How to Use Coulombs Law and How Capacitors Work for Beginners

Coulomb's Law relates electrical charge to the distance between the electrically charged objects. Coulomb's Law is used in electromagnets and capacitors, making it one of the most important laws when learning about electrical circuits.

Charles-Augustin de Coulomb, a French physicist, first formulated this important law in 1787, changing the way we understand electricity. In this article, we will look at how to use Coulomb's Law, what it is, what Coulomb's Law is used for, and how capacitors work all explained simplistically for beginners.

What is Coulomb's Law?

Coulomb's Law calculates the electrostatic force between two charged particles based on the magnitude of their charges and how far apart they are.

This may look and sound intimidating, so let's break it down simply.

Electrostatic Forces and Charged Particles

Electrostatic force is the push or pull caused by an electric charge.

Electric charges can either be positive or negative. Like magnets, like charges repel, and opposite charges attract. This means

• Two positives/negatives will repel (push away)
• One positive and one negative will attract (pull together)

These electric charges acts similarly to a magnet, except instead of magnets, it's electric charge doing the pushing and pulling.

Electrons carry negative charge, while protons carry positive charge. What makes these particles interesting is that they can exert an electrostatic charge on one another without even touching. In circuits, electrostatic forces mainly come from electrons.

Like any other force (rolling a ball, pushing a block, etc.), electrostatic force is measured in Newtons ($N$).

A common example of an electrostatic force is static electricity. When you rub a balloon on your hair, electrons move from your hair onto the balloon. This gives the balloon an excess of negative charge and leaves your hair positively charged.

Because opposite charges attract, the negatively charged balloon and the positively charged hair pull toward each other, causing the balloon to stick to your hair or make your hair stand up.

What are the Units of Coulombs?

Coulombs measure the amount of electric charge, like how meters measure the quantity of length.

The coulomb what we call an SI base unit, meaning it is not defined in terms of other electrical units like volts or ohms, which are derived units.

Coulombs can be described mathematically as:

$C = A \cdot s$ or $Q = I \cdot t$

This means that one coulomb is equal to one ampere of current flowing for one second.

Electric charge itself comes in small, fundamental units called elementary charges. An elementary charge is the amount of charge carried by a single proton or electron (negative in the case of an electron). A single coulomb represents a very large number of these elementary charges; about $6.24 \times 10^{18}$ of them.

Coulomb's Law Mathematical Formula

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

Where

• $F$ is the electrostatic force in Newtons ($N$).
• $k$ is Coulomb's constant, which is $8.99 \times 10^9 \frac{N\cdot m^2}{C^2}$, but often rounded to $9 \times 10^9$ for simplicity.
• $q_1$ and $q_2$ are the magnitudes of the charged particles, measured in coulombs ($C$).
• $r$ is the distance between the center of the two charges measured in meters ($m$).

How To Use Coulomb's Law

Let's take a look at some practice problems for Coulomb's Law.

Beginner Level (Calculating Electrostatic Force)

A particle of $-10\mu C$ is $0.5$ meters away from another particle of $5\mu C$. What is the electrostatic force between these two particles? Is this force attractive or repulsive? Round Coulomb's constant to $9 \times 10^9$ for simplicity.

Intermediate Level (Amperes to Coulombs)

A current of $2A$ flows through a wire for $5$ seconds. How much electric charge passes through the wire?

What is Coulomb's Law used for in Real Life?

As Coulomb's Law tells us, if we shove a bunch of electrons on a metal plate, they will repel each other because they are of a like charge.

However, if there was another plate nearby that held an opposite charge, the electrons would be attracted to the other plate and be held in place, storing electrical energy.

This is how capacitors work. If you aren't familiar with what a capacitor is, check out this article about the essential electronics components.

This electrical energy that's stored is called capacitance, measured in farads ($F$).

What are Farads?

Farads are a measure of capacitance. Mathematically, capacitance is described as

$C = \frac{Q}{V}$

Where

• $C$ is the capacitance, in farads ($F$)
• $Q$ is the charge, in coulombs ($C$)
• $V$ is the voltage, in volts ($V$)

Practice Problem with Farads, Coulombs, and Amperes

A capacitor of $47\mu F$ has $5V$ applied to it for $5$ seconds. How much electric charge is stored? What is the average current drawn in these $5$ seconds?

Conclusion

Coulomb's Law explains how electric charges interact through attraction and repulsion. By understanding how charge, distance, and force relate, we get a fundamental way to understand why electrons move, why static electricity occurs, and how electrical energy can be stored.

In this article, we explored what Coulomb's Law is, how electrostatic forces work, how electric charge is measured in coulombs, and how these ideas connect to real world applications like capacitors and capacitance (measured in farads). By working through practice problems, we also saw how Coulomb's Law links to current, voltage, and time.

Coulomb's Law is not just a formula to memorize, it's something to understand why it works and how it works. Learning about Coulomb's Law enables you to better understand concepts like Faraday's Law.

For beginners trying to learn about electronic circuits, Coulomb's Law is one of the fundamental laws of circuits that are important to understand.