Problems for electricity and magnetism

by Quirino Sugon Jr.

1. An electron is under a 2T magnetic field pointing out of the paper and the electron has a speed of one-tenth the speed of light and is initially moving towards the right.  What is the magnitude and direction of the  magnetic force on the electron?  What will be the orbital radius of the electron?  Is it clockwise or counterclockwise?
2. In a Hydrogen atom, what is the ratio between the electric force and the gravitational force on the electron due to the proton?
3. Prove  the rules for equivalent resistance of two resistors connected in series and parallel using Kirchoff’s voltage law.  Hint: resistors in series requires only a single loop; the resistors in parallel requires two loops.
4. Three charges are connected in 30-60-90 degree triangle with the longest side equal to 1 m.  The charge on the right angle is 1 C, the charge on the 60 deg angle is 2 C, and the charge on the 30 deg angle is 3 C.  What is the net electric force on the 2C charge? Hint: use Coulomb’s law.