Coulomb's Constant and the Speed of Light in Vacuum

In summary, Coulomb's constant, also known as the electric force or electrostatic constant, is a proportionality constant expressed as κ ≡ kC ≡ ke = 1/(4πε0) = 8987551787.36818 N•m2/C2 (exactly). This value can also be derived from the equation for lightspeed squared divided by ten million (c2/107). The seemingly unrelated dimensions of N•m2/C2 and m/s are related through the equation c = 1/√μ0εo, where the 4π factor in μ cancels out the 10^-7 in the magnetic permeation constant
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Coulomb’s (electric force, electrostatic) constant (symbol κ (kC, ke)) is a proportionality constant, expressed as:

κ ≡ kC ≡ ke = 1/(4πε0) = 8987551787.36818 N•m2/C2 (exactly)

κ can also be derived from lightspeed squared divided by ten million (c2/107)...

Can someone please help me understand how the two (seemingly unrelated) dimensions (N•m2/C2 vs. m/s) are related, the expressions yielding the exact same value?
 
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  • #2
Look at the equation for c. It has the electric field and magnetic field intrinsic to light, which is related to coulomb's constant

c = 1/√μ0εo

The μ has the 4π factor. The reason for the difference in dimensions is because you chose to divide by ten million because it gave you the right number. It cancels out the 10^-7 in the magnetic permeation constant
 
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Related to Coulomb's Constant and the Speed of Light in Vacuum

What is Coulomb's Constant?

Coulomb's Constant, denoted as k, is a proportionality constant that relates the amount of electric force between two charged particles to their distance and magnitude of charge. It is named after the French physicist Charles-Augustin de Coulomb, who first discovered it in the late 18th century.

What is the value of Coulomb's Constant?

The value of Coulomb's Constant is approximately 8.99 x 10^9 Nm^2/C^2. It is an exact value, meaning it does not depend on any other physical quantities and remains constant throughout the universe.

How is Coulomb's Constant related to the speed of light in a vacuum?

Coulomb's Constant and the speed of light in a vacuum (c) are related through the permittivity of free space (ε0). This is because ε0 is a fundamental constant that appears in the equations for both Coulomb's Constant and the speed of light. The relationship is given by k = 1/4πε0, where 1/4πε0 is equal to approximately 8.99 x 10^9 Nm^2/C^2.

Why is the speed of light in a vacuum important in relation to Coulomb's Constant?

The speed of light in a vacuum is important in relation to Coulomb's Constant because it is the maximum speed at which any material object or information can travel. This means that the electric force between two charged particles also travels at this speed, and it is essential in understanding and calculating the behavior of electric fields and charged particles.

How are Coulomb's Constant and the speed of light in a vacuum used in science and engineering?

Coulomb's Constant and the speed of light in a vacuum are used in a wide range of scientific and engineering applications. They are crucial in understanding electromagnetism, which is the foundation of many modern technologies such as electric motors, generators, and telecommunications. They are also used in various calculations and experiments in fields such as physics, chemistry, and engineering.

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