1) (10 Points) A long straight wire with radius R has a non-uniform current density J(r) directed purely along the wire axis 4 with magnitude that varies with radial distance from the center of the wire r as J (r): J 3% for 0 Sr S R and J( r) = 0 for r > R where J 9 is a constant (it's the magnitude of current density at the outer edge of the wire). The current in the wire is 1. Answer the following questions in terms of the variables given above and any listed in the questions. a) Find an expression for the constant Je so that the current is 1. Include units. HINT: I J 1R2 because J is NON- uniform. b) Find an expression for the current passing through a circular cross-section of the wire with radius r > nRz ), Draw a picture! HINT: We're nding the FLUX of electric eld through the OPEN surface dened above. (135 =I E - JA ii) Show that Maxwell's denition of the \"Displacement Current" I my: (1),; between the capacitor dt plates is the same as the current passing through the wire. Use the same circular cross-section as above. iii) Use the Ampere-Maxwell law I B 'dL =M0 (19,\" + [dim] to show that the B-eld circulates the same way between the capacitor plates as it does around the wire. HINT: Use the 1st term on right hand side for the wire, and the 2"d term for the space between the plates