K

Krish Gupta

Daniella Garcia-Loos

Coulomb's Law Constant

In this section, we will basically go over some important units and constants. Two main constants used in this unit that might be very new to you are k and *ϵ*.

k is known as the Coulomb's Law constant. You have not yet learned about Coulomb's law yet, but you will in the next section. Here, we are just going to familiarize you with some constant you'll see before we tackle the most important equation in electricity. Coulomb's Constant shows up not only in Coulomb's Law, but in many equations that you will encounter in this unit. This constant has some cool history behind it so let's do a short segment of story time.

Oliver Heaviside was an electrical engineer who noticed that when he was dealing with charge distributions and electric fields, he would always see a factor of 4*π* along with another new constant (*ϵ0)* which we will learn about later, especially in the denominator. So instead of writing 1/4*π**ϵ*0 every single time he just defined it as *k* and started writing *k*. 🤯

This is what is so special about Coulomb's constant. It itself is not super important in the derivation or theory but exists to make the math and work cleaner. So it's more of a shorthand notation constant. Because the constant itself is not necessary, you will see some books still use the full notation with the 1/4\pi*π*\epsilon_0*ϵ*0. This constant works best when we have symmetrical charges and objects which is most of the time. That's why it's not an SI unit, but more of a formality. That's why it's also called a rationalized unit.

Coulomb's law constant, denoted by the symbol "k", is a constant that appears in Coulomb's Law, which is a mathematical expression that describes the electrical force between two charged particles. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between the charges. Coulomb's Law can be written as:

F = k * (q1 * q2) / r^2

where F is the electrical force between the two charges, q1 and q2 are the charges of the two particles, r is the distance between the two charges, and k is Coulomb's law constant.

Here are some **key points to remember about Coulomb's law constant**:

- Coulomb's law constant is a constant that appears in Coulomb's Law, which is a mathematical expression that describes the electrical force between two charged particles.
- Coulomb's law constant has a value of approximately 8.9875 x 10^9 N*m^2/C^2.
- Coulomb's law constant is a constant that describes the strength of the electrical force between two charged particles.
- Coulomb's law constant is used to calculate the electrical force between two charged particles by multiplying the product of the charges by the constant and dividing by the square of the distance between the charges.
- Coulomb's law constant is a universal constant that is the same for all charged particles in the universe.

Permeability vs, Permittivity

There are 2 very important characteristics of space and objects: permittivity and permeability. Permittivity is a measure of the obstruction due to an electric field. If something has relatively high permittivity, then the electric forces and fields will be weaker. Permeability is a measure of the flow of a magnetic field. High permeability means more flow of magnetic field/force.

As you saw above, permittivity is more about electricity and polarization, and permeability is more about magnetism. So, we will learn more about permeability later, and for now, we will focus on permittivity.

Keep note that we mentioned both these constants together, even though one of them comes up a couple of units later because they are connected. Light 💡 (EM waves) is a topic that brings them together. You'll learn about electricity now, and magnetism soon, and finish the course with light, optics, and modern physics. The speed of light, arguably the most fundamental number in physics, is derived from these 2 constants. That is the beauty of physics!

Electric Permittivity

The constant *ϵ* is called permittivity. We measure permittivity relative to the permittivity of free space or a vacuum. We notate the permittivity of free space as *ϵ*0.

We can measure the permittivities of other objects relative to a vacuum. Relative permittivity (*ϵr*), also known as the dielectric constant (*κ*), is simply calculated by *ϵ*/*ϵ*0. We will come back to the dielectric constant later when we learn about conductors and circuits!

There isn't much to know more about this constant until you get into modern physics. The nuances of this constant are beyond the scope of this course and even many college courses!

Permeability and permittivity are physical properties that describe the ability of a material to transmit or allow the flow of electromagnetic waves, such as radio waves or light.

Permeability is a measure of how easily a magnetic field can pass through a material. It is represented by the letter "μ" (mu).

Permittivity is a measure of how easily an electric field can pass through a material. It is represented by the letter "ε" (epsilon).

Here are some **key points to remember about permeability and permittivity**:

- Permeability and permittivity are physical properties that describe the ability of a material to transmit or allow the flow of electromagnetic waves.
- Permeability is a measure of how easily a magnetic field can pass through a material, while permittivity is a measure of how easily an electric field can pass through a material.
- The permeability and permittivity of a material can affect the speed and intensity of electromagnetic waves as they pass through the material.
- The permeability and permittivity of a material can be affected by temperature, pressure, and other external factors.
- The permeability and permittivity of a material can be different for different types of electromagnetic waves, such as radio waves, light, or microwaves.

Permittivity Values

Substance | Permittivity (C^2/Nm^2) | Relative Permittivity |

Vacuum | 8.85x10^-12 | 1.00000 |

Air | 8.85x10^-12 | 1.00054 |

Paper | 25x10^-12 | 3 |

Water | 7.1x10^-10 | 80 |

As you can see from the table above, the relative permittivity of air to vacuum is extremely close to 1. So for the sake of our calculations, we can pretend we are in a vacuum and make calculations because the difference would be insignificant.

Practice Question:

1. Body tissue has a relative permittivity of 8. Find the permittivity of body tissue.

Answer:

- Since body tissue has a relative permittivity of 8 that means it's permittivity is 8 times the permittivity of a vacuum. The permittivity of vacuum/free space is ϵ0 = 8.85x10^-12 C^2/Nm^2 and that times 8 gives us roughly ϵB = 71x10^-12 C^2/Nm^2.

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