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# Electrostatics

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Did you know that the plastic wrap we use to wrap our package is called cling film? You must have noticed that it clings to your arm while unpacking. Well, there are two cases behind this and a single phenomenon. Let's start with each case. The first case is a rub between wraps. Due to the friction between wraps, electrons are transferred from one wrap to another, causing a net positive charge on one wrap (due to loss of electrons) and a net negative charge on another wrap (due to gain of electrons). This charged wrap balances its charge after coming into contact with our body (a conductor). The second case is the direct rubbing of plastic wrap against our arms. In this case, due to charging by friction, electrons are transferred from our arm to the plastic wrap causing a net negative charge on the plastic wrap and a net body positive charge on our arm. Now the question is, what generates the cling between our body and the plastic wrap? The phenomenon that explains this is an electrostatic force of attraction between unlike electric charges.

Fig. 1 - The figure shows a hand clinging to a plastic wrap due to an electrostatic force of attraction.

Plastic wrap is an insulator, so, when it becomes charged due to rubbing, the charge will continue to remain at rest. The study of these electric charges and their properties is called electrostatics. In this article, we will learn about the properties of static charges, an electrostatic force between like and unlike charges, an electric field, and an electric potential.

## Electrostatic Charge

Before we can talk more in depth about electrostatics, we must define what is electric charge.

Electric charge is a fundamental property of matter that causes particles or objects with this property to experience a force when placed inside an electromagnetic field.

Matter is composed of atoms. Each atom contains electrons, protons, and neutrons, where neutrons and protons are present inside the nucleus, and electrons revolve around the nucleus. Electrons are negatively charged, and protons are positively charged subatomic particles. This narrows down the types of charges to positive and negative.

The SI unit of electric charge is the coulomb $$\left(\mathrm{C}\right)$$.

One coulomb is the amount of charge carried by a steady current of one ampere in one second while traveling through a conductor.

The magnitude of the electric charge on a single electron or a proton is $$1.6\times10^{-19}\,\mathrm{C}$$. This value is called the elementary charge. Its small value indicates that one coulomb of charge is made up of quite a large number of electrons. In fact, $$6.25\times10^{18}$$ electrons/protons are required for a magnitude of one coulomb of charge.

By convention,

1. For a positive charge, the plus $$\left(+\right)$$ sign is used, e.g. $$q_\text{1}=+2\,\mathrm{\mu\,C}.$$
2. For a negative charge the minus $$\left(-\right)$$ sign is used, e.g. $$q_{\text{2}}=-2\,\mathrm{\mu\,C}.$$

From the above conventions, it is clear that a negative and a positive sign on a charge value represent its type/polarity instead of direction.

In other words, an electric charge only has a magnitude and no direction, making it a scalar quantity.

In an extensive system of charges, the size of charged bodies is tiny compared to the distance between them. So, instead of taking charge distribution on the surface of each charge body, it is assumed to be focused at the center point of each body, such that these charged bodies behave as point charges. We need to understand the properties of these point charges to deal with extensive systems of multiple charges. Three basic properties of these point charges are,

1. Additivity - The net electric charge of a system is equal to an algebraic sum of individual electric charges present in the system.

2. Conservation of electric charge - Net electric charge of an isolated system remains conserved.

3. Quantization - The amount of charge added or removed from a system is an integral multiple of the fundamental unit of charge, i.e., $$Q=ne$$ where $$n=\pm1,\pm2,\pm3,...$$ is an integer, and $$e=1.6\times10^{-19}\,\mathrm{C}$$ is the fundamental unit of charge.

There are two possible interactions between the static charges. First is like charges repel each other, and second is unlike charges attract each other.

Fig. 2 - The figure shows the repulsion between like charges and an attraction between unlike charges.

Coulomb's law explains the force acting between the charges. Let's learn about Coulomb's law to understand the force acting between like and unlike charges.

## Electrostatic Definition

Knowing all that, we can finally define what is electrostatic force in particular.

The electric force acting between static charges is called an electrostatic force.

Coulomb's law is an experimental law of physics that explains the magnitude of this force acting between electrical charges in terms of the magnitude of each charge and the distance between their centers. In this part, we will discuss the mathematical form of Coulomb's law, conventions for electrostatic force, and a comparison between gravitational force and an electrostatic force.

According to Coulomb's law, an electrostatic force acting between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

## Electrostatic Formula

Imagine two charges with opposite polarities ($$+q_1$$ and $$-q_2$$) are placed at a distance $$r$$. By using Coulomb's law, an electrostatic force acting on $$-q_2$$ due to a charge $$+q_1$$ is,

$\left|\vec{F_{21}}\right|=k\frac{\left|-q_1\,q_2\right|}{r^2}$

where $$k=9\times10^{9}\,\mathrm{N\,m^2\,C^{-2}}$$ is an electrostatic force constant. Another way to write the expression from above is

$\left|\vec{F_{21}}\right|=\frac{1}{4\pi\varepsilon_\circ} \frac{\left|-q_1\,q_2\right|}{r^2},$

where $$\varepsilon_\circ=8.85\times10^{-12}\,\mathrm{C^{2}\,N^{-1}\,m^{-2}}$$ is the electrical permittivity of free space/vacuum.

In the diagram below, we can see a negative sign in the force value. This negative sign indicates an attractive force acting on charge $$q_2$$ due to charge $$q_1$$. In the case of a repulsive force, a positive sign is used.

Fig. 3 - The figure shows an electrostatic force acting on charge $$q_2$$ due to charge $$q_1$$.

### Similarities and Differences between Gravitational Force and Electrostatic Force

Like the gravitational force, an electrostatic force is a central force, i.e., it acts along the line joining two charged bodies. Both forces follow the inverse square law (i.e. force is inversely proportional to the square of the distance between bodies) and are non-contact forces (no direct contact is required between the two bodies for a force to be exerted on one another). Some of the major differences between a gravitational force and an electrostatic force are highlighted in the following table.

Table 1 - Differences between gravitational and electrostatic forces.

 No. Gravitational Force Electrostatic Force 1. Gravitational force acts between the bodies due to their mass. An electrostatic force acts between the bodies due to their charge. 2. It does not depend upon the medium. It depends upon the medium. 3. It is only attractive. It is attractive as well as repulsive in nature. 4. It is a long-range force. It is a short-range force.

In the next part, we will learn about this physical field around a source charge (a charge which applies an electrostatic force) within which a test charge (charge on which an electrostatic force is applied) experiences a force.

## Electrostatic Field

What is an electric field?

An electric field is a region around a source charge in which other charged bodies experience an electrostatic force.

In other words, an electric field is also defined as an electrostatic force per unit charge.

$\vec{E}=\frac{\vec{F}}{q},$

Where $$\vec{F}$$ is an electrostatic force, and $$q$$ is a test charge.

The above equation shows that,

1. The electric field is in the same direction as an electric force for a positive test charge.
2. The electric field is in the opposite direction as an electric force for a negative test charge.

The unit of an electric field around a source charge exerting a force of one newton on a test charge of one coulomb is newton per coulomb $$\left(\mathrm{N\,C^{-1}}\right)$$.

There are two methods to represent an electric field in the diagrams,

1. Electric field vectors,

2. Electric field lines.

The direction of the electric field in both cases points radially outward from positive charges so that positive charges act as the sources of the field, and radially inward towards negative charges so that negative charges act as the sinks of the electric field.

Imagine a source charge $$+Q$$. Using the above methods, the diagrammatic illustration of the electric field around the source charge is as follows.

### Electric Field Vector

In this method, the direction of an electric field is represented using vectors around a source charge. The vector's length represents the magnitude, and the vector's arrow represents the direction of the electric field.

Fig. 4 - The figure shows electric field vectors radially outward from a source charge $$+Q$$.

### Electric Field Lines

In this method, arrows indicate the direction of the electric field. The closeness of the lines represents the electric field's strength. A tangent on an electric field line gives the direction of an electric field.

Fig. 5 - The figure shows electric field lines radially outward from a source charge $$+Q$$.

## Electrostatic Examples

There are many possible examples of electrostatic phenomena in real life. Some of them are,

1. The attraction of our dry hair toward a comb is due to an electrostatic force of attraction between dry hair and the comb.
2. The collection of dust particles on a television screen is due to the electrostatic force of attraction between the television screen and dust particles.
3. The ink stick on the paper in a photocopier machine is due to electrostatic attraction between paper and ink.
4. The electric shocks from a door knob are due to the collection of positive electrostatic charge on the knob.
5. Sticking rubbed balloons on the walls is due to the electrostatic force of attraction between balloons and walls.

## Electrostatics - Key takeaways

• Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field.
• The SI unit of an electric charge is the coulomb $$\left(\mathrm{C}\right)$$.
• One coulomb is the amount of charge carried by a steady current of one ampere in one second while traveling through the conductor.
• The fundamental value of an electric charge is $$1.6\times10^{-19}\,\mathrm{C}$$.
• Three basic properties of an electric charge are additivity, quantization, and conservation.
• According to Coulomb's law, an electrostatic force acting between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them, i.e., $$F=k\frac{q_1 qa_2}{r^2}$$, where $$k$$ is an electrostatic force constant, $$q_1$$ is a test charge, $$q_2$$ is a source charge, and $$r$$ is a distance between a source and a test charge.
• A physical field around a source charge in which other charged bodies experience an electrostatic force is called an electric field.
• An electric field is also defined as an electrostatic force per unit charge, i.e., $$E=\frac{F}{q}$$, where $$F$$ is an electrostatic force, and $$q$$ is a test charge.

## References

1. Fig. 1 - Person holding white plastic bag (https://unsplash.com/photos/UZOdna5_kRU) by Luis Cortés (https://unsplash.com/@luiskcortes) under Unsplash license (https://unsplash.com/license).
2. Fig. 2 - Attraction between unlike charges and repulsion between like charges, StudySmarter Originals.
3. Fig. 3 - Electrostatic force of attraction between unlike charges, StudySmarter
4. Fig. 4 - Electric field vector to represent an electric field, StudySmarter Originals.
5. Fig. 5 - Electric field lines around a positive source charge, StudySmarter Originals.

Electrostatic charge is a fundamental property of matter that causes particles or objects which have this property to experience a force when placed inside an electromagnetic field.

The properties of electrostatic charge are,

2. Conservation
3. Quantization

According to Coulomb's law, an electrostatic force acting between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

An electrostatic field is a region around a source charge in which other charged bodies experience an electrostatic force.

The electric force with which static charges attract or repel each other is called an electrostatic force.

There are many possible examples of electrostatic phenomena in real life. Some of them are,

1. The attraction of our dry hair toward a comb is due to an electrostatic force of attraction between dry hair and the comb.
2. The collection of dust particles on a television screen is due to the electrostatic force of attraction between the television screen and dust particles.
3. The ink stick on the paper in a photocopier machine is due to electrostatic attraction between paper and ink.
4. The electric shocks from a door knob are due to the collection of positive electrostatic charge on the knob.
5. Sticking rubbed balloons on the walls is due to the electrostatic force of attraction between balloons and walls.

## Electrostatics Quiz - Teste dein Wissen

Question

Neutral particles contain

an equal number of protons and electrons.

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Question

What is the fundamental value of an electric charge?

$$1.6\times10^{-19}\,\mathrm{C}$$.

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Question

According to Coulomb's law, the force of attraction or repulsion between two charged bodies is _____ proportional to the product of their charges.

directly.

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Question

According to Coulomb's law, the force of attraction or repulsion between two charged bodies is ____ proportional to the square of the distance between them.

inversely.

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Question

Coulomb's law is given by the formula

$$F=k\frac{q_1q_2}{r^2}$$.

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Question

Electric field is a ____.

vector quantity.

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Question

The SI unit of an electric charge is ____.

coulomb $$\left(\mathrm{C}\right)$$.

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Question

Electrostatic is a branch of physics that deals with moving charging.

False.

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Question

Electrostatic is a branch of physics that deals with static charges.

True.

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Question

Which of the following are the properties of electric charge?

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Question

Electric field $$\left(E\right)$$ in terms of an electrostatic force $$\left(F\right)$$ and a test charge $$\left(q\right)$$ is

$$E=\frac{F}{q}$$.

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Question

An electrostatic force is also known as ____.

Coulomb force.

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Question

The electric field is directed radially outward from a positive charge and radially inward towards a negative point charge.

True.

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Question

The electric field is directed radially outward from a negative charge and radially inward towards a positive point charge.

False.

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Question

The SI unit of an electric field is

$$\mathrm{N\,C^{-1}}$$.

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