Guass' law and RC

Guass' law and RC
1. Homework Statement

1. Find the potential due to a charged line of charge density lambda. the point of interest is on the axis of the line, and a distance afrom the near end of the lone . the line os of length b. the potential is: k lambda ln(a+b)/a).

2 Show that for two spheres connected by a conductor the ratio of the fields at the surface is given by E/e=r/R where one sphere has a radius R and Field E and the other sphere has a radius r and field e.

3. find the capacitances of two concentric spheres separated by a distance, d, small compared to their radius. show that the capacitance is approximatively the same as the capacitance of two parallel plates with the same area and separation: C= A(E)/d.

4. two capacitors 7.1x10^-6 farads and .000036 farads are connected in series and 10 volts is applied to the pair. the voltage is removed and the capacitors are connected in parallel, plus to plus. hat is the new voltage.

5. Show that the charge on a capacitor C connected in series with a resistor R is given by Q=Q initial exp(-t/RC)

6. you plan to build a large, cheap cyclotron using the earth's magnetic fields(1 E-4 t) and orbiting just above the earth;s atmospheres(radius 5.9 E6 m) what energy in volts, should protons be given to just circle the earth? q= 1.6 E-19 m clb, m = 1.67 E-27 kg.

2. Homework Equations

3. The Attempt at a Solution
so far i only know i hv to apply gauss law and DC and RC stuffs