Magnetic Force on a Moving Charge:
• The force on a moving charge in a magnetic field is equal to the cross product of the particles velocity with the magnetic field times the magnitude of the charge.

• The direction of the Magnetic Force is always at right angle to the plane formed by the velocity vector v and the magnetic field B. (Right-hand rule)

• The Magnetic Force depends upon the size of the charge q, the magnitude of the magnetic field B, and how fast the charge is moving v perpendicular to the magnetic field (equivalently, the size of v and the component of B perpendicular to the direction of the moving charge).

Properties of the Magnetic Field acting on a Moving Charge at one moment:

• When q < 0, F is in the opposite direction.
If the sign of the charge on the particle is inverted, then the direction of the magnetic force will be opposite that of a positive charge. The magnitude of the magnetic force remains the same, only its direction is inverted.

• When v is parallel to B, then F = 0.
There is one direction in space where the moving particle will experience no magnetic force acting on it; this direction is along the direction of the magnetic field.

• The direction of the magnetic force is always at 90 o to the direction of motion of the particle.

• The direction of the magnetic force is always at 90 o to the direction of the magnetic field.
(See Right-hand rule)

• Plane formed by v and B
All positive particles which have v-B planes that are identical (or parallel) will experience a magnetic force in the same direction independent of the angle between v and B. Changing the angle between v and B without changing the orientation of the v-B plane will not change the direction of the magnetic force on the charge. This direction is perpendicular to the v-B plane and determined by the right-hand rule.

• If the direction of the motion of the particle is changed, then the magnitude of the magnetic force may or may not change.

• When
If a particle moves in a plane that is perpendicular to B, then the magnitude of the magnetic force will always have the same size (but necessarily the same direction) no matter which direction the particle moves in the plane perpendicular to B. In this plane the magnetic force will be maximum.

• F is maximum, when q = 90 o.
The magnitude of the magnetic force is greatest when the charge is moving at right angles to the magnetic field.

• If the charge is not constrained by other forces then magnetic force will cause the free charge to change its direction each moment. The end results is that the free charge will move in a helix around the axis of the magnetic field. See Free Charge in Magnetic Field.