Magnetic Field Calculation Methodology

The Biot – Savart Law describes the magnetic field observed at a point P, adjacent to a section of conductor dx carrying a current I:

In order to successfully integrate this equation, we must relate the variables theta, x and r.
The two following expressions can be used to assist in this process.

By combining these equations and differentiating with respect to x, it is possible to obtain the following relationship:

This equation can be used to determine the magnetic field of any straight current-carrying wire if we know the geometry, which is turn gives the angles theta1 and theta2. In the case of a general three-phase circuit, the complex three-dimensional magnetic field vector at point P may be determined from the individual field contributions from the three phases.

Assuming that the power system is balanced such that the phase currents are symmetrical, these contributions may be derived from a further decomposition into the Cartesian plane:

These equations have been used to derive the magnetic field resulting from a cable laid in trefoil with 240mm phase spacing at a depth of 900mm, a balanced load current of 650 Amperes and single point bonding. The following diagram compares the calculated and measured magnetic fields under this scenario.