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Coulomb’s Law

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Coulomb’s Law

Over the years, experiments, especially those conducted by Charles-Augustin de Coulomb, have shown that two or more electric charges exert a force on each other. One of the most interesting and important things about this force is that it is independent of the mass of the objects under study. To understand the quantities this force depends on, we have to study Coulomb’s law.

Coulombs law definition and equation

Coulomb’s law is a law of physics that states when two or more electrically charged objects are close enough to each other, they exert a force on each other. The magnitude of this force is proportional to the net charge of the particles and inversely proportional to the square of the distance between the particles under study.

This is how we write Coulomb’s law mathematically:

F is the magnitude of the force between the charges, q1 and q2 are the charges measured in Coulombs, r is the distance between the charges measured in metres, and k is Coulombs constant with a value of 8.99 ⋅ 109 N·m2/C2.

The force is called the electrostatic force, and it is a vector quantity measured in Newtons.

Coulombs law: electrostatic force between two charges

It is important to note that there are two forces when two electric charges exert a force on each other. Take a look at the image below: the first force is the force that the first charge exerts on the second charge F12, and the second force is the force that the second charge exerts on the first charge F21. We know that like charges repel and unlike charges attract each other. In physics, this is none other than the electrostatic force itself.

Coulomb’s law Like and unlike charges electrostatic force on each other StudySmarterLike charges repel (above) and unlike charges attract each other (below), Oğulcan Tezcan - StudySmarter Originals

It is important to know that the electric force F is not a constant. When charges exert forces on each other, they either come closer or push each other apart. As a result, the distance between them (r) changes, which affects the magnitude of the electric force between them.

For this explanation, we are looking into electrostatic forces, where static” refers to the constant position for the source charges.

A hydrogen atom in its ground state consists of one electron and one proton. Calculate the force exerted on the proton by the electron if the distance between the two is 5.29 ⋅ 10-11 meters.

Solution

We know that electrons and protons have the same charge except with a different sign. In this example, we treat both the electron and proton as point charges. Lets state the electron as q1 and the proton as q2.

The distance between the two charges is also given in the question. Lets put the known variables into Coulombs law.

Since the charges are taken as point charges, the force the proton exerts on the electron will be the same. Thus, the direction of this force will be an attractive force (towards each other) since unlike charges attract.

Coulombs law: electrostatic force between multiple charges

We now know what happens when two charges exert forces on each other, but what happens when multiple charges exist? When there are multiple charges affecting one another, we must take two charges at a time into account.

The goal here is to find the net electrostatic forces these multiple charges exert on another point charge called the test charge. The reason behind this is to find the magnitude of the electrostatic force these multiple charges can provide. To find the net electrostatic force on the test charge, we use the principle of superposition. This principle allows us to calculate each charges individual electrostatic force on the test charge and then add these individual forces together as vectors. We can express this mathematically as follows:

Q is the test charge.

In figure 2, given that q1 = 2e, q2 = -4e, the charge of the test charge is Q = -3e, and d = 3.0 ⋅ 10-8m, find the net electrostatic force exerted on the test charge Q.

Coulomb’s Law Electrostatic force between multiple charges StudySmarterDiagram showing three point-like particles exerting electrostatic forces on each other, Oğulcan Tezcan - StudySmarter Originals

Solution

Since the charges and distances between these charges are given in the question, we start by finding one of the forces magnitude. Let’s find F2Q first.

Since q2 and Q are like charges, this force will be exerted on Q in the left direction on the x-axis. Now lets find the magnitude of the electrostatic force exerted on Q by q1.

Since q1 and Q are unlike charges, this force will be in the up direction on the y-axis. We must add these two vectors together to find the net electrostatic force exerted on the charged particle Q. We can see that:

If we put in the values we have found, we get:

And to find the angle between the x-axis and the resultant force vector, we can find the tangent of the angle a.

And if we solve for a, we get:

Coulombs Law - Key takeaways

  • Coulomb’s law is a law of physics that states when two or more electrically charged objects are close enough to each other, they exert a force on each other.
  • The magnitude of this force is proportional to the net charge of the particles and inversely proportional to the square of the distance between the particles.
  • The force charges exert on each other is called the electrostatic force.
  • Like charges repel and unlike charges attract each other.
  • When finding the resultant electrostatic force between multiple charges, we take two forces at a time and calculate their electrostatic forces. We then add all the forces together (as vectors) to find the resultant force.

Frequently Asked Questions about Coulomb’s Law

Coulomb’s law is a law of physics that states when two or more electrically charged objects are close enough to each other, they exert a force on each other. The magnitude of this force is proportional to the net charge of the particles and inversely proportional to the square of the distance between the particles under study.

You can find q1 and q2 in Coulomb’s law by using the equation: F = k . (q1.q2/r2) where F is the magnitude of the force between the charges, q1 and q2 are the charges measured in Coulombs, r is the distance between the charges measured in metres, and k is Coulomb's constant with a value of 8.99 ⋅ 109 Nm2/C2.

Coulomb’s law is only valid for point-like charges. This is due to the fact that when the two charged bodies are put together, the charge distribution does not remain uniform.

Final Coulomb’s Law Quiz

Question

Which of the following is true for like particles?

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Answer

They repel each other.

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Question

Which of the following quantities does the electrostatic force between two charges not depend on?

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Answer

The mass of the particles. 

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Question

Which of the following describes the relationship between the magnitude of the electrostatic force between two particles and the distance between them?

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Answer

They are inversely proportional.

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Question

What is Coulomb’s law?

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Answer

Coulomb’s law is the law that states when two or more electrically charged objects are close enough to each other, they exert a force on each other called the electrostatic force.

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Question

Why is Coulomb’s law valid for point charges?

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Answer

Coulomb’s law is only valid for point-like charges. This is due to the fact that when the two charged bodies are put together, the charge distribution does not remain uniform.

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Question

Two charges are given with the values q= (1e) and q= (-1e) and the distance between them is given as r = 6.58 ⋅ 10-11 meters. What is the value of the electrostatic force exerted on q1?

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Answer

3.51 ⋅ 10-18N

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Question

Is electrostatic force a vector or a scalar quantity?

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Answer

A vector quantity.

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Question

Which principle is used when finding the net electrostatic force acting on a charge particle by multiple charges?

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Answer

Superposition principle.

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Question

Why is electric force not constant?

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Answer

Because when charges push or pull each other, the distance between them changes.

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Question

What is the name of the electric force of particles with a constant position?

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Answer

The name of the electric force of particles with a constant position is the electrostatic force.

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Question

Which of the following laws of physics states “when two or more electrically charged objects are close enough to each other, they exert a force on each other”?

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Answer

Coulomb’s Law.

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Question

Which of the following is the symbol for the charge of a particle?

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Answer

q

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Question

Does the electrostatic force between two charges depend on the distance between them?

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Answer

Yes.

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Question

Does the electrostatic force between two charges depend on the mass of the charges?


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Answer

No.

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Question

Which of the following units is used for charge?

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Answer

Coulombs.

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