# Find the magnetic field inside the cylinder

## Homework Statement

There's a very long cylinder with radius ##R## and magnetic permeability ##\mu##. The cylinder is placed in uniform magnetic field ##B_{0}## pointed perpendicularly to the axis of cylinder. Find magnetic field for ##r < R##. Assume there's a vacuum outside the cylinder.

## Homework Equations

Boundary conditions:
$$B_{2} \cdot \hat{n} = B_{1} \cdot \hat{n}$$
$$B_{2} \times \hat{n} =\frac{\mu_{2}}{\mu_{1}} B_{1} \times \hat{n},$$
where ##\hat{n}## is a unit radial vector.

Laplace equation:
$$\Delta \phi_{M} = 0,$$
where ##\phi_{M}## is a scalar magnetic potential.

## The Attempt at a Solution

I was trying to solve it but I think something's missing here. I mean, in electrostatics I know that some potential ##\phi = 0## on a conducting electrically neutral surface. Should I assume here that there's some current density on the surface of the cylinder?