A group of science and engineering students embarks on a quest to make an electrostatic projectile launcher. For their first trial, a horizontal, frictionless surface is positioned next to the 12-cm-diameter sphere of a Van de Graaff generator, and a small, 5.0 g plastic cube is placed on the surface with its center 2.0 cm from the edge of the sphere. The cube is given a positive charge, and then the Van de Graaff generator is turned on, charging the sphere to a potential of 200,000 V in a negligible amount of time. How much charge does the plastic cube need to achieve a final speed of a mere 3.0 m/s? Does this seem like a practical projectile launcher?

One kind of e-book display consists of millions of very small spheres that float in a thin fluid layer between two conducting transparent plates. each sphere is black on one side and white on the other, and possesses an electric dipole moment directed from the white side to the black. when an electric field is applied between the plates, the spheres rotate so that their dipole moment lines up with the field. depending on the fields direction, either the black or the white sides of th espheres can be made visible. the dipole moment of the spheres can be modeled as two opposite charges of magnitude 3.5 x 10^-15 c, separated by a distancce of 100 micrometers (um). what is the maximum possible torque on a sphere if the electric field between the transparent plates is 4.0 x 10^5 n/c