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Pl tell the question.
 
Q.)Two conducting spheres A and B of the same size are situated at some distance apart.Each has a charge of +q coulomb and they repel each other with a force of 10^-5(10 raise to the power of (-5)).
A third  conducting uncharged sphere C of same size is first touched with A and then with B and placed exactly between A and B.Calculate the resultant force on C..
 
 
ThankYou!!!

Asked by neeraj.unnao 12th April 2017, 5:07 AM
Answered by Expert
Answer:
According to the Coulomb's law, the magnitude of electrostatic force between two charges is given as
begin mathsize 12px style straight F equals straight k fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r squared end fraction
where space straight k space is space the space constant space of space proportionality.
Here comma space it space is space given space that space the space initial space charge space on space sphere space straight A space as space well space as space straight B space is space plus straight q. space
Let space the space seperation space between space the space charges space be space straight r.
therefore space straight F equals straight k straight q squared over straight r squared equals 10 to the power of negative 5 end exponent space straight N space........ space left parenthesis Given right parenthesis
When space an space unchrged space spere space straight C space is space touched space wih space spere space straight A comma space then
Charge space on space sphere space straight A space equals space Charge space on space sphere space straight C space equals space straight q over 2
Now comma space when space the space sphere space straight C space is space touched space with space straight B comma space then space the space total space charge space charge space on space straight C space equals space straight q space plus space space straight q over 2
rightwards arrow space Total space charge space charge space on space straight C space equals space 1.5 straight q
therefore Total space charge space on space spere space straight C space equals space harge space on space sphere space straight B space equals space fraction numerator 1.5 straight q over denominator 2 end fraction equals 0.75 space straight q end style
 
 
begin mathsize 12px style Force space on space sphere space straight C space due space to space sphere space straight A space equals straight k space fraction numerator open parentheses begin display style bevelled straight q over 2 end style close parentheses open parentheses 0.75 straight q close parentheses over denominator open parentheses begin display style bevelled straight r over 2 end style close parentheses squared end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1.5 straight k fraction numerator straight q squared over denominator straight r squared space end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1.5 straight F space
This space force space on space sphere space straight C space due space to space sphere space straight A space will space be space towards space straight B.
Force space on space sphere space straight C space due space to space sphere space straight B space equals straight k space fraction numerator open parentheses begin display style 0.75 space straight q end style close parentheses open parentheses 0.75 space straight q close parentheses over denominator open parentheses begin display style bevelled straight r over 2 end style close parentheses squared end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2.25 straight k fraction numerator straight q squared over denominator straight r squared space end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2.25 straight F space
This space force space on space sphere space straight C space due space to space sphere space straight B space will space be space towards space straight A.
Net space force space on space sphere space straight C space equals space 2.25 space straight F space minus space 1.5 space straight F equals 0.75 space straight F
therefore Net space force space on space sphere space straight C space equals 0.75 cross times 10 space to the power of negative 5 end exponent straight N space towards space straight A.
end style
Answered by Expert 12th April 2017, 11:39 AM
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