Answered>Order 10449

 Let’s work with the solenoid used to measure the earth’s magnetic ?eld. The solenoid was wound with 79 turns over a distance of 79cm. The diameter was d = 11cm. A TA mistakenly runs the wire feeding the solenoid back across the end of the solenoid and along the top. This problem asks you to analyze the error created in the experiment by this foolish setup. The experiment measures the magnetic ?eld at point P at the center of the solenoid. The distance from the wire segment to the point P is ? = 0.5m. Since the percent error will be the same for any current, let’s analyze the system at the maximum output of out power supplies I = 17A. Note the coordinate system for the problem has the plane of the paper as the x ? z plane. 

(a) On the ?gure below draw the direction of the magnetic ?eld of the solenoid, ~ Bsole, the wire segment from A to B, ~ BAB, and the in?nite straight wire from B to C, ~ BBC, at point P.

(b) Calculate the ?eld of the solenoid at point P in the in?nite solenoid approximation. Report the ?eld as a vector.

(c) Calculate the ?eld of the wire segment AB in the ?nite current element approximation at point P. Report the ?eld as a vector.

(d) Calculate the ?eld of the wire segment BC in the approximation that it is an in?nite straight wire at point P. Report the ?eld as a vector.

(e) Calculate the magnetic ?eld of the segment BC exactly at point P. Report the ?eld as a vector. Report both a symbolic and numeric answer. Use the point P as the origin for this calculation.

(f) Does the TA bungle introduce more than 10% relative error in the experiment?