| F | = Force on the wire. (SI: N) |
| I | = Positive Current flow in the wire. (SI: Amp) |
| l | = Length of the wire. (SI: m) The direction of l is the same as the positive current flow. |
| B | = Magnetic Field (SI: T) |
| q | = Angle between flow of positive current and the magnetic field. |
The direction of the force F follows the right hand rule with the index finger pointed along the direction of the current flow.
Explaintion on an Atomic Level:
The charges moving in the direction of the current in a wire will find themselves in a magnetic field which would cause them to move in circles if they were unconstrained. The circles will be at right angles to the magnetic field with the same rotational direction. When charges collide with the "walls" of the wire, impurities, imperfections, or vibrations of the atomic lattice, the charges bounce off imparting some sizeways momentum to the wire. The overall effect of many such collision pushes the wire sideways.
Force on a Current Carrying Conductor in a Magnetic Field Movie (950K)
A conducting rod is placed between the poles of a horse-shoe magnetic. The rod also rest on two conducting rails which are connected to a battery which can be turned on and off. The rod starts off with no current flowing in it. When the battery is connected the motion of the rod show that there is a magnetic force on a current carrying conductor which follows the right hand rule..
Mathenatical Derivation:
This "law" is a result of the total force on the current carrying charges flowing in a wire that are also in a magnetic field.
Consider a small differential length dl of a wire. The differential charge dQ in the volume of the wire with the length dl can be found using the charge density in the wire rn.
The magnetic force on the differential charge dQ moving with the drift velocity vd in a magnetic field B is:
Note that since the current is in the same direction as line segment dl.