Suppose that you charge a 1 F capacitor in a circuit containing two 1.5 V batteries, so the final potential difference across the plates is 3 V. How much charge is on each plate? How many excess electrons are on the negative plate?

A capacitor with plate area $0.0440 \mathrm{~m}^2$ and plate separation $85.0\ \mu \mathrm{m}$ is to be charged to $12.0 \mathrm{~V}$ and store $7.50\ \mu \mathrm{J}$ of energy. What should be the dielectric constant of the material between the plates?

Lola is placing appetizers on plates. She has 63 spring rolls and 84 cheese cubes. She wants to include both appetizers on each plate. Each plate must have the same numbers of spring rolls and cheese cubes. What is the greatest number of plates she can make using all of the appetizers? How many of each type of appetizer will be on each of these plates?

The distance between the plates of a parallel plate capacitor is reduced by half and the area of the plates is doubled. What happens to the capacitance? a) It remains unchanged. b) It doubles. c) It quadruples. d) It is reduced by half.

The plate separation of a charged capacitor is 0.0800 m. A proton and an electron are released from rest at the midpoint between the plates. Ignore the attraction between the two particles, and determine how far the proton has traveled by the time the electron strikes the positive plate.

A parallel-plate capacitor is connected to a battery that maintains a constant potential difference $V$ between the plates. If a dielectric is inserted between the plates of the capacitor, does the electric field between the plates increase, decrease, or remain the same?

Compare the electric fields of an infinite sheet of charge, an infinite, charged conducting plate, and infinite, oppositely charged parallel plates.

A parallel-plate capacitor with plate area $2.0 \mathrm{~cm}^2$ and air-gap separation $0.50 \mathrm{~mm}$ is connected to a $12~\mathrm{V}$ battery, and fully charged. The battery is then disconnected. The plates are now pulled to a separation of $0.85 \mathrm{~mm}$. How much work was required to pull the plates to their new separation?

Suppose that in a state, license plates have three letters followed by three numbers, in a way that no letter or number is repeated in a single plate. Determine the number of possible license plates for this state.

Lola is placing appetizers on plates. She has 63 spring rolls and 84 cheese cubes. She wants to include both appetizers on each plate. Each plate must have the same numbers of spring rolls and cheese cubes. What is the greatest number of plates she can make using all of the appetizers? How many of each type of appetizer will be on each of these plates?

An electron enters a region between two large parallel plates made of aluminum separated by a distance of $2.0 \mathrm{~cm}$ and kept at a potential difference of $200 \mathrm{~V}$. The electron enters through a small hole in the negative plate and moves toward the positive plate. At the time the electron is near the negative plate, its speed is $4.0 \times 10^5 \mathrm{~m} / \mathrm{s}$. Assume the electric field between the plates to be uniform, and find the speed of electron at $(a)$ $0.10 \mathrm{~cm}$, $(b)$ $0.50 \mathrm{~cm}$, $(c)$ $1.0 \mathrm{~cm}$, and $(d)$ $1.5 \mathrm{~cm}$ from the negative plate, and $(e)$ immediately before it hits the positive plate.

The absorber plate and the adjoining cover plate of a flat-plate solar collector are at 70 and $35^{\circ} \mathrm{C}$, respectively, and are separated by an air space of 0.05 m. What is the rate of free convection heat transfer per unit surface area between the two plates if they are inclined at an angle of $60^{\circ}$ from the horizontal?

A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, $1.95 \mathrm{~cm}$ away, $14.7$ ns later. (a) What is the speed of the electron as it strikes the second plate? (b) What is the magnitude of the electric field?

A proton gun fires a proton from midway between two plates, A and $\mathrm{B}$, which are separated by a distance of $10.0 \mathrm{~cm}$; the proton initially moves at a speed of $150.0 \mathrm{~km} / \mathrm{s}$ toward plate B. Plate A is kept at zero potential, and plate B at a potential of $400.0 \mathrm{~V}$. b) If not, where will it turn around?