The radii of 2 concentric spherical conducting shells are r1 and r2 (r2>r1). The charge on outer shell is q. what is the charge on inner shell which is connected to the earth

Let the charge on the inner sheel with radius R1 let it would x. Since it is earth its potential must be equal to the potential of earth which is equal to zero .Now potential due to outer shell at the inner sheel can be written as Kq/r2 and due to inner shell at its surface can be written as Kx/R1

And the condition for zero potential is KQ/r2+Kx/r1=0 . Solving x=-qr1/r2.Eo the shell will take this much charge from earth to make its potential same equal to earth .

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