# Coulomb Law: What Does k Mean & Why Is 4π Used?

• Bern123
In summary, "k" in Coulomb's law represents a constant that is related to the surface area of a unit sphere and the vacuum permittivity, which is closely linked to the speed of light. This form of "k" is used to make fundamental results in electromagnetism appear cleaner and is important in understanding the propagation of light and electromagnetic waves.
Bern123
What k mean in coulomb law? it's 1/(4π*ε) but why is in this form? 4π it's related to the shape of an atom?

Basically "k" has been given this strange, nonintuitive shape so that deep and fundamental results in electromagnetism look cleaner on the paper

$$4\pi$$ is the surface area of a unit sphere.

The "e" is the "vacuum permittivity", closely related to the speed of light in vacuum, "c", through the formula:
$$\epsilon_{0}\mu_{0}=\frac{1}{c^{2}}$$,
where $\mu_{0}$ is called the "magnetic constant". (That formula is now used as the DEFINITION of our "e")

When we look at propagation of light waves and electromagnetic waves in general, our number "e" is so closely related to it that it pops up everywhere, and therefore, Coulomb's law has been written in such a way to make that important constant explicit, rather than using a fuzzy "k".

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## 1. What is Coulomb's Law and how does it relate to electricity?

Coulomb's Law is a fundamental law in physics that describes the relationship between electric charges. It states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law is essential in understanding the behavior of electricity.

## 2. What does the constant k represent in Coulomb's Law?

The constant k, also known as the Coulomb constant, is a proportionality constant that relates to the permittivity of a vacuum. It has a value of 8.99 x 10^9 N*m^2/C^2 and is used to calculate the force between two point charges in a vacuum.

## 3. Why is 4π used in Coulomb's Law instead of just π?

The use of 4π in Coulomb's Law comes from the calculation of the electric field. Electric field lines spread out in all directions from a point charge, creating a spherical surface. The surface area of a sphere is 4πr^2, which is why 4π is used in the denominator of the equation to calculate the electric field.

## 4. How does Coulomb's Law apply to real-life situations?

Coulomb's Law is applicable to a wide range of real-life situations, including the behavior of electric charges in circuits, the movement of particles in particle accelerators, and the force between atoms in molecules. It is also used in the design of electronic devices, such as capacitors and batteries.

## 5. What are some common misconceptions about Coulomb's Law?

One common misconception about Coulomb's Law is that it only applies to point charges. In reality, it can also be used to calculate the force between two charged objects with finite sizes. Another misconception is that the force between two charges is always attractive. However, it can be either attractive or repulsive depending on the sign of the charges.

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