- #1

fluidistic

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## Homework Statement

If we want to obtain a magnetic dipole in the interior of a sphere of a radius R, what should be the current distribution over the surface of the sphere? Note that its permeability is the one of the vacuum. Determine the magnetic field outside the sphere.

## Homework Equations

This is where I'm lost. I have Jackson's book opened on chapter 5 but I don't know where to look at.

## The Attempt at a Solution

So they ask me for ##J(\vec x )##. I know it will involve the Dirac's delta in spherical coordinates. In other words ##J(\vec x ) = \frac{\delta (r-R)}{R}f(\theta ) f (\phi )##. So I must find ##f(\theta )## and ##f(\phi )##. In fact that would be ##J(\vec x )## in all the space, not only the surface of the sphere. For the surface of the sphere only, I remove the Dirac's delta.

Maybe I must use Ampere's law under the differential form, namely ##\nabla \times \vec B = \mu _0 \vec J## but although they tell me more or less how the magnetic field is, I don't have it under any mathematical form and I'm not even sure there's only 1 possibility for such a B field given the problem statement.

Any tip will be appreciated.