Moving a magnet close to a conductor induces a current. If it consists of a superconducting material with resistance $R=0$, then my textbook says:

Then the induced current will continue to flow even after the induced emf has disappeared.

This makes sense physically - there is no resistance to stop charge flow. But then the book draws this conclusion:

Thanks to this persistent current, it turns out that the flux through the loop is exactly the same as it was before the magnet started to move, so the flux through a loop of zero resistance never changes.

If the flux $\Phi$ never changes in a superconductor, from Faraday's law this means - from what I have learned - that no electromotive force $\epsilon$ is induced:

$$\epsilon=-\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0 \:\:\:\:\text{ if }\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0$$

My conclusion is therefor: There would never be induced any current at all. Current can never be induced in a superconductor loop. Is this the case or am I misunderstanding my book?

Moving a magnet close to a conductor induces a current. If it consists of a superconducting material with resistance $R=0$, then my textbook says:

Then the induced current will continue to flow even after the induced emf has disappeared.

This makes sense physically - there is no resistance to stop charge flow. But then the book draws this conclusion:

Thanks to this persistent current, it turns out that the flux through the loop is exactly the same as it was before the magnet started to move, so the flux through a loop of zero resistance never changes.

If the flux $\Phi$ never changes in a superconductor, from Faraday's law this means - from what I have learned - that no electromotive force $\mathcal{E}$ is induced:

$$\mathcal{E}=-\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0 \:\:\:\:\text{ when }\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0$$

My conclusion is therefor: There would never be induced any current at all. Current can never be induced in a superconductor loop. Is this the case or am I misunderstanding my book?

Moving a magnet close to a conducting induces a current. If it consists of a superconducting material with resistance $R=0$, then my text book says:

Then the induced current will continue to flow even after the induced emf has disappeared.

This makes sense physically. There is no resistance to stop charge flow. But then they draw this conclusion:

Thanks to this persistent current, it turns out that the flux through the loop is exactly the same as it was before the magnet started to move, so the flux through a loop of zero resistance never changes.

If the flux $\Phi$ never changes in a superconductor, from Ampere's law this means - from what I have learned - that no electromotive force $\epsilon$ is induced:

$$\epsilon=-\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0 \:\:\:\:\text{ if }\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0$$

My conclusion is therefor: There would never be induced any current at all. Current can never be induced in a superconductor loop. Is this the case or am I misunderstanding my book?

Moving a magnet close to a conductor induces a current. If it consists of a superconducting material with resistance $R=0$, then my textbook says:

Then the induced current will continue to flow even after the induced emf has disappeared.

This makes sense physically - there is no resistance to stop charge flow. But then the book draws this conclusion:

Thanks to this persistent current, it turns out that the flux through the loop is exactly the same as it was before the magnet started to move, so the flux through a loop of zero resistance never changes.

If the flux $\Phi$ never changes in a superconductor, from Faraday's law this means - from what I have learned - that no electromotive force $\epsilon$ is induced:

$$\epsilon=-\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0 \:\:\:\:\text{ if }\frac{\mathrm{d} \Phi}{\mathrm{d}t}=0$$

My conclusion is therefor: There would never be induced any current at all. Current can never be induced in a superconductor loop. Is this the case or am I misunderstanding my book?