1. Example: One-sided magnet and plate

2. Introduction
A magnet with a one-sided flux is the type of magnets used in refrigerators.
The one-sided flux behavior is obtained by giving the magnet a magnetization that varies in the lateral direction.
One-sided magnets can be used in various applications ranging from household appliances to particle accelerators.

3. Geometry The magnet is represented by a cylinder.
The plate is included as a face object.
A surrounding control volume of air is modeled by a sphere.

4. Domain Equations and Boundary Conditions
We use the potential formulation to calculate the magnetic potential Vm.
The magnet is magnetized as:
The boundary conditions are magnetic insulation on all boundaries.

5. Results
The magnetic flux is parallel to the upper surface of the disc and no magnetic flux appears above it.
On the other side, the flux emerges outside the magnet and results in a four times stronger holding force than for a conventional magnet.

6. Nonlinear permeability

7. Nonlinear permeability