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Unformatted text preview: ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 7 — Magnetic Fields and the Vector Potential Due: Wednesday, October 29 1. 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 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 . 2. A steady current flows down a long cylindrical wire of radius R , If the current density in the wire is given by, ~ J = kr ˆ z for ≤ r ≤ R (and k is a constant), find the ~ B-field both inside and outside the wire. 3. A current I flows to the right through a rectangular bar of semiconducting material, in the presence of a uniform magnetic flux density ~ B , pointing out of the page. (a) If the moving charges are...
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- Spring '08
- Electromagnet, Magnetic Field, #, magnetic ﬂux density, Electromagnetic Fields University of Virginia