Conductive cylinder in rotating magnetic field.

**Problem Type:**

A plane problem of transient magnetics.

**Geometry:**

**Given:**

Relative magnetic permeability of air *μ* = 1;

Relative magnetic permeability of conductor *μ* = 1;

Conductivity of conductor *σ* = 6.3·10^{7} S/m;

Magnitude of external field *B*_{0} = 1 T;

Number of poles 2*p* = 6;

Frequency *f* = 50 Hz.

**Solution:**

To specify rotating magnetic field on the outer boundary of the region, B_{n} = B_{0} sin (ωt - *p*φ), we apply the Dirichlet boundary condition, using the formula: A = cos (18000*t - 3*atan2 (y/x)) / 60

The coefficient *A*_{0} = 1/60 arises from consideration

B_{n} = (1/*r*)(∂A/∂φ) = *A*_{0}*p*·sin(ωt - *p*φ) / *r*

and

*A*_{0} = *B*_{0}·*r*/*p*

Due to periodicity of the problem, only half of the model is presented, and odd periodic boundary condition *A*_{1} = -*A*_{2} is applied on the cut. In fact, it would be enough to simulate just 60° sector of the model.
In time domain, problem is simulated with automatic adaptive time step, up to 0.05 seconds (approx. 2.5 periods).

**Results:**

t = 0.0002 sec:

t = 0.048 sec:

t = 0.05 sec:

See the *Dirich1.pbm* problem in the Examples folder.