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hw4_p5406_s05

# hw4_p5406_s05 - large 3 A conducting non-magnetic sphere...

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HW 4 Phys5406 S05 due 2/17/05 1) This problem indicates how a permanent magnet works. Spherical geometry is used for simplicity. Given a sphere of radius a and constant magnetization, M . Find the magnetic field B and also H both inside and outside the sphere. Why is H tan continuous at r=a? 2) A sphere of radius a and permitivity is placed in a constant electric field E 0 . Find the resulting electric field inside and outside the sphere and the polarization. If the sphere is spun with constant angular velocity ω about a diameter, such that the direction of ω is E 0 , find the magnetic field at all points in space. Compare the magnitude of the magnetic field to that of the electric field inside the sphere. Do you think it is numerically small or
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Unformatted text preview: large? 3) A conducting, non-magnetic sphere, one described by μ = μ , with radius a and uniform surface charge density σ is spun with constant angular velocity ω about a diameter. Find the magnetic ﬁeld inside and outside the sphere. Why is H tan not continuous at r=a? 4) A grounded, conducting sphere of radius a is surrounded by a concentric, grounded, conducting spherical shell of inner radius b (b > a). In the space between the sphere and the shell lies a ring of radius c and uniform linear charge density λ . Let the plane of the ring be z = a with a 2 + c 2 < b 2 . Find the potential in the region a ≤ r ≤ b. 1...
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