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ECE3209-2009-hw8

# ECE3209-2009-hw8 - ECE 3209 Electromagnetic Fields...

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ECE 3209 — Electromagnetic Fields University of Virginia Fall 2009 Homework # 8 — Magnetic Fields Due: Friday, November 6 1. Using the Biot-Savart Law, find the magnetic flux density ( ~ B ) at point P for each of the steady current configurations given below: (a) Cheng P.6-11. A hairpin turn (b) On the axis of a tightly-wound finite solenoid consisting of n turns per unit length wrapped around a cylindrical tube of radius a and carrying current I . Express your answer in terms of the angles θ 1 and θ 2 . 2. Cheng P.6-13. A thin conducting wire is bent into the shape of a regular polygon of N sides. A current I flows in the wire. Show that the magnetic flux density at the center is, ~ B = ˆ n μ 0 NI 2 πb tan π N · , where b is the radius of the circle circumscribing the polygon and ˆ n is a unit vector normal to the plane of the polygon. Show that as N becomes very large, this result reduces to the result for the magnetic flux density at the center of a circle of radius b .

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