# Magnetic Circuits with Parallel Parts

A brief description of magnetic circuits with symmetrical, or asymmetrical, parallel parts

**Contents**

### Key Facts

**Gyroscopic Couple**: The rate of change of angular momentum () = (In the limit).

- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.

## Magnetic Circuits With Symmetrical Parallel Parts

**Key facts**For a magnetic circuit with two symmetrical parallel parts, the total number of ampere-turns/meter is given by: where is the number of ampere-turns/meter for the path of length , and so on. For a magnetic circuit with two asymmetrical parallel parts, the total flux is given by: where is the magnetic reluctance.

Consider the symmetrical magnetic circuit diagramed in Figure 1, where the path is of length and area , the path is of length and area , the path is of length and area , and so on.

In this case, we can write that the magnetic flux density for the path is: We also consider the number of ampere-turns/meter for the path as being . Following a similar reasoning, we can write that the magnetic flux density for the path is: while the number of ampere-turns/meter is . We can apply the same rationale for the other segments as well. We can thus write that the total number of ampere-turns/meter is: As the circuit is symmetrical, it is easy to find out how the magnetic flux divides. For example, in Figure 1 the magnetic flux in the center is twice that in each side.