I. Magnetic fields have their origin in charges that are moving.

  A. Wires carrying currents produce magnetic fields.

  B. Permanent magnets also produce magnetic fields that are due to the circulation of charge around atoms.

II. Forces on charges in fields

  A. Electric fields: F = qE

  B. Magnetic fields: F = qv x B

    1. Here we have to use the vector cross product since the magnetic force on a moving charge is perpendicular to the plane      containing the vectors v and B. The right-hand rule proves to be useful here.

  C. When both electric and magnetic fields are present and a charge is moving, we have the total force due to both fields:

    F = qE + (qv x B)

  D. Since a wire carrying a current has charges moving in it, we expect that if the current-carrying wire is placed in the field of   a permanent magnet there will be a force on it. This force can be written as:

    F = iL x B

III. Applications

  A. What is the path of a charged particle traveling in a constant magnetic field?

  B. What does a loop of wire carrying a current have to do with an electric motor?

  C. What is a magnetic dipole?