1. Two point charges are separated by Gem. The attractive force between them is 20 N. Find the force between them when they are separated by 12 cm. (Why can you solve this problem without knowing the magnitudes of the charges?)
2. Suppose that the charges attracting each other in the preceding problem have equal magnitude. Rearrange Coulomb's law and show that the magnitude of each charge is 2.8 x I0-6 C (2.8 microcoulombs).
3. Two pellets, each with a charge of I microcoulomb (10-6C), are located 3 cm (0.03 m) apart. Show that the electric force between them is 10 N. What would be the mass of an object that would experience this same force in Earth's gravitational field?
4. Electronic types neglect the force of gravity on electrons. To sec why, compute the force of Earth's gravity on an electron and compare it with the force exerted on the electron by an electric field of magnitude 10,000 V/m (a relatively small field). The mass and charge of an electron are given on the inside back cover.
5. Atomic physicists ignore the effect of gravity within an atom. To see why, calculate and compare the gravitational and electrical forces between an electron and a proton separated by 10-19 m. The charges and masses are given on the inside back cover.
6. A droplet of ink in an industrial ink-jet printer carries a charge of 1.6 x 10-10 C and is deflected onto paper by a force of 3.2 x 10-4 N. Show that the strength of the electric field to produce this force is 2 million N/C.
7. The potential difference between a storm cloud and the ground is 100 million V. If a charge of 2 C flashes in a bolt from cloud to Earth, what is the change of potential energy of the charge?
8. Energy of 0.1 J is stored in the metal sphere on top of a Van de Graaff generator. A spark carrying 1 microcoulomb (10-6 C) discharges the sphere. Show that the sphere's potential relative to ground is 100.000 V?
9. Find the voltage change when (a) an electric field does 12 J of work on a 0.0001-C charge; (b) the same electric field does 24 J of work on a 0.0002-C charge.
10. In 1909 Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole-number multiples of 1.6 x 10-19C-the charge of the electron. For this he won the Nobel Prize.
a. If a drop of mass 1.1 x 10-14 kg remains stationary in an electric field of 1.68 x 105 N/C, what is the charge of this drop?
b. How many extra electrons are on this particular oil drop (given the presently known charge of the electron)?
