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Cylindrical coil magnetic field

# Exercise N 5. Magnetic field of the cylindrical coil

**Task**

Make a plot of magnetic flux density at the axis of the coil with and without steel core.

**Experiment**

Magnetic flux density is measured in laboratory by webermeter.

**Problem type**

Linear axisymmetrical problem of magnetostatics.

**Geometry**

Due to problem symmetry only upper-right quarter *a0b* is defined, and at the axes of symmetry boundary conditions are set.

**Given data**

Current density in the coil *j=100000 A/m*^{2}.

Relative magnetic permeability of air and copper *μ=1.*

Relative magnetic permeability of steel of the core *μ=500.*

**Boundary conditions**

At the vertical axis of symmetry (line *Ob*) H_{t}=0. At the horizontal axis of symmetry *Oa* B_{n}=0. From **B**=rot**A** in the cylindrical coordinate system we have at the
axis *Oa* A=const. Field fades at the infinity, so at the line *Oa* A=0 due to continuity of A.

**Results:**

Dependence of the magnetic flux density upon the distance to the coil center:

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