PhyIIHW7Solutions - hopkins (tlh982) – HW07 – criss –...

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Unformatted text preview: hopkins (tlh982) – HW07 – criss – (4908) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A long cylindrical shell has a uniform current density. The total current flowing through the shell is 8 mA. The permeability of free space is 1 . 25664 × 10- 6 T · m / A . 1 k m 7 cm 2 cm b The current is 8 mA . Find the magnitude of the magnetic field at a point r 1 = 4 . 5 cm from the cylindrical axis. Correct answer: 12 . 8395 nT. Explanation: Let : L = 10 km , r a = 2 cm = 0 . 02 m , r b = 7 cm = 0 . 07 m , r 1 = 4 . 5 cm = 0 . 045 m , I = 8 mA , and μ b = 1 . 25664 × 10- 6 T · m / A . L r b r a b The current I = 8 mA . Since the cylindrical shell is infinitely long, and has cylindrical symmetry, Ampere’s Law gives the easiest solution. Consider a circle of radius r 1 centered around the center of the shell. To use Ampere’s law we need the amount of current that cuts through this circle of radius r 1 . To get this, we first need to compute the current density, for the current flowing through the shell. J = I A = I π r 2 b − π r 2 a = (8 mA) π [(0 . 07 m) 2 − (0 . 02 m) 2 ] = 0 . 565884 A / m 2 . The current enclosed within the circle is I enc = π [ r 2 1 − r 2 a ] · J = π [(0 . 045 m) 2 − (0 . 02 m) 2 ] × (0 . 565884 A / m 2 ) = 0 . 00288889 A ....
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This note was uploaded on 11/05/2008 for the course PHY 2049 taught by Professor Criss during the Fall '08 term at University of South Florida - Tampa.

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PhyIIHW7Solutions - hopkins (tlh982) – HW07 – criss –...

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