91影视

In a region with an uniform electric field, you measure a potential difference of from the origin to a position of (0,0,10) m. Now we add a uniformly charged, thin spherical plastic shell centered at the origin. The spherical shell has a radius of 5 m and a charge of -3530 nC. Draw a diagram to help answer the following questions: (a) What is the potential difference from the origin to a position of (0,0,5) m (at the surface of the spherical shell)? (b) What is the potential difference from the position of (0,0,5) m to a position of (0,0,10) m ?

(a) In Figure 16.14, what is the direction of the electric field? Is$\mathbf{鈭�}\mathbf{V}\mathbf{=}{\mathbf{V}}_f\mathbf{-}{\mathbf{V}}_{\mathbf{i}}$positive or negative? (b) In figure 16.15, what is the direction of the electric field? Is$\mathbf{鈭�}\mathbf{V}\mathbf{=}{\mathbf{V}}_f\mathbf{-}{\mathbf{V}}_{\mathbf{i}}$positive or negative?

What are the units of electric potential energy, of electric potential, and of electric field?

A dipole is centered at the origin, with its axis along the y axis, so that at locations on the y axis, the electric field due to the dipole is given by

$\stackrel{\mathbf{鈫�}}{\mathbf{E}}\mathbf{=}鉄�\mathbf{0}\mathbf{,}\mathbf{\text{鈥�}}\frac{\mathbf{1}}{\mathbf{4}{\mathbf{蟺蔚}}_{\mathbf{0}}}\frac{\mathbf{2}\mathbf{qs}}{{\mathbf{y}}^{\mathbf{3}}}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{0}鉄�\text{鈥�}\frac{\mathbf{\text{V}}}{\mathbf{\text{m}}}$

The charges making up the dipole are$\mathbf{+}\mathbf{3}\mathbf{\text{鈥塶颁}}$ and $\mathbf{-}\mathbf{3}\mathbf{\text{鈥塶颁}}$, and the dipole separation is$\mathbf{2}\mathbf{\text{鈥尘尘}}$ (Figure 16.82). What is the potential difference along a path starting at location$\mathbf{鉄�}\mathbf{0}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{0}\mathbf{.03}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{0}\mathbf{鉄�}\mathbf{\text{鈥尘}}$ and ending at location$\mathbf{鉄�}\mathbf{0}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{0}\mathbf{.04}\mathbf{,}\mathbf{\text{鈥�}}\mathbf{0}\mathbf{鉄�}\mathbf{\text{鈥尘}}$ ?

long thin metal wire with radius $\mathit{r}$and length$\mathit{L}$is surrounded by a concentric long narrow metal tube of radius $\mathit{R}$, where$\mathit{R}\mathbf{>}\mathbf{>}\mathit{L}$, as shown in Figure 16.86. Insulating spokes hold the wire in the center of the tube and prevent electrical contact between the wire and the tube. A variable power supply is connected to the device as shown. There is a charge$\mathbf{+}\mathit{Q}$on the inner wire and a charge$\mathbf{鈭�}\mathbf{Q}$on the outer tube. As we will see when we study Gauss鈥檚 law in a later chapter, the electric field inside the tube is contributed solely by the wire, and the field outside the wire is the same as though the wire were infinitely thin; the outer tube does not contribute as long as we are not near the ends of the tube. (a) In terms of the charge$\mathbf{Q}$, length$\mathit{L}$, inner radius$\mathit{r}$, and outer radius$\mathit{R}$ , what is the potential difference${\mathbf{V}}_{\mathbf{tube}}\mathbf{鈭�}{\mathbf{V}}_{\mathbf{wire}}$ between the inner wire and the outer tube? Explain, and include checks on your answer. (b) The power-supply voltage is slowly increased until you see a glow in the air very near the inner wire. Calculate this power-supply voltage (give a numerical value), and explain your calculation. The length$\mathit{L}\mathbf{=}\mathbf{80}\mathbf{\text{鈥塩尘}}$ , the inner radius$\mathit{r}\mathbf{=}\mathbf{0}\mathbf{.7}\mathbf{\text{鈥尘尘}}$, and the outer radius$\mathit{R}\mathbf{=}\mathbf{3}\mathbf{\text{鈥塩尘}}$. This device is called a 鈥淕eiger鈥揗眉ller tube鈥� and was one of the first electronic particle detectors. The voltage is set just below the threshold for making the air glow near the wire. A charged particle that passes near the center wire can trigger breakdown in the air, leading to a large current that can be easily measured.

In the region of space depicted in Figure 16.87 there are several stationary charged objects that are not shown in the diagram. Along a path $\mathbf{A}\mathbf{=}\mathbf{B}\mathbf{=}\mathbf{C}\mathbf{=}\mathbf{D}$ you measure the following potential differences:${\mathbf{V}}_{\mathbf{B}}\mathbf{鈭�}{\mathbf{V}}_{\mathbf{A}}\mathbf{=}\mathbf{12}\mathbf{\text{鈥塚}}$ ;${\mathbf{V}}_{\mathbf{C}}\mathbf{鈭�}{\mathbf{V}}_{\mathbf{B}}\mathbf{=}\mathbf{鈭�}\mathbf{5}\mathbf{\text{鈥塚}}$ ; ${\mathit{V}}_{\mathbf{D}}\mathbf{鈭�}{\mathit{V}}_{\mathbf{C}}\mathbf{=}\mathbf{鈭�}\mathbf{15}\mathbf{\text{鈥塚}}$. What is the potential difference${\mathit{V}}_{\mathbf{A}}\mathbf{鈭�}{\mathit{V}}_{\mathbf{D}}$ ?

A capacitor consists of two charged disks of radius$\mathit{R}$ separated by a distance$\mathit{s}$, where$\mathit{R}\mathbf{>}\mathbf{>}\mathit{s}$. The magnitude of the charge on each disk is Q. Consider points A, B, C, and D inside the capacitor, as shown in Figure 16.88. (a) Show that$\mathit{螖}\mathit{V}\mathbf{=}{\mathit{V}}_{\mathbf{C}}\mathbf{鈭�}{\mathit{V}}_{\mathbf{A}}$is the same for these paths by evaluating 鈭哣 along each path: (1) Path 1:A = B = C, (2) Path 2:$\mathbf{A}\mathbf{=}\mathbf{C}$, (3) Path 3:$\mathit{A}\mathbf{=}\mathit{D}\mathbf{=}\mathit{B}\mathbf{=}\mathit{C}$. (b) If,$\mathit{Q}\mathbf{=}\mathbf{43}\mathbf{\text{鈥坝糃}}$,$\mathit{R}\mathbf{=}\mathbf{4}\mathbf{\text{鈥尘}}$,${\mathit{s}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.5}\mathbf{\text{鈥尘尘}}$ and${\mathit{s}}_{\mathbf{2}}\mathbf{=}\mathbf{0}\mathbf{.7}\mathbf{\text{鈥尘尘}}$, what is the value of$\mathit{螖}\mathit{V}\mathbf{=}{\mathit{V}}_{\mathbf{C}}\mathbf{鈭�}{\mathit{V}}_{\mathbf{A}}$? (c) Choose two different paths from point A back to point A again, and show that$\mathbf{鈭�}\mathit{V}\mathbf{=}\mathbf{0}$for a round trip along both of these paths.

Four voltmeters are connected to a circuit as shown in figure 16.90. As is usual with voltmeters, the reading on the voltmeter is positive if the negative lead (black wire, usually labled COM) is connected to a location at lower potential, and the positive lead(red) is connected to a location at higher potential. The circuit contains two devices whose identity is unknown and a rod (green) of length 9 cm made of conducting material. At a particular moment, the reading observed in the voltmeters are, voltmeter A: -1.6 V, voltmeter B: -6 V, voltmeter A: -3.5 V. (a) At this moment, what is the reading on voltmeter D, both magnitude and sign? (b) What are the magnitude and direction of the electric field inside the rod?

In Figure 16.58, what is the direction of the electric field? Is 鈭哣 = Vf 鈭扸i positive or negative?

What is the electric potential at a location $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{脳}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{鈥�}\mathbf{m}$from an electron?