**Case Studies**** > Magnetic**

## Case List

__Case 1: Halbach Array__

Case 2: Designs to Maximize Uniform Fields

Case 2: Designs to Maximize Uniform Fields

**Case 1: Halbach Array**

Halbach array is a special arrangement of permanent magnets which makes magnetic filed stronger in specific area. In this case study, two 2D cases are simulated using COMSOL Multiphysics. In the first case shown on at left below, 5 square magnets (a side length of 0.1 m) with the unidirectional north poles, and magnetically they work the same as a single long magnet. In the second case shown at right below, 5 square magnets has various direction of north poles. Another square part (with a side length of 20 m) is defined with a constitutive relation of "Relative permeability" and the corresponding material is defined as "Air".

The magnetic field strength of the Halbach array shown on the left is equally strong on the left and right sides. In contrast, the Halbach array shown at right has a very strong field on the top, while a fairly weak field on the bottom.

The magnetic field strength of the Halbach array shown on the left is equally strong on the left and right sides. In contrast, the Halbach array shown at right has a very strong field on the top, while a fairly weak field on the bottom.

**Case 2: Designs to Maximize Uniform Fields**

In this case study, COMSOL Multiphysics is applied to simulate and predict four designs, which were developed to maximize uniform magnetic filed within an array of permanent magnets. The Halbach 4-square design can only have a homogeneous magnetic field in a middle area within 4 square magnets. Using the same number and same shapes of magnets, Halbach 8-square design 2 provides a more uniform magnetic field than Halbach 8-square design 1. It can be seen that Halbach cylinder design produces a perfectly uniform magnetic filed within eight cylindrical magnets.