Quiz Questions: Magnetic Field & Energy in a Paramagnetic Cylinder (PHYS4210) - Prof. Jame, Quizzes of Physics

Download Quiz Questions: Magnetic Field & Energy in a Paramagnetic Cylinder (PHYS4210) - Prof. Jame and more Quizzes Physics in PDF only on Docsity! Name: PHYS4210 Electromagnetic Theory Quiz #10 18 Apr 2011 This is a closed book quiz! You have thirty minutes to complete it. A uniform magnetic field B = B0x̂ fills all space in a vacuum. A long, paramagnetic cylinder with radius R and permittiv- ity µ is then inserted into the field, with its axis along the z-axis. Find the resulting magnetic field B(r, θ) inside the cylinder, in terms of B0, R, and µ. Show that you get the correct answer for µ = 1, that is, susceptibility χ = 0. It is useful to know that a solution to Laplaces’ Equation in cylindrical coordinates takes the general form ∞∑ n=1 [ anr n + bnr −n ] cos(nθ) Also find the magnetic energy per unit length in the cylinder. R x yB0