210 Sources of the Magnetic FieldP30.71Consider the sphere as being built up of little rings of radius r,centered on the rotation axis. The contribution to the field fromeach ring isdBrdIxr=+µ0222322ejwhere dIdQtdQ==ωπ2dQdVrdr dxρρ2bgafdBrdx=+µρω032where ρ=QR433BrdxrRxxRR=+=−=−+zz0302rxdrdxωRFIG. P30.71Let vr x=+, dvrdr=2, and rvxBvxdvvdxvdvxvdv dxBvxvdxRxxdxBxRvxRRRRRxRxRRR=−LNMMOQPPLNMOQP+−FHGIKJLNMMOQPP+LNM=+−−==−zzzzz020122020202224441142422222222222chOQP+LNMOQP+FHGIKJ=−dxxRdxBRRRRRRRR242242342230200202P30.72Consider the sphere as being built up of little rings of radius r,centered on the rotation axis. The current associated with eachrotating ring of charge isdIdQtrdr dxρπ22af.The magnetic moment contributed by this ring isdA dIrrdr dxr drdxµππωρ=2322rxdrdxωRFIG. P30.72=LNMMOQPP=−FHIK=−+=−FHGIKJ+LNMMOQPP+FHGIKJ=FHGIKJ==−++++zzzxdx
This is the end of the preview. Sign up
access the rest of the document.