# Magnetic force

• If a charge is moving through a magnetic field, the force on the charge is given by:

F = qvB

• q = charge (C)
• v = velocity of the charge moving through the field (m/s)
• B = the perpendicular flux density through which the charge moves (T)

• The direction of the applied force is given by the right hand rule.
• If the charge is negative, the force will be in the opposite direction.

### Right Hand Rule

1. Thumb points in the direction of the force (positive)
2. Index point in the direction of velocity
3. Middle finger points in the direction of the magnetic field

### Force on a current-carrying conductor

If a current carrying wire produces its own magnetic field, and it were placed in an external magnetic field,

• The magnetic fields will interact
• In some instances, the magnetic field will apply a force to the wire.

Using the formula,

F = ILB

• I = current (A)
• L = length (m)
• B = magnetic flux density perpendicular to the current (T)

Direction is given by the right hand rule.

### Angled magnetic flux

If the magnetic flux is not at right angles to the current carrying conductor, the perpendicular flux is equal to Bsinθ, where theta = angle that the flux makes to the conductor.

Hence,

F = ILBsinθ