How is the strength of two magnetic poles related to the force between them?

The strength of two magnetic poles is related to the force between them by what is known as the inverse square law. This law states that the force between two magnetic poles is directly proportional to the product of their strengths (magnetic charges) and inversely proportional to the square of the distance between them.

To explain this relationship mathematically, let's consider two magnetic poles:

1. First, let's define the strength of one pole as "m₁" and the strength of the other pole as "m₂".

2. The force between the two poles, which we'll denote as "F", can be expressed as:

F ∝ (m₁ * m₂) / (r²)

Where:
∝ denotes proportionality
r is the distance between the centers of the two poles

3. The above equation tells us that the force between the poles is directly proportional to the product of their strengths (m₁ * m₂).

4. It also tells us that the force is inversely proportional to the square of the distance between them (1/r²).

5. To find the exact relationship, we need to introduce a constant of proportionality, which we'll call "k".

F = k * (m₁ * m₂) / (r²)

The value of "k" depends on the units used to measure magnetic strength and distance. It can also be affected by the medium between the two poles if it's not vacuum.

So, in summary, the strength of two magnetic poles is directly proportional to the product of their strengths and inversely proportional to the square of the distance between them. This relationship is described by the inverse square law.