A current is set up in a wire loop consisting of a semicircleof radius 3.80 cm,

Question

A current is set up in a wire loop consisting of a semicircleof radius 3.80 cm, a smaller, concentricsemicircle, and two radial straight lengths, all in the same plane.Figure (a) shows the arrangement but is not drawn toscale. The magnitude of the magnetic field produced at the centerof curvature is 47.50 µT. Thesmaller semicircle is then flipped over (rotated) until the loop isagain entirely in the same plane seen in Figure (b). Themagnetic field produced at the (same) center of curvature now hasthe magnitude of 16.25 µT, and itsdirection is now reversed. What is the radius of the smallersemicircle?
what is the theta in the biot-savart equation and how do youcalculate it? A current is set up in a wire loop consisting of a semicircleof radius 3.80 cm, a smaller, concentricsemicircle, and two radial straight lengths, all in the same plane.Figure (a) shows the arrangement but is not drawn toscale. The magnitude of the magnetic field produced at the centerof curvature is 47.50 µT. Thesmaller semicircle is then flipped over (rotated) until the loop isagain entirely in the same plane seen in Figure (b). Themagnetic field produced at the (same) center of curvature now hasthe magnitude of 16.25 µT, and itsdirection is now reversed. What is the radius of the smallersemicircle?
what is the theta in the biot-savart equation and how do youcalculate it?

Explanation / Answer

a ) Here from the figure( a ) there are two carryingsemicircular loops with radiii   R and r Now magnetic field at Centre due to loop having radiusR    is B1 =0i/4R magnetic field at Centre due to loop havingradius r    is B2= 0i/4r Now net magnetic field at centre is Ba = B1 +B2 =  (0i/4R) +(0i/4r) Ba = 47.50 T Now from figure b net magnetic field at centre isBb = B2 - B1 =  (0i/4r)  -(0i/4R) Bb= 16.25 T Then Ba/Bb   = (0i/4R) +(0i/4r)/ (0i/4r)  -(0i/4R)               Ba/Bb         = (1/R +   1/r)/(1/r - 1/R) Ba/Bb    = 47.50 T/16.25 T =2.923 2.923 = (1/R + 1/r)/(1/r - 1/R)              = (r + R)/R -r          2.923 (R-r) =r + R       1.923 R = 3.923r Then r = 0.49018 R Here R = 3.80 cm Then radius of the smaller semi circle is r = 0.49018*3.80cm = 1.86 cm

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