A silicon-based MOSFET has a square gate 0.50 mm on edge. The insulating silicon oxide layer that separates the gate from the p-type substrate is 0.20 mm thick and has a dielectric constant of 4.5. (a) What is the equivalent gate – substrate capacitance (treating the gate as one plate and the substrate as the other plate)? (b) Approximately how many elementary charges e appear in the gate when there is a gate – source potential difference of 1.0 V?

Why do we need to be careful about work done on the system versus work done by the system in calculations?

The probability of fusion occurring is greatly enhanced when appropriate nuclei are brought close together, but mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high- temperature gas ions or by accelerating the nuclei toward one another. (a) Calculate the potential energy of two singly charged nuclei separated by 1.001012. (b) At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?

Two concentric, metal spherical shells of radii a = 4.0 cm and b = 8.0 cm are separated by aluminum as shown in Figure P28.33. The inner sphere has a total charge Q at any time. If the two spheres are maintained at a potential difference of 2.0 V via an external source, calculate the current from one sphere to the other.

A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity , with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: ChargeconductionThermalconductiondqdt=A|dVdx|dQdt=kA|dTdx| In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State analogous rules relating the direction of the electric current to the change in potential and relating the direction of energy flow to the change in temperature.

Check Your Understanding How would the strategy change to calculate the at a point a distance z above of the finite line segment?

How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?

The temperature near the center of the Sun is thought to be 15 million degrees Celsius ( 1.5107oC ) (or kelvin). Through what voltage must a singly charged ion be accelerated to have the same energy as the average kinetic energy of ions at this temperature?

Check Your Understanding How much energy does a 1.5-V AAA battery have that can move 100C ?

A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 250 V and disconnected from the source. The capacitor is then immersed in distilled water. Assume the liquid is an insulator. Determine (a) the charge on the plates before and after immersion, (b) the capacitance and potential difference after immersion, and (c) the change in energy of the capacitor.