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Initially the space between the plates of the capacitor is filled with air, and the field strengthin the gapis equalto E_(0). Thenhalf the gap is filled with uniformisotropicdielectric with permittivity epsilonas shown in Fig. Find the moduli of the introduction of the dielectric (a) deos not change the voltageacross the plates, (b) leaves the charges at the plates constant. |
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Answer» SOLUTION :(a) We have `D_(1) = D_(2)`, or EPSILON `E_(2) = E_(1)` Also,`E_(1) (d)/(2) + E_(2) (d)/(2) = E_(0) d` or, `E_(1) + E_(2) = 2 E_(0)` Hence, `E_(2) = (2 E_(0))/(epsilon + 1)` and `E_(1) = (2epsilon E_(0))/(epsilon + 1)` and `D_(1) =D_(2) = (2 epsilon epsilon_(0) E_(0))/(epsilon + 1)` (b) `D_(1) = D_(2)`, or `epsilon E_(2) = E_(1) = (sigma)/(epsilon_(0)) = E_(0)` THUS, `E_(1) = E_(0), E_(2) = (E_(0))/(epsilon)` and `D_(1) = D_(2) = epsilon_(0) E_(0)` |
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