If a circular shaped flat magnet had a sheet of copper placed over one side with that direct magnetic field more strongly out the other side?

Placing a sheet of copper over a circular magnet will not significantly enhance the magnetic field on the opposite side. Copper is not a superconductor, and therefore it does not have the ability to reflect magnetic fields as efficiently as superconductors do.

1. **Copper's Magnetic Properties**: Copper is a good conductor of electricity and heat, but it is not magnetic in nature. It does not generate its own magnetic field and is not attracted to magnets to the same extent as ferromagnetic materials like iron or nickel.
2. **Effect of Copper on Magnetic Field Direction**: When a magnetic field encounters a sheet of copper, the electrons in the copper will rearrange and rotate, creating resistance. This can lead to a slight decrease in the magnetic field strength as the magnetic field is partially shielded by the copper sheet. However, this effect is not significant compared to the shielding provided by superconductors.
3. **Magnet Shielding Comparison**: Superconductors offer a higher level of shielding compared to copper. They can completely reflect magnetic fields, repelling them more efficiently than materials like steel.

In conclusion, while copper is a good conductor and can slightly shield a magnetic field, it does not reflect magnetic fields as strongly as superconductors do. Therefore, placing a sheet of copper over a magnet will not significantly enhance the magnetic field on the opposite side.