Week 13 Solns - Electromagnetics Workshop Week 13 Solutions...

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Electromagnetics Workshop – Week 13 Solutions Magnetostatics 1 Problem 1: A long solenoid of length L is wound with many layers of thin wire. A cross section of the solenoid is shown in the figure. There are a total of N turns, each carrying a current I . The inner radius of the solenoid is a and the outer radius is b . Neglect fringing of the fields near the end of the solenoid. a) What is the magnetic field H in the region b ρ > ? b) Find the magnetic field H in the region a < . c) Find the magnetic field H in the region ab < < . Problem 1 Solution: . encl dI ⋅= H A v (a) b > : . 00 encl I =⇒ = H (b) a < : . encl z z NI IN I H L N I H L = [A/m] (c) << : At b = : . encl I = H At a = : . encl z z I H L N I H L = [A/m] The field should vary smoothly between these two points. . encl z z bb N I b I N IH L N L ab ρρ −− ⎛⎞ = ⎜⎟ ⎝⎠ [A/m]
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Electromagnetics Workshop – Week 13 Solutions Magnetostatics 2 Problem 2: Determine the magnetic field H at the point ( x , 0, 0) due to the infinitely long wire with a right- angle bend, as shown below (the wire goes to infinity in the – x and – y directions). Helpful integral: () 32 2 22 1 du u a ua = + + Problem 2 Solution: This is the superposition the magnetic field of two semi-infinite wires. “Wire 1” is the wire on the x -axis. “Wire 2” is the wire on the y -axis. Wire 1: ˆ x x =− 1 Rx ( ) 2 ˆˆ 0 4 C I dx xx π × = = 1 H Wire 2: 2 x y y 0 00 2 2 2 ˆˆˆ 44 4 4 Ix y I xd y I y I dy x x xy ππ −∞ −∞ −∞ ⎡⎤ −× ′′ ⎢⎥ == = = + ++ ⎣⎦ ∫∫ yxy Hz z z [A/m] I I x y
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Electromagnetics Workshop – Week 13 Solutions Magnetostatics 3 Problem 3: The operation of a magnetic compass depends on the presence of the earth’s magnetic field. At a certain location the tangential component of the earth’s magnetic field is 20 [ μ
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This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.

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Week 13 Solns - Electromagnetics Workshop Week 13 Solutions...

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