An element dl with current I produces a magnetic in- duction dB=Addl×t=0 i sin edl 4丌 4丌 where 0 is the angle between dl and ri, and ol unit vector in the azimuthal direction Now using sin Adl cos adl=rda and p=r cos a, sin odl rda da cos ada 2 Thus integration yields the magnetic induction B= m/2 cos ada (0 4丌-7 P1 2TP See「ig8-4
Figure 8-4 Lines of B in a plane perpendicular to a long straight wire carrying a current i. The density of the lines is inversely proportional to the distance to the wire Lines close to the wire are not shown
Example 2 Circular Loop Magnetic Dipole Moment See Fig. 8-5 for a loop of radius a wit a current l We want to know the component of b along the z axis produced by the loop dB=0,d×r1.dBz4rr2, 0,dcos日 4丌 4O 2Ta cos 0 B7 T llo, a cos 0 By cos 0=a/r, and r2=z2+a2, we have Ia B 2(2+a2)1/2