Electrostatics

Electrostatic Charge

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

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

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 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.

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.

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.

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?

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.