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Thin infinite sheet of width w contains uniform charge distribution sigma. Find out electric field intensity at following points : (a) A point which lies in the same plane at a distance d from one of its edge. (b) A point which is on the symmetry plane of sheet at a perpendicular distance d from it. |
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Answer» Solution :(a) consider a thin strip of width dx. Linear charge DENSITY of strip : `lambda= sigma dx` So, electric field due to this strip at point P `dE= (2 k sigma d X)/x` `E_("net")= underset(d)OVERSET(d+w)(int) sigma/(2 pi epsi_(0)) (dx)/x` `= sigma/(2 pi epsi_(0)) ln ((d+w)/d)` (b) Consider a thin strip of width dx. Linear charge density of strip : `lambda=sigma dx` `:. E_(p) =int 2d E cos theta` or `E_(p)=2. int_(0)^(w//2) (sigma dx)/(2 pi epsi_(0) sqrt(d^(2)+x^(2))). d/sqrt(d^(2)+x^(2))` `=(sigma d)/(pi epsi_(0)) int_(0)^(w//2) (dx)/(d^(2)+x^(2))=sigma/(pi epsi_(0))"tan"^(-1) w/(2d)` 
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