# Example: flux density in Steady state AC Magnetic applications

## Introduction

In the Steady state AC Magnetic applications the flux density (B) is a complex vector.

## Computation of flux density

It is possible to compute:

• The vector modulus of the flux density ModV(B), which is a complex scalar:

At the phase ω t = 0°: ModV (Inst(B,0) = ModV(Real(B))

At the phase ω t = 90°: ModV (Inst(B,90) = ModV(Imag(B))

• The complex modulus of the flux density:

ModC(B) is a real vector

• The general modulus of the flux density:

Mod(B) = ModV(ModC(B) is a real scalar

## Physical meanings of modulus functions

To compare the Flux results with the measurement results, we can use one of the following methods:

1 st possibility:

The measurement of flux density is carried out in three main directions X, Y, Z. The result is a vector, defined by the three components: Bx, By, Bz

• The ModC(B) formula of Flux returns a real vector as result whose components are Bx, By, Bz.
• The formula ModV(ModC(B)) returns a real scalar as result; this is the modulus of the previously result, i.e. the peak value of the flux density.

2 nd possibility:

The measurement of the flux density is carried out along a given direction.

The Flux formulas Mod(B*Vec3(i, j, k)) and ModC(B*Vec3(i, j, k)) return as result a real scalar that is the peak value of flux density.

( Vec3(i,j,k is the unit vector that provide the measurement direction )

Example:

If the measurement is carried out along the OX axis, the formula ModC(B*Vec3(1, 0, 0)) yields the peak value of the flux density on OX direction.