A potential difference is applied between a conducting sphere and a conducting plate ("plus" on the sphere and "minus" on the plate). The dimensions of the plate are much larger than the distance between sphere and plate. A point positive charge is moved from point $1$ to point $2$ parallel to the plate. Is any work done in the process?

         

Two parallel-plate capacitors with different distances between the plates are connected in parallel to a voltage source. A point positive charge is moved from a point $1$ that is exactly in the middle between the plates of a capacitor $C1$ to a point $2$ (or a capacitor $C2$) that lies at a distance from the negative plate of $C2$ equal to half the distance between the plates of $C1$. Is any work done in the process?

The space between the rectangular plates (with sides $a$ and $b$) of a parallel-plate capacitor (the distance between the plates is $l$) is filled with a solid dielectric whose dielectric constant is $\epsilon$. The capacitor is charged to a certain potential difference and disconnected from the voltage source. After that the dielectric is slowly moved out of the capacitor, which means that the section $x$ not filled with the dielectric gradually increases in size. How will the potential difference between the plates and the surface charge densities on both parts of the capacitor (with and without the dielectric) change in the process?

At which of the two points, $1$ or $2$, of a charged capacitor with nonparallel plates is the surface charge density greater?

The diameter of the outer conductor of a cylindrical capacitor is $D_2$. What should the diameter of the core, $D_1$, of this capacitor be so that for a given potential difference between the outer conductor and the core the electric field strength at the core is minimal?

Four capacitors, $C1, C2, C3,$, and $C4$, are connected as shown in the figure. A potential difference is applied between points $A$ and $B$. What should the relationship between the capacitances of the capacitors so that the potential difference between points $a$ and $b$ is zero?

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?