Problem 5 (40 points) Consider the configuration of current carrying wires shown below. A semi-infinite wire carrying a

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Problem 5 40 Points Consider The Configuration Of Current Carrying Wires Shown Below A Semi Infinite Wire Carrying A 1 (60.98 KiB) Viewed 47 times

Problem 5 (40 points) Consider the configuration of current carrying wires shown below. A semi-infinite wire carrying a current I = 1 ribs in from - along the axis as shown below. At Point A this current splits to form currents 1, and I, which run around two semi-circular arcs of radius a in the x-y plane. These currents combine again at Point B to form 14, which is carried away in a second semi-infinite wire along the + axis 2R I= 1 B 20 4 The lower semicircular arc hus elextrical resistance 2. For the upper semicircular are, the left half (slown in black) has resistance R. and the right belf (slow in Orange) has resistance 2R. (a) What is the equivalent resistance in measured between Points A and B? (b) What is the potential difference between Points A and B, AV-V-V? (c) What are the currents I, and 13? Problem 5 Contine: For the remainder of the problem, we will calculate the magnetic field at the coordinate origin. For reference, the Biot-Savart laws ds 1 = 1 1. = 1 ds A (d) Find the increment of the magnetic field 2B at the coordinate origin arising from a very short segment ds, of length d at the position 1 = -1, on the straight wire segment which carries the incoming current 1. Justify your answer (e) Gulded by your result from Part (dl), find the magnetic fields, and Bproduced at the coordinate origin by the currents 1; and I towing in the two straight wire seginents. Hint you should be able to do this part wuthout computing any complicated integrals. (f) Find the increment of the magnetic field dB, at the coordinate origin arising from a very short section of length is on the upper semicircular are (8) Guided by your result from Paut (1), find the magnetic fields , and produced at the coordinate origin by the currents and 1s that flow in the two semicircular arcs Hint you may find it helpful to also consider a short segment des such as that shown on the lower arr. (h) Use your results from Parts (c) anel () to find the total magnetic field at the militate origin.