- #1
issacnewton
- 998
- 29
Hi
I was trying to do one problem from Griffiths's EM book. The problem says to find the
magnetic force of attraction between the northern and southern hemispheres of a spinning
charged spherical shell. There was an earlier problem in the book to find the electric
force of attraction between the two hemispheres of a stationary but charged spherical shell.
That was in earlier chapter. On page 103 , he gives the reasoning to calculate the electric
field to be used to calculate the force on the northern hemisphere, since the total electric
field is contributed from both the hemispheres. Giving the example of the electric field near the infinite plane, he says,
[tex] \mathbf{E}_{other}=\frac{1}{2}(\mathbf{E}_{above}+\mathbf{E}_{below}) [/tex]
and I understood the reasoning given. I have attached the two pages where he gives the explanation as png images.
Now coming to the magnetic force problem, even though he doesn't give any such reasoning
in the chapter of the Magneto-statics (chapter 5) , in the solution manual , he says that
[tex] \mathbf{B}_{avg}=\frac{1}{2}(\mathbf{B}_{in}+\mathbf{B}_{out}) [/tex]
where Bin and Bout are the magnetic fields inside
and outside of the spherical shell. I want to know where does this reasoning come from ?
I was trying to do one problem from Griffiths's EM book. The problem says to find the
magnetic force of attraction between the northern and southern hemispheres of a spinning
charged spherical shell. There was an earlier problem in the book to find the electric
force of attraction between the two hemispheres of a stationary but charged spherical shell.
That was in earlier chapter. On page 103 , he gives the reasoning to calculate the electric
field to be used to calculate the force on the northern hemisphere, since the total electric
field is contributed from both the hemispheres. Giving the example of the electric field near the infinite plane, he says,
[tex] \mathbf{E}_{other}=\frac{1}{2}(\mathbf{E}_{above}+\mathbf{E}_{below}) [/tex]
and I understood the reasoning given. I have attached the two pages where he gives the explanation as png images.
Now coming to the magnetic force problem, even though he doesn't give any such reasoning
in the chapter of the Magneto-statics (chapter 5) , in the solution manual , he says that
[tex] \mathbf{B}_{avg}=\frac{1}{2}(\mathbf{B}_{in}+\mathbf{B}_{out}) [/tex]
where Bin and Bout are the magnetic fields inside
and outside of the spherical shell. I want to know where does this reasoning come from ?