,

- Work out the forces between each pair of charges.
- Finish with a vector addition to merge the pairwise forces into a single resultant force.

For a situation with distributed charge, creatively model the distributed charge as a collection of point charges,

- Invent a little \(dQ\) representing an infinitesimal charge within the region of distributed charge.
- Work out the forces pairwise between the point charge and each little \(dQ\).
- Sum up the forces with an integral. This is a vector sum to get the resultant force.

**FAQs**

**What is the electric force formula?**

What is the formula of electric force? Electric force formula can be obtained from Coulomb’s law as follows: $$\vec F = K\frac{q_0.q_1}{r^2}\hat{r}$$ Where \(\vec{F}\) is the electric force-directed between two charged bodies.

**What are the examples of electric force?**

Electric circuits, A charged bulb, Exertion of static friction which is formed when a cloth is being rubbed by a dryer.

**What is the law of electric force?**

Coulomb’s law states that the electrical force between 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 the two objects.

**What is the symbol for electric force?**

\(F_E\)

**What are two applications of electric force?**

- The Van de Graaff Generator.
- Xerography.
- Laser Printers.
- Ink Jet Printers and Electrostatic Painting.
- Smoke Precipitators and Electrostatic Air Cleaning.

**Why is electric force important?**

In general, electrostatic forces become important when particle material is electrically insulating so the electric charge can be retained. In electrophotography, electrostatic forces are utilized to move charged toner particles from one surface to another for the purpose of producing high-quality prints.