1.[5] Consider two parallel-plate conductors. Use them in two alternative ways, as a parallel- plate capacitor and as a resistor as shown below in the figure. In the capacitor the space between the plates is filled by the dielectric of permittivity e, while in the case of a conductor the space between the plates is filled with a homogeneous material of finite conductivity o. By considering separately these cases of the capacitor and conductor prove the relation RC = = where C is the capacitance of the capacitor on the left and R is the resistance of the resistor on the right. Q -Q 2.[5] The resistivity of seawater is about 0.25 ohm m. The charge carriers are chiefly Na* and CI ions, and of each there are about 31026 per m. If we fill a plastic tube 2 meters long with seawater and connect a 12 volt battery to the electrodes at each end, what is the resulting average drift velocity of the ions? 3.[5] If the voltage at the terminals of an automobile battery drops from 12.3 to 9.8 volts when a 0.5 ohm resistor is connected across the battery, what is the internal resistance? 4.[5] A beam of protons traveling at 1.20 km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction (see the figure). The beam travels a distance of 1.18 cm while in the field. What is the magnitude of the magnetic field? X IX X X