A current is set up in a wire loop consisting of a semicircle of radius 4.80 cm,

Question

A current is set up in a wire loop consisting of a semicircle of radius 4.80 cm, a smaller concentric semicircle, and two straight lengths, all in the some plane. Part (a) of the figure shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 16.02 mu T. The smaller semicircle is then flipped over (rotated) until the loop entirely in the some plane (part (b) of the figure). The magnetic field produced at the (same) center of curvature now has the magnitude 15.34 mu T, and its direction is reversed. What is the radius of the smaller semicircle?

Explanation / Answer

magnetic field at the center due to semicircel B = uo*I/(4R)

R = 4.8 cm

(a)

B1 = uo*I/(4r) + uo*I/(4R)

B1 = (uo*I/4)*(1/r + 1/R)

B1 = (uo*I/4)*(R+r)/(R*r)

B1 = 46.02*10^-6 T

(b)

B2 = uo*I/(4r) - uo*I/(4R)

B2 = (uo*I/4)*(1/r - 1/R)

B2 = (uo*I/4)*(R-r)/(R*r)

B2 = 15.34*10^-6 T

B1/B2 = (R+r)/(R-r)

(46.02*10^-6)/(15.34*10^-6) = (4.8+r)/(4.8-r)

radius of smaller circle = r = 2.4 cm <<<<-----answer

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