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CBSE Class 12-science Answered

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Asked by arup.isro | 25 Jun, 2019, 11:25: PM
answered-by-expert Expert Answer
Physics behind the problem is,  when two charged conductors are in contact, they are at same potential after sharing the charge.
Charge transfer depends on capacitance of each conductor.
 
Initially plate has charge Q  and insuated conductor uncharged.
At first contact, charge of plate will become Q-q and conductor gets charge q.
 
Since both plate and insulated conductor has same potential, we have  (Q-q)/q = constant ................... (1)
 
after first contact, plate has charge Q and insulated conductor has charge q.
 
Let q1 be the charge transferred at second contact.  Hence as mentioned above, ( Q - q1 ) / q1 = constant ...........(2)
 
By equating (1) and (2) and solving for q1 , we get  q1 = ( q2 / Q )
 
If q2 be the charge transferred at third contact, as derived above, we get q2 = ( q3 / Q2 )
 
hence charge acquired after infinite number of contacts,  q∞ = q + ( q2 / Q ) + ( q3 / Q2 ) + ...........................
 
Above series is in G.P with first term q and (q/Q) as common ratio.   Hence q∞ = begin mathsize 12px style q cross times fraction numerator 1 over denominator 1 minus begin display style q over Q end style end fraction space equals space fraction numerator q space Q over denominator Q space minus space q end fraction end style
Answered by Thiyagarajan K | 26 Jun, 2019, 03:46: PM

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