(8c30p66) The figure at the top shows, in cross section, two wires that are stra

Question

(8c30p66) 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 = 1.96 nJ/m3 as x goes to infinity, and the horizontal axis scale is set by xs = 60.0 cm.

a.)What is the value of i1?

Explanation / Answer

magnetic field is given by B = u0*I/2*pie*r

energy density is given by B2/2*u0

we have i1/i2 = 1/3 or i2 = 3*i1

the energy density is 0 at x = 20 cm ; so the position of the wire 1 has to be at 20/3 cm.

the curve has an asymptote of 1.96 uJ/m3 ; so this will only take into account the energy density by the 1st wire.

so B1 = (8*pie*1.96*10-9*10-7)0.5 = 7.01*10-8 T

and this is equal to (4*pie*10-7* I *3) / (2*pie*0.2)

so i1 = 0.023 A

and i2 0.069 A

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.