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CBSE Class 12-science Answered

The magnitude of electric potential difference between A and B for a given line charge having uniform density lambda is approximately ? ( Lambda = 10 ^ -8 C/m & ln 2 = 0.7 )
question image
Asked by arunavamitra50 | 24 Jul, 2019, 04:36: PM
answered-by-expert Expert Answer
Electric field E at a distance r from an infinte line charge = λ / (2 π εo  r )  ......................(1)
 
where λ is charge/unit length  and εo is permitivity of free space.
 
Potential difference VAB  between A and B is given by
  VAB = begin mathsize 14px style negative integral subscript 2 r subscript o end subscript superscript r subscript o end superscript E space d r space equals space minus space integral subscript 2 r subscript o end subscript superscript r subscript o end superscript fraction numerator lambda space d r over denominator 2 pi epsilon subscript o r end fraction space equals space minus space fraction numerator lambda over denominator 2 pi epsilon subscript o end fraction open square brackets ln space r close square brackets subscript 2 r subscript o end subscript superscript r subscript o end superscript space equals space fraction numerator lambda over denominator 2 pi epsilon subscript o end fraction space ln 2 space equals space fraction numerator 10 to the power of negative 8 end exponent cross times 0.7 over denominator 2 straight pi cross times 8.85 cross times 10 to the power of negative 12 end exponent end fraction space equals space 126 space V end style
Answered by Thiyagarajan K | 24 Jul, 2019, 10:17: PM

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