The figure at the top shows, in cross section, two wires that are straight, para

Question

The figure at the top shows, in cross section, two wires that are straight, parallel, and very long. The ratio i1/i2, of the current carried by wire 1 to that carried by wire 2 is 1/3. Wire 1 is fixed in place. Wire 2 can be moved along the positive side of the x axis so as to change the magnetic energy density uB set up by the two currents at the origin. The lower figure gives uB as a function of the position x of wire 2. The curve has an asymptote of uB = 1.90 nJ/m3 as x goes to infinity, and the horizontal axis scale is set by xs = 66.0 cm. What is the value of i1?

What is the value of i2?

Explanation / Answer

Given that, xs= 66 cm, total magnetic energy density is zero at x= 22 cm, or x= 2*(66/6).

At this location the magnitudes if magnetic fields are the same. That is

uoi1/2d = uoi2/2*0.12

Hence , d= 0.22*(1/3)=0.07333 m

The relation between field and energy density is,

B1=sqrt (2uBuo)

The magnetic field due to first wire is

B1=uoi1/2d

Use the above two relations we get

i1=2d*sqrt (2uB/uo)

= 25.34*10^-3 A

= 25.34 mA

But we have the below relation,

i2=3i1 = 76.02 mA

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