Question

A cylindrical capacitor of length 1 cm, inner radius 0.010 cm, and outer radius 0.015 cm is filled with water, which has dielectric constant K = 80.10 at 20◦C. Assume the capacitor has been connected to an ideal 6V battery for a long enough time for the system to have reached equilibrium.

a). Find the surface charge densities in the water on both the inner and outer surface. What is the field ~ D as a function of r inside the water? What is ~ E as a function of r inside the water?
b). The capacitor is then discharged when a gold wire 1 mm in diameter and 50 cm in length is attached one end to each of the two conducting plates. If the gold has a resistivity of 2.3×10−8 Ω·m, find the amount of time the capacitor takes to discharge 95% of its initial charge.
c). What is the initial drift velocity of the electrons in the gold? Assume each gold atom contributes one conducting electron. (Note: Gold has a density of 19.32 g/cm3 and has a molar mass of 197 g/mol.)

Answer 1