(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A long wire is bent into semicircle of radius R at its center and continues on to infinity in both direcions with the straight segments remaining parallel, as shown in the figure below. Use your knowledge of superposition, Ampere's Law, and the Biot-Savart Law to determine the magnetic field at the center of the semicircle by way of the following steps:

a) determine the contribution due to the semicicular wire segment

b) determine the conribution of each straight wire segment by considering them to be semi-infinite using symmetry, as they each represent "half" of an infinite wire.

c) determine the vector sum of these three contributions, including both magnitde and direction of the result

2. Relevant equations

dB=uI/2(pi)R

B = μ0I/2(pi)R

3. The attempt at a solution

a) The magnetic field at the point P due to the wire of radius 'R' is

B = (1/2)(μ0I / 2R)

b) For an infinite wire, B = μ0I/2(pi)R

c) Sum gives: μ0piI+2μ0I/4(pi)R

correct?

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# Homework Help: Magnetic fied at center of semicircle Ampere's Law Biot-Savart Law

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