A charged isolated metal sphere of diameter$15 \mathrm{cm}$ has a potential of $6500 \mathrm{V}$ relative to $V=0$ at infinity.

(a) Calculate the energy density in the electric field near the surface of the sphere.

(b) If the diameter is decreased, does the energy density near the surface increase, decrease or remain the same?

Plot $1$ in Fig. (a) gives the charge $q$ that can be stored on capacitor $1$ versus the electric potential $V$ set up across it. The vertical scale is set by $q_s=16.0 \mathrm{\mu C},$ and the horizontal scale is set by $V_s=2.0 \mathrm{V}.$ Plots $2$ and $3$ are similar plots for capacitors $2$ and $3$, respectively. Figure (b) shows a circuit with those three capacitors and a $10.0 \mathrm{V}$ battery. What is the charge stored on capacitor 2 in that circuit?

(a)                                                                                (b)

Given figure shows a $24.0 \mathrm{V}$ battery and four uncharged capacitors of capacitance $C_1=1.00 \mu \mathrm{F},$ $C_2=2.00 \mu \mathrm{F}, C_3=3.00 \mu \mathrm{F},$ and $C_4=4.00 \mu \mathrm{F}$. If only switch ${\mathrm{S}}_1$ is closed, what is the charge on (a) capacitor $1$, (b) capacitor $2,$ (c) capacitor $3,$ and (d) capacitor $4 ?$ If both switches are closed, what is the charge on (e) capacitor $1,$ (f) capacitor $2,$(g) capacitor $3,$ and (h) capacitor $4 ?$

You have two flat metal plates, each of area $1.00 {\mathrm{m}}^2,$ with which you have to construct a parallel-plate capacitor. (a) If the capacitance of the device is to be $2.00 \mathrm{F}$ , what must be the separation between the plates? (b) Could this capacitor actually be constructed?

The two metal objects shown below have $+70 \mathrm{pC}$ and $-70 \mathrm{pC}$ charges and results in a $35 \mathrm{V}$ potential difference between them. (a) What is the capacitance of the system? (b) If the charges are changed to$+200 \mathrm{pC}$ and $-200 \mathrm{pC}$, what will happen to the capacitance? (c) What will happen to the potential difference?