Part (a) of the figure below shows, in cross section, three current-carrying wir

Question

Part (a) of the figure below shows, in cross section, three current-carrying wires that are long, straight, and parallel to one another. Wires 1 and 2 are fixed in place on an x axis, with separation d. Wire 1 has a current of 0.750 A, but the direction of the current is not given. Wire 3, with a current of 0.250 A out of the page, can be moved along the x axis to the right of wire 2. As wire 3 is moved, the magnitude of the net magnetic force F2-vector on wire 2 due to the currents in wires 1 and 3 changes. The x component of that force is F2x and the value per unit length of wire 2 is F2x/L2. Part (b) of the figure gives F2x /L2 versus the position x of wire 3. The plot has an asymptote of F2x/L2 = -0.621 mu N/m as x - > infinity. The horizontal scale is set by xs = 21.0 cm. (a) What is the size of the current in wire 2? (b) What is the direction of the current in wire 2?

Explanation / Answer

as thw curve passes throught zero, it means Currents in wire 1 and wire 3 are exactly same

Wire 3 is at greatest distance from wire 2 ,

Magnetic force between parallel wires is given by F = uo i1 i2 L/2pid

when wire is at x = 0.04 m, Curve passes through zero

so Distance between wire 1 and wire 2 is

d = 0.04 * 0.75 /0.25 = 0.12 m

so current i2 = 0.621 e -6 * 2* 3.14 * 0.12/(4*3.14 e -7 * 0.75)

i2 = 0.496 Amps

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direction of current is out of page

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