# Why Are The Units of Coulombs Law What They Are?

• PurelyPhysical
In summary: Coulomb's_lawIn summary, the units of force are used when applying Coulomb's law because the relationship between force and charge is expressed in the physical law discovered by Coulomb. The units of the constant K in the equation F = K(Q1Q2)/r^2 are worked out after the physical law is discovered, and the units of the constant must be Newton*Meter^2/Coulomb^2 in order for the equation to hold. This is why we can refer to Coulomb's law as a force, even though it involves units of charge.
PurelyPhysical
Why are the units of force used when applying coulombs law (N-M^2)/(C^2)? This is actually a three part question.

1. Why are the units of the permitivity constant (C^2)/(N-M^2)?
2. Why do Q1 and Q2 not contribute to the final units? Each charge is measured in coulombs, but those units don't reflect in the final units.
3. Units of force are Newtons. Why then can we say that coulombs law equals force? What's going on with the other units that makes it so that we can still refer to it as a force?

Q1 times Q2 is canceled out by Coulomb's constant (which contains a coulomb-2 term).

David Lewis said:
Q1 times Q2 is canceled out by Coulomb's constant (which contains a coulomb-2 term).
Thank you. That makes a lot of sense.

PurelyPhysical said:
Why are the units of force used when applying coulombs law (N-M^2)/(C^2)? This is actually a three part question.
3. Units of force are Newtons. Why then can we say that coulombs law equals force? What's going on with the other units that makes it so that we can still refer to it as a force?

There is nothing mysterious with the units that makes the final result to be expressed in units of force.
In physics the first thing are the physical laws. The relationship between the units (and the units of possible constants that are used, like the coulomb constant K) are worked out after we discover the physical laws.

In our case the physical law that Coulomb discover is that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance. In order to complete the equality we need a constant K so we can write down
##F=K\frac{Q_1Q_2}{r^2}## (1)
Now that we know this law holds, we can figure out the units of the constant K and the relationship between the units. So it will be because (1) holds

Newton=(units of constant K)*Coulomb*Coulomb/Meter^2. (2)

so the units of constant K have to be Newton*Meter^2/Coulomb^2 cause only if it is so then (2) holds.

Dale
Delta[2]

Do you mean F = [m1m2]/r^2?

Oh! What a popular equation! Newton, coulomb, La Place is there more?

## 1. What are the units of Coulomb's Law?

The units of Coulomb's Law are Newtons (N) for force, Coulombs (C) for electric charge, and meters (m) for distance.

## 2. Why are the units of Coulomb's Law in Newtons, Coulombs, and meters?

Coulomb's Law describes the force between two electrically charged particles, which can be calculated using the equation F = k * (q1 * q2)/r^2, where k is a constant. The units of force, electric charge, and distance are necessary for this equation to balance and make physical sense.

## 3. How do the units of Coulomb's Law relate to the fundamental units of the SI system?

The units of Coulomb's Law, Newtons (N), Coulombs (C), and meters (m), are all derived from the fundamental units of the SI system. N is derived from kg*m/s^2, C is derived from A*s, and m is a fundamental unit.

## 4. Can Coulomb's Law be applied to non-SI units?

Yes, Coulomb's Law can be applied to non-SI units as long as the units for force, electric charge, and distance are consistent with each other. For example, it can be expressed in dynes, statcoulombs, and centimeters.

## 5. Are there any exceptions to the units of Coulomb's Law?

There are no exceptions to the units of Coulomb's Law, as they are derived from the fundamental units of the SI system and are necessary for the equation to be physically meaningful. However, in some specialized cases, different unit systems may be used for convenience or historical reasons.

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