电磁场与电磁波第五课.ppt

5 Magnetostatics Ampere’s Force Law The force exerted by current-carrying circuit 1 upon 2 is where R is the distance vector from to . The magnetic force exerted on the moving charge element dq is The magnetic force exerted on the moving charge q is The magnetic flux density (magnetic induction intensity) produced at point P from a current element is where is the permeability in vacuum and R is the distance vector from source point to field point . Integrating, we obtain the magnetic flux density at point P due to a wire carrying steady current I. (T)（Wb/m2） The current element may be expressed as The magnetic flux density in terms of J is The magnetic flux density in terms of JS is Example 5.1.1 An infinitely long filamentary wire located along z axis carries a current in the z direction, as shown in Figure 5.1.3. Find an expression of magnetic flux density at any point in space. Solution Since the wire is infinitely long , the magnetic flux density is not a function of z. We may choose a field point P in the plane. From Figure, we have and Thus, Substituting these expressions into The magnetic flux lines are circles surrounding the wire. 5.2 Guass’s Law and Ampere’s Circuital Law Guass’s Law for Magnetic Field Taking the divergence, we get Since we have Using we obtain Note that the curl operation represents partial differentiation with respect to x, y, and z and the di