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CBSE Class 12-science Answered

Two  small  charged  spheres  contain  charges  +Q1 ,-Q2  respectively . A charge  dQ is  removed from  sphere  carrying  charge +Q1 and  is  transferred  to  the  other.  Find  charge  on  each  sphere for  MAXIMUM  ELECTRIC  FORCE between  them.  [PLEASE  ANSWER  THE  QUESTION  STEP  BY  STEP DO  NOT  SKIP ANY  STEP  SPECIALLY  MATHEMATICAL ]  
Asked by pardeepkumar2281 | 22 May, 2018, 09:27: PM
answered-by-expert Expert Answer
Let us assume initial charges are +Q1 and -Q2. Let us remove small amount of charge q from +Q1 and add it to -Q2.
After transferring, the charges are (+Q1-q) and (-Q2+q). 
 
Force F  between them is given by,  
 
begin mathsize 12px style F space equals space fraction numerator open parentheses plus Q 1 minus q close parentheses open parentheses negative Q 2 plus q close parentheses over denominator 4 πε subscript 0 cross times straight d squared end fraction space equals space K open parentheses plus Q 1 minus q close parentheses open parentheses negative Q 2 plus q close parentheses space equals space K space open curly brackets open parentheses negative Q 1 cross times Q 2 close parentheses space plus open parentheses Q 1 plus Q 2 close parentheses q minus space q squared close curly brackets end style
It is assumed d remains constant and hence all constants are clubbed together in K. By comparing q2 wih Q1×Q2, we can write q2  << Q1×Q2
 
hence the force F is written as 
 
begin mathsize 12px style F space equals space space K space open curly brackets open parentheses negative Q 1 cross times Q 2 close parentheses space plus open parentheses Q 1 plus Q 2 close parentheses q close curly brackets end style ............................(1)
Maximum force will be obtained by finding the condition thta satisfies (dF/dq)  = 0 
 
hence begin mathsize 12px style fraction numerator d F over denominator d q end fraction space equals space K space space left parenthesis Q 1 plus Q 2 right parenthesis space equals space 0 semicolon............................... left parenthesis 6 right parenthesis end style
 
from (6) we get that when +Q1 = - Q2  Force is maximum

Answered by Thiyagarajan K | 23 May, 2018, 03:37: PM

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