Electrostatics
Electrostatics is that branch of physics which deals with "static", i.e. constant in time, electric fields. A static electric field can only be achieved if the charges producing it are stationary.
However we will encounter some situations where the test charge will be moving without the above constraint. This is because the test charge by definition is a charge which produces a negligible amount of electric field thus not affecting the field around it.
The reason for studying electrostatics before electrodynamics ("dynamics" means movement) is that a detailed study of electromagnetism is quite complicated and hence some special conditions are imposed on the subject to make it easier. Once you understand electrostatics, I will be able to confront you with more challenging aspects of electromagnetism where the restrictions of electrostatics will be removed.
It was known before the time of Coulomb that all objects having mass attract each other by a force called gravity. Newton had given a mathematical equation to calculate such a force between two mass points. So you would expect all elementary particles to attract each other. But this is not what is found experimentally.
You would expect that two electrons, due to their masses, should attract each other by the quantitative law enunciated by Newton. However, contrary to this notion it is found that the two electrons repel each other. Similarly the protons which one would expect to attract, repel each other too.
Electric charge
It was known before the time of Coulomb that all objects having mass attract each other by a force called gravity. Newton had given a mathematical equation to calculate such a force between two mass points. So you would expect all elementary particles to attract each other. But this is not what is found experimentally.
You would expect that two electrons, due to their masses, should attract each other by the quantitative law enunciated by Newton. However, contrary to this notion it is found that the two electrons repel each other. Similarly the protons which one would expect to attract, repel each other too.
The interaction between a proton and an electron is also strange. Though they attract each other but the force of attraction between them is found to be much larger than what is being predicted by Newton's law.
These evidences indicate that there is one more property of Nature besides gravity which is responsible for such anomalous interactions. This property was named as charge.
Definition of charge: A property of matter by which an electron repels another electron.
Note that I did not say that charge is a property by which an electron attracts a proton. Why? Because they attract each other not only due to charge but because of gravity also.Two kinds of charges
Charges come in two categories which were named as positive and negative to signify their opposite nature.
It was found that:
- Positive and positive charges repel each other.
- Negative and negative charges repel each other.
- Positive and negative charges attract each other.
To put it in one sentence: Like charges repel while unlike charges attract.
By arbitrary convention the electron was said to possess a negative charge and the proton a positive charge. The word "negative" here does not mean that the charge of an electron is somehow inferior to the charge of the proton. If their signs were reversed, it would have made no difference to the workings of nature.
Quantization of charge
If something occurs only in discrete quantities then we say it is quantized and the smallest discrete unit in which it is found is known as its quantum.
Suppose that the minimum amount that the Indian government publishes its currency in is ₹1. Then a person can have only ₹1 or ₹2 or ₹3 or ₹100 or ₹1000000 etc. One cannot have ₹52.63 (say) because ₹.63 cannot exist. He can have ₹52 or ₹53 but not in between.
Hence Indian currency is quantized and ₹1 is its quantum.
A similar elegant result holds for charges. The minimum amount of charge that exists in Nature is
$e = 1.6 \times 10^{-19}$ coulomb
which is usually denoted by the letter $e$. A proton is found to possess this much charge. An electron too has the same charge but with a negative sign.
All other charges exist in integral multiples of this basic charge $e$.
So if an object has a charge $Q$ then the following result will always hold true:
\[ Q = ne \]
where $n$ belongs to integers, positive or negative.
where $n$ belongs to integers, positive or negative.
Conservation of charge
Charge can neither be created nor be destroyed. This means that the total amount of charge just after the Big Bang is equal to the total amount of charge at any time after it.
In the following two processes it seems on a first look that the conservation of charge law is being violated.
\[e^- + e^+ \rightarrow \gamma + \gamma \qquad \qquad (1) \] \[\gamma \rightarrow e^- + e^+ \qquad \qquad (2) \]
The process described by equation (1) is known as pair annihilation while equation (2) represents its inverse process called pair production.
\[e^- + e^+ \rightarrow \gamma + \gamma \qquad \qquad (1) \] \[\gamma \rightarrow e^- + e^+ \qquad \qquad (2) \]
The process described by equation (1) is known as pair annihilation while equation (2) represents its inverse process called pair production.
In equation (1) an electron combines with a positron (antiparticle of the electron) and they both annihilate each other to produce two gamma ray photons. (Each photon has an energy of at least 0.51 MeV.) The equation appears to have lost all charge on the right-hand side when it had two charges on the left.
Equation (2) describes the situation when a gamma ray photon produces an electron and a positron. (The photon should have an energy of at least 1.02 MeV for pair production to take place.) The equation seems to have created two charges out of nowhere as its left-hand side had no charge.
Well a careful look gives the following results.
The net charge on the left-hand side of equation (1) is zero since there is as much positive charge as negative charge. The charge on right is also zero. Hence no charge is lost as it didn't have any.
Similarly the right-hand side of equation (2) has a net charge of zero because the two charges will add up to zero.
Conservation of charge holds in both these processes.
Coulomb's Law
Just saying that like charges repel while unlike charges attract is obviously not the complete story. Two questions immediately arise:
1. What is the machinery behind this force? What causes the two charges to attract or repel each other?
2. What is the mathematical law governing the force?
The answer to the first question is beyond the scope of this article. Answer to the second one is described below.
After performing a series of experiments Coulomb came to the following correct conclusion. He found that the force $F$ between any two point charges $q_1$ and $q_2$ separated by a distance $r$ can be written as:
\[F = k\frac{q_1q_2}{r^2} \]
where $k$ is a constant called the Coulomb constant or the electrostatic constant. It depends on the medium in which the charges are placed.
For vacuum $k \approx 9 \times 10^9$ Nm2C-2.
For some reasons, physicists found it convenient to write $k$ as: \[ k = \frac{1}{4\pi\epsilon_0}. \]
Here $\epsilon_0$ is known as the permittivity of free space and its value is $\epsilon_0 = 8.85 \times 10^{-12}$ C2N-1m-2.
Therefore Coulomb's Law for vacuum becomes:
Therefore Coulomb's Law for vacuum becomes:
\[F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2}. \]
Coulomb's Law is valid only for point charges. (A point is an entity which has a position in space but no extent.) For larger objects with continuous charge distibutions, methods from the integral calculus should be used to calculate the required forces.(Image courtesy of Hal Gatewood at Unsplash)
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