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For this the electric field R. r2 would be 0 correct? Because charge enclosed is 0?

And for the electric field between r1 and r2 it would be equal to E = (+Q)/(4pi*R^2*Epsilon_0)?

After disconnecting the battery we ground the outer shell. Now calculate the electric field R>r2 and R<r1.

For R<r1, the electric field is 0 because charge enclosed is 0, correct?

And for R>r2 the electric field is now equal to E = (+Q)/(4pi*R^2*Epsilon_0) because charge enclosed is now +Q +Q -Q = +Q.

Could you guys please verify if my reasoning is correct for these problems. Thank you so much for your help!