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A $Q_1$ charged spherical shell $A$ with radius of $a$ is inside a $Q_2$ charged spherical shell $B$ with radius $b$.

Now $A$ is grounded. Since no force is acting on $Q_1$, all of them should be neutralized, and at the end it charge on $A$ should be zero.

But when we equate the potential on $A$ to zero, since it is grounded we will get an answer that $A$ is charged by $-aQ_2/b$. And I know that's the right answer, and what I said earlier that the charge should be zero, is wrong.

My doubt is grounding should remove the excess charges which is free to move then how a negative charge came there? Explain me what is happening inside.

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Grounding doesn't set the charge to zero - it sets the potential to zero. That means the residual charge will be whatever it needs to be to achieve that.

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