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bifilar coil inductance, spiral coil inductance

Tesla flat bifilar coil is an electromagnetic coil that contains two closely spaced, parallel windings.

**Problem Type**

Axisymmetric problem of AC magnetics.

**Geometry**

Schematic image of the Tesla's flat inductive bifilar coil

**Given**

Number of turns = 48;

Outer diameter of coil = 154 mm;

Wire diameter = 3 mm.

Electric current *I* = 1 A;

Frequency *f* = 400 Hz.

**Task**

Estimate the change in inductance between two cases of electric current direction:

1. Same (parallel) direction;

2. Opposite directions.

**Solution**

Tesla bifilar coil can be modeled as concentric closed circles.

In this formulation, the problem can be solved as a plane axisymmetric 2D problem of the magnetic field of alternating currents.

The magnetic field energy of the coil is associated with coil inductance by the formula:
*W = (L*I²)/2*

From this formula it follows that the inductance is directly proportional to the stored energy of the magnetic field.

**Results**

Magnetic field energy for the case of current flowing in:

Parallel direction: *W* = 10.7 uJ.

Reverse direction *W _{reverse}* = 0.23 uJ.

In the case of reverse connection the coil features low energy (and inductance), which is only 2% of the inductance value in case of parallel current direction.

Magnetic field lines, distribution of current density and the stored energy of the magnetic field for the case of reverse windings connection: