A parallel-plate capacitor of width w, length L, and separation d is partially filled with...

A parallel-plate capacitor of width w, length L, and separation d is partially filled with a dielectric medium of dielectric constant εr, as shown in Fig. A battery of V0 volts is connected between the plates.

a) Find D, E, and ρs in each region.

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b) Find distance x such that the electrostatic energy stored in each region is the same.

Figure: A parallel-plate capacitor