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bowlbase
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Done editing I hope.
If Jf = 0 everywhere, then (as we showed in class), one can express H as the gradient of a scalar potential, W. W satisfies Poisson’s equation with ∇⋅M as the source. Use this fact to find the field inside a uniformly magnetized sphere. (Griffiths has some additional verbiage
intended to help, but I think you already know what he says.) Compare your answer with
example 6.1 (p. 264-5), which is this problem solved by another method.
##H^\perp_{above} - H^\perp_{below}=-(M^\perp_{above}- M^\perp_{below})##
My question is with the constraints and in particular the one I have in the equations section. I had this as ##∇W^\perp_{in} - ∇W^\perp_{out}=M^\perp## Since at r=R they are equivalent. I know that ##M^\perp## must writable as some version of M but I cannot determine what. I know the solutions manual has ##M\hat{z}\hat{r}= Mcos(θ)## but I don't understand how they have ##\hat{z}## in spherical coordinates...
Thanks for any clarification.
Homework Statement
If Jf = 0 everywhere, then (as we showed in class), one can express H as the gradient of a scalar potential, W. W satisfies Poisson’s equation with ∇⋅M as the source. Use this fact to find the field inside a uniformly magnetized sphere. (Griffiths has some additional verbiage
intended to help, but I think you already know what he says.) Compare your answer with
example 6.1 (p. 264-5), which is this problem solved by another method.
Homework Equations
##H^\perp_{above} - H^\perp_{below}=-(M^\perp_{above}- M^\perp_{below})##
The Attempt at a Solution
My question is with the constraints and in particular the one I have in the equations section. I had this as ##∇W^\perp_{in} - ∇W^\perp_{out}=M^\perp## Since at r=R they are equivalent. I know that ##M^\perp## must writable as some version of M but I cannot determine what. I know the solutions manual has ##M\hat{z}\hat{r}= Mcos(θ)## but I don't understand how they have ##\hat{z}## in spherical coordinates...
Thanks for any clarification.
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