26. Capacitors & Dielectrics

A parallel plate capacitor with air separating the plates is fully charged by a battery. The battery is disconnected and an insulator with dielectric constant of 1.5 is inserted between the plates by somebody wearing insulating gloves. What happens to the potential difference between the plates?

When a 360-nF air capacitor (1 nF = 10^-9 F) is connected to a power supply, the energy stored in the capacitor is 1.85x10^-5 J. While the capacitor is kept connected to the power supply, a slab of dielectric is inserted that completely fills the space between the plates. This increases the stored energy by 2.32x10^-5 J. (a) What is the potential difference between the capacitor plates? (b) What is the dielectric constant of the slab?

Polystyrene has dielectric constant 2.6 and dielectric strength 2.0x10^7 V/m. A piece of polystyrene is used as a dielectric in a parallel-plate capacitor, filling the volume between the plates. (a) When the electric field between the plates is 80% of the dielectric strength, what is the energy density of the stored? (b) When the capacitor is connected to a battery with voltage 500.0 V, the electric field between the plates is 80% of the dielectric strength. What is the area of each plate if the capacitor stores 0.200 mJ of energy under these conditions?

A constant potential difference of 12 V is maintained between the terminals of a 0.25-uF, parallel-plate, air capacitor. (a) A sheet of Mylar is inserted between the plates of the capacitor, completely filling the space between the plates. When this is done, how much additional charge flows onto the positive plate of the capacitor (see Table 24.1) ? (b) What is the total induced charge on either face of the Mylar sheet? (c) What effect does the Mylar sheet have on the electric field between the plates? Explain how you can reconcile this with the increase in charge on the plates, which acts to increase the electric field.

A parallel-plate capacitor has capacitance C0 = 8.00 pF when there is air between the plates. The separation between the plates is 1.50 mm. (a) What is the maximum magnitude of charge Q that can be placed on each plate if the electric field in the region between the plates is not to exceed 3.00x10^4 V/m? (b) A dielectric with K = 2.70 is inserted between the plates of the capacitor, completely filling the volume between the plates. Now what is the maximum magnitude of charge on each plate if the electric field between the plates is not to exceed 3.00x10^4 V/m?