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 = 21.4 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 = 6.5 ?T), and Figure (c) gives the y component By (the vertical scale is set by Bys = 4.3 ?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 ) there is no y compont of magnetic field from wire 1 , the total ycomponet of magnetic field is zero . means wire 2 either at 90 degree or -90 degree .

wire 2 must be at -90 degree , the bottom of the cylinder . it would pose an obstacle for the motion of wire 1 if it were anywhere in the top semicircle .

part b )

looking at theta = 90 degree Bnetx = maximum (6.5 muT )

conclude that B1x = 6.5 - 2.167 = 4.33 muT

i1 = 2pi*R*B1x/uo =

i1 = 0.214 * 4.13 x 10^-6 / 2*10^-7

i1 = 4.4191 A

part c )

current is out of the page

part d ) we note that there is no x component of magnetic field from wirewhen theta1 = 0

so B2x = 2.167 muT

i2 = 2pi*RB2/uo = 2.31869 A

part e )

current is into the page

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