Yes, there is an equivalent theory for the magnetic field in a shell, known as the magnetic shell theorem. The magnetic shell theorem states that the magnetic field inside a uniformly magnetized shell is zero.
To understand this concept intuitively, let's consider a uniformly magnetized shell, which means that the magnetic field is the same at every point on the shell. Inside the shell, the magnetic field generated by the magnetization of the shell material cancels out due to the symmetry of the configuration.
Just like in the gravitational shell theorem, the cancellation occurs because the contributions from different portions of the shell in generating the magnetic field add up to zero at any point inside the shell. The magnetic field vectors from different parts of the shell cancel each other out due to the opposite directions of their magnetic fields.
This cancellation effect arises from the symmetrical distribution of magnetic dipoles within the shell. For every magnetic dipole pointing in one direction, there is an equivalent dipole pointing in the opposite direction on the opposite side of the shell. The magnetic fields produced by these dipoles cancel each other out, resulting in a net magnetic field of zero inside the shell.
Outside the shell, the magnetic field follows the same inverse square law as for a point magnetic dipole, similar to the gravitational field outside a uniformly dense spherical shell. This means that outside the shell, the magnetic field behaves as if all the magnetic dipoles of the shell were concentrated at its center.
It's important to note that the magnetic shell theorem applies to situations where the shell is uniformly magnetized. If the magnetization is not uniform, the cancellation effect may not hold, and the magnetic field inside the shell can be nonzero.
In summary, the magnetic shell theorem states that the magnetic field inside a uniformly magnetized shell is zero, similar to how the gravitational field inside a uniformly dense spherical shell is zero. This theorem is a useful concept when analyzing magnetic field configurations and helps understand the behavior of magnetic fields in symmetrical systems.