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HW14Sol - Jim Guinns PHYS2212 Assignment#14 Solutions 1 Two...

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Jim Guinn’s PHYS2212 Assignment #14 Solutions 1. Two long straight wires lie in the x-y plane and are parallel to the x-axis. One wire is at y = -6cm and the other is at y = +6cm . The current in each wire is 20A in the negative x- direction. Find at the point on the y-axis at a) y = -3cm , b) y = 0 , c) y = +3cm , and d) y = +9cm . Each wire produces a field of magnitude B = μ o I / 2 π R . The direction of the field is given by the right hand rule. a) In this case, the wire at y = -6cm produces a field in the negative z-direction, whereas the wire at y = +6cm produces a field in the positive z-direction, so = ( μ o I / 2 π ) (1 / 0.09m – 1 / 0.03m) = = -8.89x10 -5 T . b) At y = 0 , the fields are of equal magnitude, but opposite direction, so = 0 . c) For y = 3cm , the fields of part a) have been reversed, so = 8.89x10 -5 T . d) For y = 9cm , the fields are both in the negative z-direction, which gives = ( μ o I / 2 π ) (- 1 / 0.03m – 1 / 0.15m) = = -1.6x10 -4 T . 2. A wire of length L is wound into a circular coil of N loops and carries a current I. Show that the magnetic field at the center of the coil is given by B = μ o π
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