The electric field in an "empty" capacitor can be obtained using Gauss' law. Consider an ideal capacitor (with no fringing fields) and the integration volume shown in Figure 9. The area of each capacitor plate is A and the charges on the plates are +/-Q. The charge enclosed by the integration volume shown in Figure 9 is equal to +Q. Gauss' law states that the electric flux [Phi] through the surface of the integration volume is related to the enclosed charge:
If a dielectric is inserted between the plates, the electric field between the plates will change (even though the charge on the plates is kept constant). Obviously, Gauss' law, as stated in eq.(48), does not hold in this case. The electric field E between the capacitor plates is related to the dielectric-free field Efree:
where [kappa] is the dielectric constant of the material between the plates. Gauss' law can now be rewritten as
Gauss' law in vacuum is a special case of eq.(50) with [kappa] = 1.
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