Force on a current-carrying wire in a magnetic field

A wire carrying a current experiences a force when it is placed in a magnetic field. The force acts perpendicular to both the direction of the conventional current and the direction of the magnetic field.

For a straight length of wire perpendicular to a uniform magnetic field, the magnitude of the force is:

Here, $$F$$ is the force in newtons ($$\mathrm{N}$$), $$B$$ is the magnetic flux density in teslas ($$\mathrm{T}$$), $$I$$ is the current in amperes ($$\mathrm{A}$$), and $$l$$ is the length of wire within the field in metres ($$\mathrm{m}$$).

For a perpendicular wire, increasing the current, the length in the field, or the magnetic flux density increases the force.

Magnetic flux density

Magnetic flux density measures the strength of a magnetic field in terms of the force it exerts on a current-carrying wire. Rearranging the force equation for a wire perpendicular to the field gives:

One tesla is the magnetic flux density that produces a force of one newton on a one-metre length of wire carrying one ampere, when the wire is perpendicular to the field.

Force direction: Fleming’s left-hand rule

Hold the thumb, first finger and second finger of your left hand mutually perpendicular:

• First finger: magnetic field direction.
• Second finger: conventional current direction.
• Thumb: force direction.

Point the first and second fingers in the field and conventional current directions. The thumb then shows the direction of the force on the wire.