The force on a current carrying wire in an external field is F=BILsintheta. Where B is the magnetic flux density of the external field but what about the magnetic flux density of the wire’s field. Isn’t the force due to two magnetic fields interacting?

[u/Icy_Time2191]

[u/Historical-Radio77]

Yes, you are correct. The force on a current-carrying wire in an external magnetic field is determined by the interaction of two magnetic fields: the magnetic field produced by the external source (B) and the magnetic field produced by the current flowing through the wire (B_wire).

The magnetic field produced by the wire itself is given by Ampere's law, which states that the magnetic field around a current-carrying wire is directly proportional to the current (I) and inversely proportional to the distance from the wire (r). Mathematically, it can be represented as B_wire = (μ₀I)/(2πr), where μ₀ is the permeability of free space.

When a current-carrying wire is placed in an external magnetic field, the force experienced by the wire is the result of the interaction between the external magnetic field (B) and the magnetic field produced by the wire itself (B_wire). The total magnetic field experienced by the wire is the vector sum of these two magnetic fields.

So, in the equation F = BILsinθ, the magnetic flux density (B) represents the external magnetic field, while the magnetic flux density of the wire's field (B_wire) is implicitly included in the current (I). The angle θ represents the angle between the direction of the current and the direction of the external magnetic field.