Introduction

Consider the five sets of coils used for generating a known magnetic flux density within a volume:

iec-field-measurement.pdf
  • The IEC coil

olivares_paper.pdf
  • Section 1.1 Helmholtz coil

  • Section 1.2 Merritt 3-coil

  • Section 1.2 Merritt 4-coil

  • Section 1.4 Reuben coil

The documents list each of these coil systems' expected magnetic flux density \(\vec{B}\) at the center in terms of the number of turns (N), the coil current (I) and a length.

1. Earth simulator

For each of the five coil sets, find the current needed to generate a magnetic flux density of 140 μT when constructed using 100 turns and whose outer structure fits within a 1 m cube?

Why 140 μT?

The Earth’s magnetic field varies between roughly 25-65 μT at its surface. Testing a satellite’s magnetic field sensors and its magnetorquers requires the testing setup be able to generate any value of magnetic field between zero and at least ±65 μT in at least one axis. Doing so requires generating a magnetic flux density strong enough to cancel the natural magnetic field from the Earth in the laboratory and then enough to change its direction.

The control system for the field generator should also be able to cancel time-varying fields present in the laboratory, such as from power line currents and Earth (soil) currents.

2. Derivations

Choose two of the coil systems and derive the magnetic flux density at the center of each one using the given geometries and dimensions. Compare your results to those stated in the papers.