8.5 Molecular Model of a Dielectric

Repeat the calculations of the reference for the case in which the battery remains connected while the dielectric is placed in the capacitor.

Distinguish between dielectric strength and dielectric constant.

Water has a high dielectric constant. Explain why it is then not used as a dielectric material in capacitors.

Explain why the dielectric constant of a substance containing permanent molecular electric dipoles decreases with increasing temperature.

Elaborate on the way in which the polar character of water molecules helps to explain water’s relatively large dielectric constant.

For a Teflon™-filled, parallel-plate capacitor, the area of the plate is $50.0 \text{cm}^{2}$ and the spacing between the plates is 0.50 mm. If the capacitor is connected to a 200-V battery, find (a) the free charge on the capacitor plates, (b) the electrical field in the dielectric, and (c) the induced charge on the dielectric surfaces.

(a) What is the capacitance of a parallel-plate capacitor with plates of area $1.50 \text{m}^{2}$ that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?

The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of $1.60 \times 10^{7} \text{V} / \text{m}$. The capacitor has to have a capacitance of 1.25 nF and must be able to withstand a maximum potential difference 5.5 kV. What is the minimum area the plates of the capacitor may have?

A parallel-plate capacitor has square plates that are 8.00 cm on each side and 3.80 mm apart. The space between the plates is completely filled with two square slabs of dielectric, each 8.00 cm on a side and 1.90 mm thick. One slab is Pyrex glass and the other slab is polystyrene. If the potential difference between the plates is 86.0 V, find how much electrical energy can be stored in this capaci…

An air-filled (empty) parallel-plate capacitor is made from two square plates that are 25 cm on each side and 1.0 mm apart. The capacitor is connected to a 50-V battery and fully charged. It is then disconnected from the battery and its plates are pulled apart to a separation of 2.00 mm. (a) What is the capacitance of this new capacitor? (b) What is the charge on each plate? (c) What is the electr…

Earth can be considered as a spherical capacitor with two plates, where the negative plate is the surface of Earth and the positive plate is the bottom of the ionosphere, which is located at an altitude of approximately 70 km. The potential difference between Earth’s surface and the ionosphere is about 350,000 V. (a) Calculate the capacitance of this system. (b) Find the total charge on this capac…

Three capacitors having capacitances of 8.40, 8.40, and 4.20 $\mu \text{F}$, respectively, are connected in series across a 36.0-V potential difference. (a) What is the charge on the $4.20 - \mu \text{F}$ capacitor? (b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What i…

(a) An $8.00 - \mu \text{F}$ capacitor is connected in parallel to another capacitor, producing a total capacitance of $5.00 \mu \text{F}$. What is the capacitance of the second capacitor? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) A certain parallel-plate capacitor has plates of area $4.00 \text{m}^{2}$, separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. The inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor. (a) What is the capacitance of the capacitor? (b) What is the magnitude of the electrical field at $r = 12.6 \text{cm}$, just outside the inner sphere? (c) What is the magnitude o…

Electronic flash units for cameras contain a capacitor for storing the energy used to produce the flash. In one such unit the flash lasts for 1/675 fraction of a second with an average light power output of 270 kW. (a) If the conversion of electrical energy to light is 95% efficient (because the rest of the energy goes to thermal energy), how much energy must be stored in the capacitor for one fla…