Capacitance

11-1

Two metal objects have net charges of $+70 \rm pC$ and $-70 \rm pC$, and this results in a 20 V potential difference between them. (a) What is the capacitance of the system? (b) If the charges are changed to $+200 \rm pC$ and $-200 \rm pC$, what does the capacitance become? (c) What does the potential difference become?

11-2

After you walk over a carpet on a dry day, your hand comes close to a metal toaster and a 5 mm spark results. Such a spark means that there must have been a potential difference of possibly 15 kV between you and the toaster. Assuming this potential difference, how much charge did you accumulate in walking over the carpet? For this extremely rough calculation, assume that your body can be represented by uniformly charged conducting sphere 25 cm in radius and isolated from its surroundings.

11-3

A one megabit computer memory chip contains many 60.0 fF capacitors. Each capacitor has a plate area of $21.0\times 10^{-12} \rm m^2$. Determine the plate separation of such a capacitor (assume a parallel plate configuration). The characteristic atomic diameter is $10^{-10} \rm m = 0.100 \rm nm$. Express the plate separation in nanometres.

11-4

A potential difference of 300 V is applied to a $2.0  \rm\mu F$ capacitor and an $8.0 \rm\mu F$ capacitor connected in series. (a) What are the charge and the potential difference for each capacitor? (b) The charged capacitors are disconnected from each other and from the battery. They are then reconnected with their positive plates together and their negative plates together, no external voltage being applied. What are the charge and potential difference for each? (c) The charged capacitors in part (a) are reconnected with plates of opposite sign together. What are the steady state charge and potential difference for each?

11-5

Evaluate the equivalent capacitance of the configuration shown in Fig. 17. All the capacitors are identical, and each has capacitance $C$.

Figure 17: Prob 11-5

11-6

An isolated metal sphere whose diameter is 10 cm has a potential of 8000 V. Calculate the energy density in the electric field near the surface of the sphere.