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CBSE Class 12-science Answered

sir please solve the numerical:-
two similarly and equally charged identical metal sphere A and B repel each other with a force 5*0.00005N . a third identical sphereuncharged sphere C is touched with A and then placed at the mid point betweenA and B.calculate the net electric flux on C
Asked by anu Mishra | 19 Feb, 2016, 12:20: PM
answered-by-expert Expert Answer
Consider the two identical sphere A and B each having charge q are placed at a distance r apart as shown below.
Now,
begin mathsize 14px style straight F equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator straight q cross times straight q over denominator straight r squared end fraction end style
Syntax error from line 1 column 330 to line 1 column 350. Unexpected 'mathvariant'.    ... (1)   [5×0.00005 N = 5×10-5 N]
When an identical uncharged sphere C is touched to A, both will share the charge on A equally i.e., each of the spheres A and C will now possess charge q/2. The sphere C placed at the mid point between A and B experiences forces FCA (due to sphere A) and FCB (due to sphere B) in the directions as shown in the figure below.
Now, begin mathsize 14px style straight F subscript CA equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator straight q divided by 2 cross times straight q divided by 2 over denominator left parenthesis straight r divided by 2 right parenthesis squared end fraction space space space space space space equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q squared over straight r squared space space space space left parenthesis along space CB right parenthesis end style
and 
begin mathsize 14px style straight F subscript CB equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator straight q divided by 2 cross times straight q over denominator left parenthesis straight r divided by 2 right parenthesis squared end fraction space space space space space space equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator 2 straight q squared over denominator straight r squared end fraction space space space space left parenthesis along space CA right parenthesis end style
Since FCB>FCA, the resultant force on the sphere C is given by,
begin mathsize 14px style straight F apostrophe equals space straight F subscript CB space minus space straight F subscript CA space space space equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator 2 straight q squared over denominator straight r squared end fraction minus fraction numerator 1 over denominator 4 πε 0 end fraction straight q squared over straight r squared space space space equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction straight q squared over straight r squared space space space left parenthesis along space CA right parenthesis end style
Using eqn (1), we have,
F' = 5×10-5 N   (along CA)
Answered by Faiza Lambe | 19 Feb, 2016, 01:53: PM

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