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Question

Two identical conducting spheres, one having an initial charge +Q and the other initially uncharged, are brought into contact.

1. What is the new charge on each sphere?

2. While the spheres are in contact, a positively charged rod is moved close to one sphere, causing a redistribution of charges on the two spheres, so the charge on the sphere closest to the rod has a charge - Q. What is the charge in the other sphere?

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Solution

When the sphere are brought into contactthey become equipotential.

q14πεr=q24πrε

q1=q2.............(1)

But, from conservation of charge,

q1+q2=Q

Fom eq(1) and eq(2)

2q1=Q⟹q1=Q2=q2

Net induced charge is always is zero,

Hence net charge on two sphere remains unchanged

−Q+Q′=Q

2Q=Q '

Hence, +2Q will be charge on second sphere.

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