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Electric Charges And Fields

Question
CBSEENPH12039523
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A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is

  • fraction numerator straight Q over denominator 8 πε subscript straight o straight L end fraction
  • fraction numerator 3 space straight Q over denominator 4 space πε subscript straight o straight L end fraction
  • fraction numerator straight Q over denominator 4 πε subscript straight o straight L space In space 2 end fraction
  • fraction numerator straight Q space In space 2 over denominator 4 πε subscript straight o straight L end fraction

Solution

D.

fraction numerator straight Q space In space 2 over denominator 4 πε subscript straight o straight L end fraction
dv space equals space kdQ over straight x straight V space equals space integral subscript straight L superscript 2 straight L end superscript dV straight V space equals space integral subscript straight L superscript 2 straight L end superscript kdQ over straight x space equals integral subscript straight L superscript 2 straight L end superscript fraction numerator straight k space open parentheses begin display style straight Q over straight L end style close parentheses space dx over denominator straight x end fraction space equals space fraction numerator straight Q over denominator 4 πε subscript straight o straight L end fraction integral subscript straight L superscript 2 straight L end superscript open parentheses 1 over straight x close parentheses space dx space equals space fraction numerator straight Q over denominator 4 πε subscript straight o straight L end fraction left square bracket log subscript straight e space equals space straight x right square bracket subscript straight L superscript 2 straight L end superscript space equals space fraction numerator straight Q over denominator 4 πε subscript straight o straight L end fraction left square bracket log subscript straight e 2 straight L space minus space log subscript straight e straight L right square bracket space equals space fraction numerator straight Q over denominator 4 πε subscript straight o straight L space end fraction open square brackets log subscript straight e space fraction numerator 2 straight L over denominator straight L end fraction close square brackets space equals space fraction numerator straight Q over denominator 4 πε subscript straight o straight L end fraction space In space left parenthesis 2 right parenthesis

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point? 

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