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Derive an expression for capacitance between two parallel lines having charge density and suspended by a distance 
Asked by Leeshmadevandira | 11 Apr, 2019, 01:00: PM
answered-by-expert Expert Answer
Let us consider the long parallel wires as line-charge dipole as shown in figure, +λ and -λ are charge/unit length .
 
Potential at location begin mathsize 16px style r with rightwards arrow on top end style is given by,   begin mathsize 12px style V left parenthesis space r with rightwards arrow on top space right parenthesis space equals space fraction numerator lambda over denominator 2 pi epsilon subscript o end fraction ln open parentheses r subscript minus over r subscript plus close parentheses end style
potential at left wire surface , V+  begin mathsize 12px style space equals space fraction numerator lambda over denominator 2 pi epsilon subscript o end fraction ln open parentheses d over a close parentheses end style
potential at right wire surface , V- begin mathsize 12px style space equals space fraction numerator lambda over denominator 2 pi epsilon subscript o end fraction ln open parentheses a over d close parentheses end style
potental difference between left and right wires ,  V+ - V- = V  begin mathsize 12px style space equals space fraction numerator lambda over denominator pi epsilon subscript o end fraction ln open parentheses d over a close parentheses end style
Capacitance/unit Length begin mathsize 12px style space equals space fraction numerator lambda over denominator fraction numerator lambda over denominator pi epsilon subscript o end fraction ln open parentheses d over a close parentheses end fraction space space equals space fraction numerator pi epsilon subscript o over denominator ln open parentheses d over a close parentheses end fraction end style
Answered by Thiyagarajan K | 12 Apr, 2019, 08:08: AM

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