Coulomb's Law: Study with Video Lessons, Practice Problems & Examples

Coulomb's Law is essential for understanding the forces between charged particles, as it allows the calculation of potential energy, which is proportional to the magnitude of the charges and inversely proportional to the distance between them. The law's formula is:

$E=k\frac{Q_1{Q}_2}{r^2}$

where E represents the potential energy or force, k is the permittivity constant ($9.0\times {10}^9 N·m^2/C^2$), Q1 and Q2 are the charges of the particles, and r is the distance between the ion centers in meters. The absolute charge of an ion is $1.602\times {10}^{-19} C$. This relationship indicates that a greater potential energy corresponds to a stronger ionic bond. Understanding Coulomb's Law is crucial for predicting the behavior of ionic compounds and the strength of their bonds.

Coulomb's Law Concept 1

Now Coulomb's law is used to determine the attractive and repulsive forces between a pair of charged particles. Now using Coulomb's law formula allows you to determine the potential energy between the particles.

Now we're going to say that potential energy is directly proportional to the charges of the particles, meaning the larger the charges, the larger the potential energy. But potential energy is inversely proportional to the distance between the particles. So basically, the larger the distance between the particles, the lower their potential energy will be.

And what we need to realize here is that the greater the potential energy than, the stronger the ionic bond between our opposed charges will be or charged particles will be. So just remember these fundamental theoretical ideas behind Coulomb's law.

Click on the next video and let's investigate Coulomb's law formula.

Coulomb's Law Concept 2

With Coulomb's law we have our Coulomb's law formula where E which is our potential energy or force in Newtons. In physics you would see this variable as 14π, same variable with sub zero, but for simplicity I'm just having it as that single variable. Here we're going to say that it is in place of what we call the permittivity constant which is 9.0×109 Newtons times meters squared over Coulomb squared.

Q1 and Q2 represent our particles one and two that are in Coulombs, or absolute charge R, which down here would actually be R2 equals the distance of the ion centers in meters. Now finally, just remember that the absolute charge of an ion is equal to 1.602×10-19 Coulomb's. That would mean that if you had a charge of let's say +2, that's your absolute charge. But how would you convert it to Coulomb? You would just multiply it by that same value and that would be 3.204×10-19 Coulombs.

So now that we know Coulomb's law formula, let's move on to the next video and take a look at the example question.

Coulomb's Law Example

A charge of +4.13 * 10^-19 coulombs is placed 8.03 * 10^-7 meters apart from another charge of -3.37 * 10^-17 coulombs. What is the force of attraction between the charged particles? Now we know there's a form of attraction because they have opposite signs. One's positive, one's negative. In chemistry, opposites attract.

So, potential energy equals our permittivity constant, which is 9.0 * 10⁹ Newtons times meters squared over Coulomb squared. That's going to multiply with the two charges Q1 and Q2. And then we have our radius squared. When you do this, notice what's going to cancel out? Our meter squares cancel out and our Coulomb squares cancel out.

We'll have our answer in Newtons, which comes out to -1.94 * 10^-13 Newtons. So this would be the attraction felt between the two charged particles.

A force of 3.24 x 10^-12 N exists between a +3 charge and another charged particle. The ions are 2.53 x 10^-8 m apart. What is the charge of the unknown charged particle?  (Rework numbers since you went from +15 to +3)

• A. 4.79 x 10^-19 C
• B. 7.59 x 10^-18 C
• C. 5.89 x 10^-18 C
• D. 4.12 x 10^-19 C

Here’s what students ask on this topic:

What is Coulomb's law?

Coulomb's Law is a fundamental principle in physics, named after the French physicist Charles-Augustin de Coulomb who introduced it in the 1780s. It describes the force between two charged objects. According to Coulomb's Law, the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between their centers.

The law is often expressed by the equation:

F = k * (|q₁ * q₂| / r²)

where:

• F is the force,
• q₁ and q₂ are the charges,
• r is the distance,
• k is Coulomb's constant (8.9875 x 10⁹ Nm²/C² in vacuum).

The force is attractive if the charges have opposite signs and repulsive if they have the same sign. Coulomb's Law is a cornerstone in the study of electrostatics and plays a crucial role in understanding the interactions between charged particles.

What is "k" in Coulomb's law?

In Coulomb's Law, "k" represents the Coulomb's constant, which is a proportionality factor that helps to determine the magnitude of the electrostatic force between two point charges. The value of "k" depends on the medium in which the charges are located and the units used for measurement. In a vacuum, "k" is approximately equal to 8.9875 × 10⁹ N m²/C² when using the International System of Units (SI). This constant arises from the equation:

$F=k\cdot \frac{|q_1\cdot q_2|}{r^2}$

where F is the force between charges, q₁ and q₂ are the magnitudes of the charges, and r is the distance between the centers of the two charges. Coulomb's constant allows us to calculate the force of attraction or repulsion between two charged particles accurately.

What are q₁ and q₂ in Coulomb's law?

In Coulomb's law, Q₁ and Q₂ represent the magnitudes of electric charges on two point charges for which you are calculating the electrostatic force between them. The law states that the electrostatic force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (Q₁ and Q₂) and inversely proportional to the square of the distance (r) between their centers. The formula is given by:

$F=k\frac{|Q{}_1\cdot Q{}_2|}{r^2}$

Here, k is Coulomb's constant (approximately $8.9875\times {10}^9 N·m^2/C^2$ in a vacuum), and r is the distance between

What is Coulomb's law used for?

Coulomb's law is a fundamental principle in physics that quantifies the electric force between two charged objects. It states that the force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (q₁ and q₂), and inversely proportional to the square of the distance (r) between their centers. The law is mathematically expressed as:

$F=k\cdot |q{}_1\cdot q{}_2|/r^2$

where k is Coulomb's constant.

Coulomb's law is used to calculate the magnitude and direction of the electrostatic force in various applications, such as determining the strength of the electric field generated by a particular charge distribution, analyzing the forces between charged particles in atomic and molecular systems, and in the design of electrical equipment and circuits. It is also essential for understanding concepts like electric potential energy and is foundational for studies in electromagnetism and electronics.