# 2. (30 points) A very long, straight, solid copper cylinder of radius R (>2R) is oriented with it...

2. (30 points) A very long, straight, solid copper cylinder of radius R (>2R) is oriented with its axis along e z-direction. The cylinder carries a current whose current density is j(r), where r is the radial distance from the cylinder axis. The current density, although symmetric about the cylinder axis, is not constant but varies with r according to 31o a) (10) Obtain an expression for the current /(in terms of Jo, r and R) flowing in a circular cross section b) (10) Starting with Ampere's law, derive an expression for the magnitude of the magnetic field in c) (5) Starting with Ampere's law, derive an expression for the magnitude of the magnetic field in the 2d) (5) The diagram below shows a cross section of the cylinder. Indicate on the diagram the direction of of radius rsR the region rS R, in terms of Jo, r and R. region r 2 R, in terms of Jo, r and some constants. Simplify your answer as much as possible. Sthe magnetic field at point P 了Jo Sters in ba o ean cheeh

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