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The diagram shows three infinitely long uniform line charges placed on the `X, Y` and ` Z` axis . The word done in moving a unit positive charge from (1,1,1) to (0 , 1,1,) is equal to .A. ` ( lambda ln2 ) / 2 pi varepsilon_(0)`B. `(lambda ln 2 ) // 2 pi varepsilon_(0)`C. `(3lambdal ln 2) //2 pivarepsilon_(0)`D. None |
Answer» Correct Answer - B Displacement is only along x-axis `Delta =- underset (1) overset (3) (Ò)E_(x) dx` ` E_x ` is field due to dharged wire lying along y-axis `E_(x) =(2K(3lambda))/(x) +(2K(lambda))/(x)rArr E_(x) =(2K(lambda))/(x)xx4` `E_x = (2lambda) (pi in_0 x)` ….(2) From (1) and (2) `Delta V =- underset (1) overset (2) (Ò) (1l)/(phat I_0 x) dx` `Delta V = (2 lambda)/(pi in_(0)) [ln x]_(1)^(2) rArrDelta V =(2 lambda)/(piin_(0)) ln1` `DeltaV=(lambda)/(pi in_(0)) ln2` |
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