A current-carrying conductor in a magnetic field experiences a force due to the magnetic interaction between the moving charges within the conductor and the external magnetic field. This force is quantified by the equation: \[ F = I L B \sin(\theta) \] In this formula, \( F \) represents the force, \( I \) denotes the current, \( L \) is the length of the conductor exposed to the magnetic field, \( B \) signifies the magnetic field strength, and \( \theta \) is the angle between the magnetic field and the conductor.
For two infinitely long, straight, parallel conductors carrying constant currents \( I_1 \) and \( I_2 \), Ampère's law provides the force per unit length between them: \[ F = \frac{\mu_0 I_1 I_2}{2 \pi d} \] Here, \( \mu_0 \) is the magnetic constant (permeability of free space), and \( d \) is the separation distance between the conductors.
This equation quantifies the force between two parallel steady currents and serves as the definition of Ampère's law.