1. a. Particle accelerators work by creating a large potential difference for electrically charged particles to experience, and thus gain energy. The SLAC national laboratory is the largest linear accelerator in the world, and can accelerate electrons through a potential difference of 90 billion volts (9x10^10 V) through a tube 3.2 km long. How much energy do the electrons have at the end of this process?

b. What is the average electric field during this process?

2. a.Four charged particles are arranged in a diamond around the origin. There is a +2nc charge located at 4mx, a -8nC charge located at 5my, -6nC charge located at -4mx and a fourth charge located at -5my. What should the fourth charge be so that the voltage at the origin is zero?

b. What is the electric field at the origin. Is it surprising that it is not zero?

3. A hydrogen atom consists of a single proton and a single electron bound together by the electric force. When in the ground state, they are separated by 52.9pm (2.29x10^-11m). How much energy is required to separate these two particles? (Note: It actually takes less than what you calculate in this problem, since the electron has a significant amount of kinetic energy to start with).

4. In Star Wars, Luke Skywalker uses something called a proton torpedo to blow up the Death Star. If these things are, as suggested, made of protons (or merely contained a large positive charge), then he could have used a simple linear accelerator to launch them. Lets assume that a 100kg proton torpedo has a net charge of 1MC (1x10^6 C), and it can be launched with a 5kV (5x10^3 V) accelerator, how fast are they moving?