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Two uniformly charged large plane sheets...

Two uniformly charged large plane sheets `S_1` and `S_2` having charge densities `sigma_1` and `sigma_2 (sigma_1 gt sigma_2)` are placed at a distance d parallel to each other. A charge `q_0` is moved along a line of length `a (a lt d)` at an angle `45^(@)` with the normal to `S_1`. Calculate the work done by the electric field.
(##BMS_V03_C03_E01_060_Q01##).

Text Solution

Verified by Experts

The correct Answer is:
`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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