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Magnetism
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. 31, 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 i_{r} 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 i_{r} 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 i_{r} in accordance with the righthand rule.


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