NASA tele-transporter, magnetic field direction, generator, motor

1. Two test charges suspended in vacuum attract each other with a force of 1x10-6 N. What will the attractive force be if the vacuum is replaced with water at 20o C? The permittivity of water at this temperature is 7.07x10-10 C2/N-m2.

2. Three test charges, each with a charge of +1x10-6 C, are located at the points of an equilateral triangle. If the legs of the triangle are 10 cm long, what is the total force acting on each charge? (Assume vacuum, or dry air.)

3. NASA has designed a tele-transporter (teleporter) system similar to the "beam me up, Scotty" device made famous on Star Trek. NASA doesn't want to teleport people; that would be too dangerous and, if successful, could result in big budget cuts. They do, however, want to teleport simple supplies, such as water and oxygen, from Johnson SFC, Houston, to Armstrong Base on the Moon (a distance of 385,000 km).

The teleporter consists of two pods, designated A and B. When the system is operating as designed, the contents of pod A are transported with the speed of light into pod B, and vice versa.

The test-model pods have a volume of exactly 1 L each. For the first test, NASA decides to play it safe and try transporting an inert gas, helium. Pod A, on Earth, is filled with helium at Earth-standard atmospheric pressure and 0 degrees Celsius. (If you remember your high school chemistry, you can prove that this is 1/22.4 mole of helium, or 2.509*1022 atoms.) Pod B, on the Moon, is filled with something that Armstrong Base has in abundance, which is vacuum.

More data: Each helium atom consists of two negatively charged electrons orbiting a positively charged nucleus. The charge of one electron is -1.602*10-19 C. The charge of the nucleus is twice the charge of one electron, and has the opposite sign.

Something unexpected happens during the first test. The teleporter pulls the atoms of helium apart. All of the electrons are sent to the Moon, while all the nuclei stay behind in Texas.

Do the two pods, so far apart, feel any electrostatic attraction? If so, how much? Show your work in detail.

4. An electron travels along the x-axis in a horizontal (x-y) plane, in the positive direction. It experiences a force in the vertical (z) direction due to a uniform magnetic field. (The force can be either up or down.) Which are the possible directions for the magnetic field? Explain using the right hand rule.

5. Briefly explain the relationship between an electric generator and an electric motor. Be sure to outline their basic operation, in terms of the physical laws studied in this module.