In the region of space between the plates of a parallel-plate capacitor there is a uniformly distributed positive charge with a volume density $\rho$. The plates are connected electrically and their potential is set at zero. Calculate and draw a sketch of the distributions of the potential and electric field strength between the plates.

Two series-connected capacitors of the same size, one filled with air and the other with a dielectric, are connected to a voltage source. To which of the capacitors a higher voltage is applied?

Two identical air capacitors are connected in series. How will the charge on and potential difference across each capacitor change when the distance between the plates of one capacitor is increased in the following cases: when the capacitors are connected to a DC source, and when the capacitors are first charged and then disconnected from the DC source?

Two identical parallel-plate air capacitors are connected in one case in parallel and in the other in series. In each case the plates of one capacitor are brought closer together by a distance $a$ and the plates of the other are moved apart by the same distance $a$. How will the total capacitance of each system change as a result of such manipulations?

A parallel-plate capacitor is filled with a dielectric up to one-half of the distance between the plates. The manner in which the potential between the plates varies is illustrated in the figure. Which half ($1$ or $2$) of the space between the plates is filled with the dielectric and what will be the distribution of the potential after the dielectric is taken out of the capacitor provided that ($a$) the charges on the plates are conserved or ($b$) the potential difference across the capacitor is conserved?

A capacitor is partially filled with a dielectric. In which of its parts is the electric field strength greater? What about the electric displacement and the energy density?

Two parallel-plate capacitors, one filled with air and the other with a dielectric, have the same geometric dimensions, are connected in parallel, and are charged to a certain potential difference. In which of the two capacitors is the electric field strength greater, in which is the electric displacement greater, in which is the energy density greater, and in which is the surface charge density on the plates greater?

Three point-like charges are positioned at the vertices of an equilateral triangles. Two are equal in magnitude and are like, while the third is opposite in sign. What should the magnitude of the third charge be so that the total interaction energy of the charges is zero?

The dielectric filling the space between the plates of a capacitor that has been charged and then disconnected from the voltage source is removed. How should the distance between the plates be changed so that the energy stored in the capacitor remains the same? Explain the origin of the change in energy.