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- Is electric field inside a superconductor always zero ?

I was reading chapter 3 of this book https://blackwells.co.uk/bookshop/product/Superconductivity-by-James-Arnett/9780198507567, which is a brief introduction to superconductivity. It is stated that inside a superconductor the Electric filed is always zero. This is deduced from the equation ##\mathbf j = \sigma \mathbf E## and taking as an experimental evidence that ##\sigma \rightarrow \infty## for a superconductor (page 51).

What if I apply an external time-varying electric field ? Is ##\mathbf E## still zero ? It would be like the electrons instantaneously move to adapt to the new field... Is is possible ?

What if I apply an external time-varying electric field ? Is ##\mathbf E## still zero ? It would be like the electrons instantaneously move to adapt to the new field... Is is possible ?