Electromagnetism Recitation 6: Magnetic Fields from Wires and Currents in Tori, Assignments of Engineering

Download Electromagnetism Recitation 6: Magnetic Fields from Wires and Currents in Tori and more Assignments Engineering in PDF only on Docsity! PHGN200: All Sections Recitation 6 March 27, 2007 1. Those damn infinite and semi-infinite (half-infinite) wires! (a) Consider a semi-infinite wire carrying current I, see Fig. 1. Find the magnetic field, ~B, in the first quadrant, i.e., x ≥ 0, y > 0, z = 0. You may find∫ ∞ 0 η [(ζ − w)2 + η2]3/2 dw = 1 η + ζ η √ ζ2 + η2 (1) useful. x y I Figure 1: A semi-infinite wire (from 0 to ∞) carrying current I is shown in blue. Ans: ~B = µoI 4π ( 1 y + x y √ x2+y2 ) k̂. (b) Consider an infinite wire carrying current I, see Fig. 2. Find the magnetic field, ~B, in the first quadrant, i.e., x ≥ 0, y > 0, z = 0. You may find∫ ∞ −∞ η [(ζ − w)2 + η2]3/2 dw = 2 η (9) useful. x y I Figure 2: An infinite wire (from −∞ to ∞) carrying current I is shown in blue. Ans: ~B = µoI 2πy k̂. (c) Where does the magnetic field due to a semi-infinite wire equal one half the magnetic field of an infinite wire, i.e., ~Bsemi-infinite = ~Binfinite/2? Ans: x = 0, i.e, on the y-axis PHGN200: All Sections Recitation 6 March 27, 2007 2. A blue wire carrying current I = Iot 3/3 is wound evenly on a torus of rectangular cross section. There are N turns of the blue wire in all. A red wire is thrown over the torus and is connected to a resistor, R, see Fig. 3. Find the magnitude and direction (clockwise or counterclockwise) of the current in the red wire, Ired wire. z w y x I R r1 r2 Figure 3: A blue wire carrying current I = Iot 3 is wound evenly on a torus of rectangular cross section, with inner radius r1 and outer radius r2. There are N turns of the blue wire in all. A red wire is thrown over the torus and is connected to a resistor, R. Ans: Ired wire = µoNwIo2πR ln ( r2 r1 ) t2, clockwise Page 2