A very small object with mass 8.20 * 10-9 kg and positive charge 6.50 * 10-9 C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density 5.90 * 10-8 C/m2. The object is initially 0.400 m from the sheet. What initial speed must the object have in order for its closest distance of approach to the sheet to be 0.100 m?

An electron is shot directly toward the center of a large metal plate that has surface charge density −2.50 ✕ 10−6 C/m2. If the initial kinetic energy of the electron is 1.50 ✕ 10−16 J and if the electron is to stop (owing to electrostatic repulsion from the plate) just as it reaches the plate, how far from the plate must the launch point be? ____________m

The figure below shows three small, positively charged beads at three corners of a rectangle. The particle at upper left has a charge q1 = 3.00 nC, the one at the lower left has a charge of q2 = 6.00 nC, and the one at lower right has a charge q3 = 4.00 nC. The rectangle's horizontal side has length x = 7.00 cm and its vertical side has length y = 2.00 cm. Three positive charges lie at three of the corners of a rectangle of horizontal side length x and vertical side length y < x. An charge labeled q1 is at the upper left corner. A charge labeled q2 is at the lower left corner. A charge labeled q3 is at the lower right corner. (a) What is the electric potential (in V) at the upper-right corner of the rectangle? (Assume the zero of electric potential is at infinity.)  V (b) What would be the potential (in V) at the upper-right corner if the charge q2 at lower left was  −6.00  nC instead?  V

Measuring the Charge. You and your team are designing an experiment where two spherical insulating beads of diameter 0.45 cm and mass 0.15 g are strung together on a fine thread that passes through microscopic holes drilled through their centers. When hung vertically, the lower bead rests on a knot at the bottom of the thread and the upper bead rests upon the lower bead. When placed inside a vacuum chamber and exposed to X-rays (highly energetic electromagnetic radiation), the beads acquire equal, uniform distributions of positive charge on their surfaces due to the loss of electrons ejected when struck by the X-rays. During this experiment, the beads are hung vertically, and a gap forms between them as if the top bead were levitating above the lower one, presumably due to the repulsive electrostatic force between them. The gap, that is, the vertical separation between the top of the lower bead and the bottom of the upper bead, is 0.27 cm. (a) How much excess charge is on each bead?…