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Q.

There are two uncharged identical metallic spheres 1 and 2 of radius r separated by a distance d(d>>r). A charged metallic sphere of same radius having charge q is touched with one of the sphere. After some time it is moved away from the system. Now the uncharged sphere is earthed. Charge on earthed sphere is

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a

q/2

b

−qr/d

c

−qr/2d

d

−q/2

answer is C.

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Detailed Solution

Let third sphere be touched with '1'. Then q/2 charge will be transferred to '1'. Now '2' is earthed. Potential of '2' is zero. kq2d+kq1r=0                    or   q1=−qr2d
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There are two uncharged identical metallic spheres 1 and 2 of radius r separated by a distance d(d>>r). A charged metallic sphere of same radius having charge q is touched with one of the sphere. After some time it is moved away from the system. Now the uncharged sphere is earthed. Charge on earthed sphere is