Initially the space between the plates of the capacitor is filled with air, and the field strength in the gap is equal to `E_(0)`. Then half the gap is filled with uniform isotropic dielectric with permittivity `epsilon` as shown in Fig. Find the moduli of the introduction of the dielectric (a) deos not change the voltage across the plates, (b) leaves the charges at the plates constant.

Initially the space between the plates of the capacitor is filled with

1.	Initially the space between the plates of the capacitor is filled with air, and the field strength in the gap is equal to `E_(0)`. Then half the gap is filled with uniform isotropic dielectric with permittivity `epsilon` as shown in Fig. Find the moduli of the introduction of the dielectric (a) deos not change the voltage across the plates, (b) leaves the charges at the plates constant.
Answer» (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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