Magnetic Force between Two Parallel Currents

Definition

The magnetic force between two parallel current-carrying wires is described by the formula F = (μ0I1I2L)/(2πr), where μ0 is the permeability of free space, I1 and I2 are the currents in the two wires, L is the length of the wires, and r is the distance between the wires. This formula allows for the calculation of the attractive or repulsive force between the two parallel currents.

5 Must Know Facts For Your Next Test

1. The magnetic force between two parallel current-carrying wires can be either attractive or repulsive, depending on the direction of the currents.
2. The magnitude of the magnetic force is directly proportional to the product of the two currents (I1 and I2) and the length of the wires (L), and inversely proportional to the distance between the wires (r).
3. The formula F = (μ0I1I2L)/(2πr) is derived from Ampere's law and the Biot-Savart law, which describe the relationship between current, magnetic field, and distance.
4. The permeability of free space, μ0, is a physical constant that represents the ability of free space to support a magnetic field.
5. The direction of the magnetic force can be determined using the right-hand rule, which relates the direction of the current, the magnetic field, and the resulting force.

Review Questions

• Explain how the magnetic force between two parallel current-carrying wires is affected by the magnitude of the currents in the wires.
  • According to the formula F = (μ0I1I2L)/(2πr), the magnetic force between two parallel current-carrying wires is directly proportional to the product of the currents in the two wires, I1 and I2. This means that as the currents in the wires increase, the magnetic force between them will also increase. Conversely, if the currents decrease, the magnetic force will decrease. The magnitude of the currents is a key factor in determining the strength of the magnetic force between the parallel wires.
• Describe how the distance between the two parallel current-carrying wires affects the magnetic force between them.
  • The formula F = (μ0I1I2L)/(2πr) shows that the magnetic force between two parallel current-carrying wires is inversely proportional to the distance between the wires, r. This means that as the distance between the wires increases, the magnetic force between them decreases. Conversely, if the distance between the wires decreases, the magnetic force will increase. The distance between the parallel wires is a critical factor in determining the strength of the magnetic force, with the force becoming stronger as the wires are brought closer together.
• Analyze the role of the permeability of free space, μ0, in the formula for the magnetic force between two parallel current-carrying wires.
  • The permeability of free space, μ0, is a fundamental physical constant that appears in the formula for the magnetic force between two parallel current-carrying wires, F = (μ0I1I2L)/(2πr). This constant represents the ability of free space to support a magnetic field. The inclusion of μ0 in the formula indicates that the magnetic force is influenced by the properties of the medium in which the currents are flowing. Specifically, the magnetic force will be stronger in a medium with a higher permeability, such as certain ferromagnetic materials, compared to the magnetic force in free space, where μ0 has a fixed value. Understanding the role of μ0 in this formula is crucial for accurately calculating the magnetic force between parallel current-carrying wires.

Related terms

Permeability of Free Space (μ0): The permeability of free space, also known as the magnetic constant, is a physical constant that describes the magnetic field produced by a steady electric current. It has a value of 4π × 10^-7 N/A^2.

Ampere's Law: Ampere's law states that the magnetic field created by a current-carrying wire is proportional to the current and inversely proportional to the distance from the wire.

Biot-Savart Law: The Biot-Savart law describes the magnetic field produced by a steady electric current. It relates the magnetic field to the current, the length of the current-carrying element, and the distance from the element.