The currents in each coil of a pair of Helmholtz coils should circulate in the same direction. This configuration is essential for achieving the desired uniform magnetic field between the coils.
When the currents flow in the same direction, the magnetic fields produced by each coil add together. This superposition results in a more uniform magnetic field in the central region between the coils, which is the primary purpose of using Helmholtz coils. If the currents were to flow in opposite directions, the magnetic fields would partially cancel each other out, leading to a less uniform field and diminishing the efficiency of the setup.
In applications such as precision measurements and experiments requiring a stable magnetic field, using the same current direction ensures that the field remains consistent and predictable. This makes Helmholtz coils an excellent choice for various scientific research and experimental setups.