DEFINITION OF THE MAGNETIC FIELD

A charge which is moving parallel to a current of other charges experiences a force perpendicular to its own velocity. We can see it happening in the deflection of the electron beam in Fig. 5.3. We discovered in Section 5.9 that this is consistent with—indeed, is required by—Coulomb's law with charge invariance and special relativity. And we found that a force perpendicular to the charged particle's velocity also arises in motion at right angles to the current-carrying wire. For a given current the magnitude of the force, which we calculated for the particular case in Fig. 5.20a, is proportional to the product of the particle's charge q and its speed v in our frame. Just as we defined the electric field E as the vector force on unit charge at rest, so we can define another field B by the velocity-dependent part of the force that acts on a charge in motion. The defining relation was introduced at the beginning of Chapter 5. Let us state it again more carefully.

At some instant t a particle of charge q passes the point (x, y, z) in our frame, moving with velocity v. At that moment the force on the particle (its rate of change of momentum) is F. The electric field at that time and place is known to be E.