Thanks Faraday we learned the change of magnetic flux through a conductor results in a circular current appearing in this conductor. The Lenz’s law defines such a direction of this current that magnetic field induced by the current compensates the change of the magnetic flux. So this law hints at conservation of the magnetic flux. Indeed, let first there is a magnetic field piercing the conductor in a laboratory and next you switch it off. The instant change of the flux results in a circular current which restores the lost magnetic field in the conductor. Due to the heat released in the conductor, the current then will fade at the rate determined by the conductor resistivity. For example the current responsible for the Earth’s magnetic field should have disappeared in a million year. Now imagine this conductor has zero resistance. That is realistic if you low the temperature down to several Kelvin degrees so that the phenomenon of superconductivity takes place. Afterwards heat stops being released so the energy of the current stored in the conductor is conserved. The steady current means a fixed magnetic flux on the other hand. You can now decrease the area of the circular current by squeezing the conductor or, on the contrary, add more turns if your conductor is a coil. Since the flux is not going to change, what will change is the current and consequently the magnetic field created by it.
On a super strong flux 🙂