Two long straight thin wires with current lie against an equally long plastic cy

Question

Two long straight thin wires with current lie against an equally long plastic cylinder, at radius R = 21.8 cm from the cylinder's central axis. Figure (a) shows, in cross section, the cylinder and wire 1 but not wire 2. With wire 2 fixed in place, wire 1 is moved around the cylinder, from angle ?1 = 0° to angle ?1 = 180°, through the first and second quadrants of the xy coordinate system. The net magnetic field at the center of the cylinder is measured as a function of ?1. Figure (b) gives the x component Bx of that field as a function of ?1 (the vertical scale is set by Bxs = 7.7 ?T), and Figure (c) gives the y component By (the vertical scale is set by Bys = 5.1 ?T). (a) At what angle ?2 is wire 2 located? (assume that angle ?2 lays in the range from -180° to 0°) What are the (b) magnitude and (c) direction (into or out of the page) of the current in wire 1 and the (d) magnitude and (e) direction (into or out of the page) of the current in wire 2?

Explanation / Answer

PART A

at pi/2

PART B

i = 2*pi*R/mi*B1x

i = (2*pi*0.218/(4*pi*10-7)) *(4*10-6) = 4.36 A out of the page

PART C

Current is in out of the apge

PART D

i = 2*pi*R/mi*B1x

i = (2*pi*0.218/(4*pi*10-7)) *(2*10-6) = 2.18 A

PART E

Current is in into the page

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