When an electrical wire is exposed to a magnet, the current in that wire will be affected by a magnetic field. The effect comes in the form of a force. The expression for magnetic force on current can be found by summing the magnetic force on each of the many individual charges that comprise the current. Since they all run in the same direction, the forces can be added.
The force (F) a magnetic field (B) exerts on an individual charge (q) traveling at drift velocity vd is:
In this instance, θ represents the angle between the magnetic field and the wire (magnetic force is typically calculated as a cross product). If B is constant throughout a wire, and is 0 elsewhere, then for a wire with N charge carriers in its total length l, the total magnetic force on the wire is:
Given that N=nV, where n is the number of charge carriers per unit volume and V is volume of the wire, and that this volume is calculated as the product of the circular cross-sectional area A and length (V=Al), yields the equation:
The terms in parentheses are equal to current (I), and thus the equation can be rewritten as:
The direction of the magnetic force can be determined using the right hand rule, demonstrated in . The thumb is pointing in the direction of the current, with the four other fingers parallel to the magnetic field. Curling the fingers reveals the direction of magnetic force.
Right Hand Rule
Used to determine direction of magnetic force.