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Raihan amin
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Homework Statement
A superconducting spherical shell of radius R is placed in a uniform magnetic field ##\vec{B_0}##
1)Find the magnetic field everywhere outside the shell
2)the sutface current density
Homework Equations
Inside the shell the net magnetic field is 0, and at the surface also.
The magnetic field of a magnetic diople of moment ##\vec{m}## is
$$\vec{B_m}=\frac{μ_0}{4\pi}[\frac{3(\vec{m}.\vec{r})\vec{r}}{r^5} - \frac{\vec{m}}{r^3}]$$
The Attempt at a Solution
The boundary condition at the surface which is at an angle ##\theta## with the vertical is
$$\vec{B_{0,\hat{n}}}+\vec{B_{m,\hat{n}}}=0$$
So,$$B_0\cos{\theta}+\frac{μ_0}{4\pi}(\frac{2m\cos{\theta}}{R^3} )=0$$
Therefore at $$\vec{m}=-(\frac{2\pi}{μ_0})R^3 \vec{B_0} $$,the boundary condition are satisfied on the surface of the shell.Hence,$$\vec{B}=\vec{B_0}-\frac{(3R^3)(\vec{B_0}.\vec{r})\vec{r}}{2r^5} + \vec{B_0}(\frac{R^3}{2r^3})$$
But i can't find the surface current density in this way. In my textbook,the author has written that we can find that using tangential B's continuity though i didn't get that.
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