Q1. I guess the flux will not change if the ring is rotated about a diameter through 180 degree. because

flux =   Edscos 

though you rotate by 180 the angle made by the area vector to the field remains 0. they are parallel.

 

2) the field at the centre of the shell or any conductor is always 0.

 if it is conductor. the field will not change if another charge is brought near it.

Electrostatic shielding.

 

 I guess this question and the next have already been discussed. Do search.

 

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