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Advanced Physics Homework Help
Force of magnetic attraction between hemispheres
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[QUOTE="Pouyan, post: 5878456, member: 549817"] [h2]Homework Statement [/h2] Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω and surface charge density σ. [h2]Homework Equations[/h2] Maxwell Tensor : T[SUB]m[/SUB] = [/B](1/μ) *[B] ((B*n)B - (1/2)*[/B]B[B][SUP][/SUP][/B][SUP]2[B][/B][/SUP][B] n) B_in = [/B](2/3)*μσRω[B]*z B_out = [/B]μm[B]/([/B]4πr[B][SUP][/SUP][/B][SUP]3[B][/B][/SUP][B]) * ([/B]2cosθ[B] r + [/B]sinθ[B] θ) where [/B]m = (4/3)*πR[SUP]3[/SUP](σωR)[B] [/B][h2]The Attempt at a Solution[/h2] I do see in my solution that : 1-We use a surface consisting of the entire [B]equatorial plane[/B], CLOSING IT with a hemispherical surface at infinity where (since the field is zero out there) contribution is zero.[B][/B] for r>R : B = μm/(4πr[SUP]3[/SUP]) [B]θ = [/B]- μm/(4πr[SUP]3[/SUP]) [B]z (Why ?! ) 2- [/B]We have a equatorial circular disk. We use B inside and da = rdrdφ. Direction is in z-axis! [B]I don't want the solution because I already have it but MY QUESTIONS are : A) How should think and imagine this spheres ?! Should I think like this and use those formulas : [ATTACH=full]214705[/ATTACH] B) Why we do write B = μm/(4πr[SUP]3[/SUP]) [B]θ = [/B]- μm/(4πr[SUP]3[/SUP]) [B]z Why is θ =-z in this case ?! I don't get it ! [/B] I know the rest. That is just integrating [/B] [/QUOTE]
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Force of magnetic attraction between hemispheres
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