Two 2.0-cm-diameter disks spaced 2.0 mm apart form a parallel-plate capacitor. The electric field between the disks is $5.0 \times 10^{5} \mathrm{V} / \mathrm{m}$. a. What is the voltage across the capacitor? b. How much charge is on each disk? c. An electron is launched from the negative plate. It strikes the positive plate at a speed of $2.0 \times 10^{7} \mathrm{m} / \mathrm{s}$. What was the electron's speed as it left the negative plate?

Two 2.0-cm-diameter disks face each other, 1.0 mm apart. They are charged to $\pm 10 n C$. a. What is the electric field strength between the disks? b. A proton is shot from the negative disk forward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

A parallel-plate capacitor is formed from two $4.0 \mathrm { cm } \times 4.0 \mathrm { cm }$ electrode spaced 2.0 mm apart. The electric field strength inside the capacitor is $1.0 \times 10 ^ { 6 } \mathrm { N } / \mathrm { C }$. What is the charge in (in nC) on each electrode?

A parallel-plate capacitor is formed from two 6.0-cm-diameter electrodes spaced 2.0 mm apart. The electric field strength inside the capacitor is $1.0 \times 10^{6} \mathrm{N} / \mathrm{C}$. What is the charge (in nC) on each electrode?

_____ development links echinoderms and chordates.

Let $f(x)=(x+1)^3-3(x+1)^2+3(x+1)$. Sketch the graph of the function using the approach presented in this section.

In Fig. 16–38, a. how much voltage is across each individual capacitor? b. how much charge is stored by $C_1$? c. how much charge is stored by $C_2$? d. how much charge is stored by $C_3$? e. what is the total charge stored by all capacitors? f. how much is $C_\text{T}$?

A proton follows the path shown in as we discussed earlier. Its initial speed is $v_0=1.9 \times 10^6 \mathrm{~m} / \mathrm{s}$. What is the proton's speed as it passes through point $\mathrm{P}$ ?

A -2.0 nC charge and a +2.0 nC charge are located on the x-axis at x = -1.0 cm and x = +1.0 cm, respectively. a. At what position or positions on the x-axis is the electric field zero? b. At what position or positions on the x-axis is the electric potential zero? c. Draw graphs of the electric field strength and the electric potential along the x-axis.

To provide the pulse of energy needed for an intense bass, some car stereo systems add capacitors. One system uses a $2.0 \mathrm{~F}$ capacitor charged to $24 \mathrm{~V}$, double the normal $12 \mathrm{~V}$ provided by the car's battery. How much energy does the capacitor store at $12 \mathrm{~V}$? At $24 \mathrm{~V}$ ?

The gecko in the photo is sticking upside down to a smooth ceiling. The remarkable adhesion might be due to static electricity. Gecko feet are covered with microscopic hairs. When these hairs rub against a surface, charges separate, with the hair developing a positive charge and a negative charge forming below the surface. There is an attractive force between the separated charges. This is an effective means of adhering to a surface, but it comes at a cost: Two planes of charge are like two charged plates of a capacitor, which takes energy to charge. Doubling the amount of charge on each surface increases the attractive force, but also increases the energy required to separate the charge. By what factor does this energy increase?

A parallel-plate capacitor is connected to a battery and stores 4.4 nC charge. Then, while the battery remains connected, a sheet of Teflon is inserted between the plates. a. Does the capacitor's charge increase or decrease? b. By how much does the charge change?

A proton is released from rest at the positive plate of a of a parallel-plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the proton's final speed if the experiment is repeated with double the amount of charge on each capacitor plate?

The flash unit in a camera uses a special circuit to "step up" the 3.0 V from the batteries to 300 V, which charges a capacitor. The capacitor is then discharged through a flashlamp. The discharge takes $10 \mu s$, and the average power dissipated in the flashlamp is $10 ^ { 5 } \mathrm { w }$. What is the capacitance of the capacitor?