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
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .