How much energy is stored by the electric field between two square plates, 8.0 cm on a side, separated by a 1.5-mm air gap? The charges on the plates are equal and opposite and of magnitude 420 μC.

An air capacitor is made from two flat parallel plates $1.50$ mm apart. The magnitude of charge on each plate is $0.0180$ $\mu$C when the potential difference is $200$ V.

(a) What is the capacitance?

(b) What is the area of each plate?

(c) What maximum voltage can be applied without dielectric breakdown? (Dielectric breakdown for air occurs at an electric-field strength of $3.0\times {10}^6$ V/m.)

(d) When the charge is $0.0180$ $\mu$C, what total energy is stored?

A 3500-pF air-gap capacitor is connected to an 18-V battery. If a piece of mica fills the space between the plates, how much charge will flow from the battery?

A huge 4.0-F capacitor has enough stored energy to heat 2.4 kg of water from 21°C to 95°C. What is the potential difference across the plates?

The electric field near the Earth is about 150 N/C. (a) What is the energy density near the Earth? (b) Approximately how much electric energy is stored in the Earth’s electric field in the first 10 m above the Earth’s surface? (c) Compare (by a ratio) the answer to part (b) with the daily output from a 2000-MW power station.

How much energy must a 24-V battery expend to charge a 0.45-μF and a 0.20-μFcapacitor fully when they are placed in series?

How much work would be required to remove a metal sheet from between the plates of a capacitor (as in Problem 18a), assuming the battery remains connected so the voltage remains constant?

A cylindrical capacitor (Example 24–2) has Rₐ = 3.5 mm and R₆.= 0.50 mm. The two conductors have a potential difference of 625 V, with the inner conductor at the higher potential. Calculate the energy stored in a 1.0-m length of the capacitor.

Suppose the capacitor in Example 24–13 remains connected to the battery as the dielectric is removed. What will be the work required to remove the dielectric in this case?