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There are two large parallel metallic plates `S_(1)` and `S_(2)` carrying surface charge densities `sigma_(1)` and `sigma_(2)` respectively `(sigma_(1) gt sigma_(2))` placed at a distance d apart in vacuum. Find the work done by the electric field in moving a point charge q at distance `a(a lt d)` from `S_(1)` towards `S_(2)` along a line making an angle `pi//4` with the normal to the plates. |
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Answer» Correct Answer - `W=((sigma_(1)-sigma_(2))qa)/(sqrt(2) in_(0))` Electric field near a large metallic plate is given by `E=sigma//epsilon_(0)`. In between the plates the two field will be in opposite direction. Hence, `E_("net")=(sigma_(1)-sigma_(2))/epsilon_(0)=E_(0)` (say) Now, `W=(q)` (potential difference)`=q(E_(0)a cos 45^(@))` `(q)((sigma_(1)-sigma_(2))/epsilon_(0))(a/sqrt(2))=((sigma_(1)-sigma_(2))qa)/(sqrt(2)epsilon_(0))` |
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