P31_079 - 79(a The energy density at any point is given by...

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79. (a) The energy density at any point is given by u B = B 2 / 2 µ 0 ,where B is the magnitude of the magnetic Feld. The magnitude of the Feld inside a toroid, a distance r from the center, is given by Eq. 30-26: B = µ 0 iN/ 2 πr ,where N is the number of turns and i is the current. Thus u B = 1 2 µ 0 µ µ 0 iN 2 πr 2 = µ 0 i 2 N 2 8 π 2 r 2 . (b) We evaluate the integral U B = R u B d V over the volume of the toroid. A circular strip with radius r ,he ight h ,andth ickness dr has volume d V =2 πrhdr ,so U B = µ 0 i 2 N 2 8 π 2 2 πh Z b a dr r = µ 0 i 2 N 2 h 4 π ln µ b a
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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