We defined the electric field in terms of the force per unit charge on a small positive test charge. We will again use a small positive test charge to define the magnetic field. Unfortunately, the definition of the magnetic field cannot be made as simply because the magnetic force does not act on the test charge unless it is moving. To complicate matters, the magnitude and direction of this force depend on the magnitude and direction of the velocity of the test charge. We find that the magnitude of the force is directly proportional to the component of the velocity that is perpendicular to the magnetic field.

 The implications of this expression include:

1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B.

2. The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero.

3. The direction of the force is given by the right hand rule. The force relationship above is in the form of a vector product.

Definition provided by HyperPhysics