Capacitors, Magnetic Circuits, and Transformers is a free introductory textbook on the physics of capacitors, coils, and transformers. See the editorial for more information....


Electric charges in motion produce a magnetic field. Thus, when an electric charge q moves with a velocity v a magnetic field is produced as shown in Fig. 3-1, in which v shows the direction of motion and P indicates the point at which the magnetic field intensity is H. If the velocity vector v and the point P are in the plane of the paper, then for a positive charge the direction of H is away from the observer and into the plane of the paper. The magnitude of the magnetic field intensity at P is


However, both the magnitude of H and its direction are specified when this relationship is expressed in vector form as


Where v is the vector that represents the velocity, and ir the unit vector in the direction of the line joining the charge q with the point P. It is well to remember that the magnitude of the cross product is equal to the area of the parallelogram in which v and ir are the adjacent sides. This corresponds to the quantity v sin Θ. Also, the direction of the vector, resulting from the cross product, is at right angles to the plane containing the vectors v and ir in accordance with the right-hand rule.

Figure 3-1. Magnetic field is produced in space surrounding a moving charge

Last Update: 2011-01-09