Question

IV. Loss of symmetry and two components of the magnetic field. Suppose instead of the full ring of current in Il you only had half the ring. Assuming the same orientation so that the center of the semicircle is the same as the center of the circle and the y axis runs through the center. As in the previous example you want to determine the magnetic field at a point on the y axis. Is the y component of the magnetic field the same as in II, 22 of that value or some other value? Explain your reasoning. In this case the symmetry that allows you not to integrate is gone for the x and z components of the field must be determined by integration. Using dĩ = Rdo where 0 is the angle along the arc in the xz plane (the plane of the semicircle) write down the integrals for the x and z components of the magnetic field. Explain you reasoning.

Answer 1

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