An element dl with current I produces a magnetic in duction dB= 0,dl×r1p0,sin6dl 4丌 4丌 where 0 is the angle between dl and rI, and 1 is the 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=4r//2 cos ada 4丌-m2p d12丌 See Fig 8-4
( 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 m 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- bo, dl X I1, dBi 4T r2 COS 4丌 B Z 4丌 By cos 0= a/r, and r=z+a, we have 22 a 2)1/2