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Unformatted text preview: PHYS 153 Term 2, 2008-09 Homework 8B Mar. 16 - 20 Problem 1 A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is J . The current density, although symmetrical about the cylinder axis, is not constant and varies according to the relationship J = b r e ( r- a ) / k for r a = 0 for r a (1) where the radius of the cylinder is a = 5 . 00 cm, r is the radial distance from the cylinder axis, b is a constant equal to 600 A / m, and is a constant equal to 2 . 50 cm. (a) Let I be the total current passing through the entire cross section of the wire. Obtain an expression for I in terms of b , , and a . Evaluate your expression to obtain a numerical value for I . (b) Using Amperes law, derive an expression for the magnetic field B in the region r a . Express your answer in terms of I rather than b . (c) Obtain an expression for the current I contained in a circular cross section of radius r a and centered at the cylinder...
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