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Unformatted text preview: HW-9 1.Starting from the Lorentz force law, show that the torque on any steady current loop in a uniform magnetic field is Bm. Hint: CBABCACBA)()()(AldrldrA21)(for any constant vector A. Solution:The force on a segment of current I is BlId. Then the total torque on the current loop is. BldrIldBrIBldrIBlIdrN)()()(Note ldis rd. Thus the second term )(21)(212rdrrdrdrldr. Then BldrIldBrIN2)(. But ldr21is nothing but the areal vector of the current loop ldrS21. Therefore BmBSIN. 2.In infinite long circular cylinder carries a uniform magnetization Mparallel to its axis. Find the magnetic field Band Hinside and outside the cylinder. Solution:Since is zMMa constant vector, the bound current density MJb. But there exists a surface bound current with a surface density of eMezMnMKrb. Then the cylinder is equivalent to a current coil except the NI(where Nis the number of turns per unit length) is replaced by Kb. Then the magnetic field is outsideinsidezMzKzNIBbThe Hcan be calculated by MBH. Then we find Heverywhere. everywhere....
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This note was uploaded on 02/06/2010 for the course PHYSICS 11 taught by Professor Qiu during the Fall '09 term at Berkeley.
- Fall '09