Distance dependence in Ampere's force law

• Sunfire
In summary, Ampere's force law is a fundamental law in electromagnetism that describes the force between two current-carrying wires. It states that the force between two parallel wires is directly proportional to the product of their currents and inversely proportional to the distance between them. Distance dependence in Ampere's force law refers to the fact that the force between two parallel wires decreases as the distance between them increases, as the magnetic field created by one wire at the location of the other wire decreases with distance. The mathematical expression for Ampere's force law is F = (μ0I1I2)/2πd, where F is the force between the two wires, μ0 is the permeability of free space, I1 and
Sunfire
Hello,

In the Ampere's force law

F=2ka$\frac{I_{1}I_{2}}{r}$

Ampere law,

the force between 2 parallel conductors doesn't seem to depend on the distance between them.

F is given in [N/m], instead of just [N]...

What is the rationale behind this?

Thank you.

Does it stem from the definition of Ampere

Reading some other threads on the subject helps... I see that the force is per unit of cable length, while r on the RHS is the distance betw the 2 cables, okay :)

Hello,

Thank you for bringing up this interesting topic. The distance dependence in Ampere's force law is a result of the inverse square relationship between the force and the distance between the two conductors. This means that as the distance between the conductors increases, the force between them decreases exponentially.

The reason for including the distance in the denominator is to account for the fact that the magnetic field generated by a current-carrying conductor decreases with distance. This is due to the spreading out of the field lines as they move away from the conductor. Therefore, the closer the conductors are to each other, the stronger the magnetic field and hence the stronger the force between them.

As for the units of force in Ampere's law, it is given in [N/m] because it is a force per unit length. This is necessary in order to compare the force between conductors of different lengths.

I hope this helps to clarify the rationale behind the distance dependence in Ampere's force law. Thank you for your question.

1. What is Ampere's force law?

Ampere's force law is a fundamental law in electromagnetism that describes the force between two current-carrying wires. It states that the force between two parallel wires is directly proportional to the product of their currents and inversely proportional to the distance between them.

2. What is distance dependence in Ampere's force law?

Distance dependence in Ampere's force law refers to the fact that the force between two parallel wires decreases as the distance between them increases. This is because the magnetic field created by one wire at the location of the other wire decreases with distance.

3. What is the mathematical expression for Ampere's force law?

The mathematical expression for Ampere's force law is F = (μ0I1I2)/2πd, where F is the force between the two wires, μ0 is the permeability of free space, I1 and I2 are the currents in the two wires, and d is the distance between the wires.

4. How does distance dependence in Ampere's force law affect the strength of the force?

The strength of the force between two parallel wires decreases as the distance between them increases. This means that the force will be stronger if the wires are closer together and weaker if they are farther apart.

5. Are there any real-life applications of distance dependence in Ampere's force law?

Yes, distance dependence in Ampere's force law is used in many real-life applications, such as in the design of electric motors, generators, and transformers. It is also important in understanding the behavior of electromagnetic waves and in the development of wireless technologies.

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