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CBSE Class 12-science Answered

 
Point charge q0 is placed at centre of a cylinder as shown in figure. Find electric flux through curved surface :-
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Asked by shubhamjindal107 | 17 Feb, 2016, 06:51: PM
answered-by-expert Expert Answer
begin mathsize 14px style integral subscript negative straight R end subscript superscript straight R straight E space ds space cos space straight theta integral subscript negative straight R end subscript superscript straight R fraction numerator straight K space straight q subscript 0 over denominator left parenthesis straight R squared plus straight r squared right parenthesis end fraction cross times 2 straight pi space straight R space dr cross times fraction numerator straight R over denominator square root of straight R squared plus straight r squared end root end fraction straight K space straight q subscript 0 cross times 2 πR squared integral subscript negative straight R end subscript superscript straight R fraction numerator 1 over denominator left parenthesis straight R squared plus straight r squared right parenthesis 3 to the power of divided by 2 end exponent end fraction dr space Let space left parenthesis straight K space straight q subscript 0 cross times 2 πR squared right parenthesis space be space straight P. straight P cross times 2 integral subscript 0 superscript straight R fraction numerator 1 over denominator left parenthesis straight R squared plus straight r squared right parenthesis 3 to the power of divided by 2 end exponent end fraction dr straight K space straight q subscript 0 cross times 4 πR squared cross times open square brackets fraction numerator straight r over denominator straight R cubed square root of begin display style straight r squared over straight R squared end style plus 1 end root end fraction close square brackets subscript 0 superscript straight R straight K space straight q subscript 0 cross times 4 πR squared cross times 1 over straight R squared fraction numerator 1 over denominator square root of 2 end fraction equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction cross times straight q subscript 0 cross times 4 straight pi cross times fraction numerator 1 over denominator square root of 2 end fraction equals fraction numerator straight q subscript 0 over denominator square root of 2 straight epsilon subscript 0 end fraction end style
Answered by Faiza Lambe | 18 Feb, 2016, 07:31: PM

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