Question

Page 5 3) The cross section of a long metal rod of radius R - 50 mm is shown below. The rod carries a current/= 3,000 A directed out of the page and spread uniformly across the cross section of the rod. Find the magnetic field B at a radial distance r= 10 mm from the center of the rod using the following steps: a) (2.5 pts) Write an expression, in symbols, for current density J in terms of land R. b) (2.5 pts) Draw an Amperian loop appropriate for finding the magnetic field at r<R. c) (5 pts) Get an expression for the current enclosed by the Amperianloop in terms of I, R, and r. d) (5 pts) Apply Ampere's law to get an equation (in symbols) for the magnitude of the B-field at r < R. The result should be in terms of r, R, I, and any constants. e) (5 pts) Insert numbers to get the B-field at r= 10 mm. 1) (5 pts) Sketch a graph of the magnetic field magnitude as a function of t, including both r and r>R

Answer 1

1 - 3000 A R=40m, 10 min current density 3 I 1 1 2 A Area of rod 6 for ear, shown in abone figure Current enclsed in e radius loup Iene - Ja @ Amperers Law & Bdd o ho Toneloset - B(2712) = 4o I s 18 - Hotel mit Here Bolig ☺ {strarght line patterns ☺ . 10mm , an UTIX107x300 x 10X103 2T (US) B = 2.471067 magnetic fied for r>R using ampere's how & Bld = Mootsend. Tenche: I , death anh ane B24