When two long straight parallel conductors, A and B, carry steady currents I_a and I_b respectively, they generate a magnetic field around them. This magnetic field interacts with each other, resulting in a force between the two conductors.
The magnitude of the force, F, between the conductors can be calculated using Ampere's Law and the right-hand rule for magnetic fields:
F = (μ₀ * I_a * I_b * L) / (2π * d)
Where:
- F is the magnitude of the force between the conductors.
- μ₀ is the permeability of free space (constant value).
- I_a and I_b are the currents in conductors A and B respectively.
- L is the length of the conductors over which the currents flow.
- d is the distance between the conductors.
The direction of the force can be determined using the right-hand rule. If the currents in the conductors are in the same direction, the force will be attractive, pulling the conductors towards each other. If the currents are in opposite directions, the force will be repulsive, pushing the conductors away from each other.
It's important to note that this formula assumes the conductors are infinitely long, and the magnetic field generated by each conductor is uniform along the length of the conductors. In practice, the force between finite-length conductors may vary along their lengths. Additionally, the force calculation becomes more complex if the conductors are not straight or are not parallel.