An air-filled parallel-plate capacitor that has gap width

Chapter , Problem 92

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An air-filled parallel-plate capacitor that has gap width has plates that each have an area The capacitor is charged to a potential difference and is then removed from the voltage source. A dielectric slab that has a dielectric constant of 2.00, a thickness and an area is then inserted, as shown in Figure 24-52. Let s1 be the free charge density at the conductordielectric surface, and (a) Explain why the electric field must have the same value inside the dielectric as in the free space between the plates. (b) Show that (c) Show that the final capacitance (after the slab is inserted) is 1.50 times the capacitance when the capacitor is filled with air. (d) Show that the final potential difference is (e) Show that energy stored after the slab is inserted is only two-thirds of the energy stored before insertion.