A vacuum tube, in its simplest conceptual form, is a parallel- 12 plate capacitor enclosed in a glass tube so that all the air can be pumped out. A potential difference is applied, and if the negative plate is heated, some electrons will spontaneously pop out of the metal and be accelerated across the gap. The density of the electrons in flight is nonuniform because of their acceleration, and an analysis by Richardson around 1901 showed that the potential would have the form o = cr*/3, where c is a constant. Find the electric field.

I have placed an electron at the origin. The grid spacing is 1 Angstrom per small square. Now you have a nucleus with 7 protons at x = 3.5 Angstroms on the x-axis. What is the value of the electrostatic potential V at a point on the positive y-axis, at y = 2.5 Angstroms? (image included)        -5.8 V     23.4 V     7.1 V     17.7 V

A paper-filled capacitor is charged to a potential difference of Vo = 2.1 V. The dielectric constant of paper is K = 3.7. The capacitor is then disconnected from the charging circuit and the paper filling is withdrawn, allowing air to fill the gap between the plates. Find the new potential difference V of the capacitor. Vị = V While the capacitor is disconnected from the charging circuit, an unknown substance is inserted between the plates. The plates then attain a potential difference that is 0.47 times the original potential difference Vo (when paper filled the capacitor). What is this unknown substance's dielectric constant K? Ku =