350 nF. Will they work? 53 A cubical region 1.0 m on a side is located between x = 0 and K=1 m. The region contains an electric field whose magni- 65. R re 66. A tude varies with x but is independent of y and z: E = Eo(x/xo), 24 kV/m and xo = 6.0 m. Find the total energy in where Eo the region. 54. The electric field within a spherical region of radius R is in- versely proportional to the distance r from the center of the re- gion: E = E,R/r, where E, is a constant. Find an expression for %3D CH 67. CH %3D the electrostatic energy stored within the region. 55. A sphere of radius R carries total charge Q distributed uniformly over its surface. Show that the energy stored in its electric field is U = kQ²/2R. 56. We live inside a giant capacitor! Its plates are Earth's surface and the ionosphere, a conducting layer of the atmosphere begin- ning about 60 km up. (a) Find the capacitance of this system, 68. CH approximating it as a parallel-plate capacitor. (This is justified because the atmosphere is so thin compared with Earth's radius; however, your answer is an underestimate because the atmo- spheric electric field isn't uniform.) (b) The potential difference between Earth's surface and the ionosphere is about 400 kV (this is maintained by the action of thunderstorms). Estimate the total energy stored in the planetary capacitor. . Two widely separated 4.0-mm-diameter water drops each carry 15 nC. Assuming all charge resides on the drops' surfaces, find the change in electrostatic potential energy if they're brought to- gether to form a single spherical drop.in lanoioal . A 2.1-mm-diameter wire carries a uniform line charge density 1 = 28 µC/m. Find the electric energy stored in a region 1.0 m long within one wire diameter of the wire surface. . A typical lightning flash transfers 30 C across a potential differ- ence of 30 MV. Assuming such flashes occur every 5 s in the thunderstorm of Example 23.4, roughly how long would the %3D otorm loat if :t
350 nF. Will they work? 53 A cubical region 1.0 m on a side is located between x = 0 and K=1 m. The region contains an electric field whose magni- 65. R re 66. A tude varies with x but is independent of y and z: E = Eo(x/xo), 24 kV/m and xo = 6.0 m. Find the total energy in where Eo the region. 54. The electric field within a spherical region of radius R is in- versely proportional to the distance r from the center of the re- gion: E = E,R/r, where E, is a constant. Find an expression for %3D CH 67. CH %3D the electrostatic energy stored within the region. 55. A sphere of radius R carries total charge Q distributed uniformly over its surface. Show that the energy stored in its electric field is U = kQ²/2R. 56. We live inside a giant capacitor! Its plates are Earth's surface and the ionosphere, a conducting layer of the atmosphere begin- ning about 60 km up. (a) Find the capacitance of this system, 68. CH approximating it as a parallel-plate capacitor. (This is justified because the atmosphere is so thin compared with Earth's radius; however, your answer is an underestimate because the atmo- spheric electric field isn't uniform.) (b) The potential difference between Earth's surface and the ionosphere is about 400 kV (this is maintained by the action of thunderstorms). Estimate the total energy stored in the planetary capacitor. . Two widely separated 4.0-mm-diameter water drops each carry 15 nC. Assuming all charge resides on the drops' surfaces, find the change in electrostatic potential energy if they're brought to- gether to form a single spherical drop.in lanoioal . A 2.1-mm-diameter wire carries a uniform line charge density 1 = 28 µC/m. Find the electric energy stored in a region 1.0 m long within one wire diameter of the wire surface. . A typical lightning flash transfers 30 C across a potential differ- ence of 30 MV. Assuming such flashes occur every 5 s in the thunderstorm of Example 23.4, roughly how long would the %3D otorm loat if :t
Chapter7: Electric Potential
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The following question starts in the first picture at the bottom of the page (#56) and continues onto the first chunk of text on the top of the second picture:
We live inside a giant capacitor! Its plates are Earth's surface and the ionosphere, a
Transcribed Image Text:350 nF. Will they work?
53 A cubical region 1.0 m on a side is located between x = 0 and
K=1 m. The region contains an electric field whose magni-
65. R
re
66. A
tude varies with x but is independent of y and z: E = Eo(x/xo),
24 kV/m and xo = 6.0 m. Find the total energy in
where Eo
the region.
54. The electric field within a spherical region of radius R is in-
versely proportional to the distance r from the center of the re-
gion: E = E,R/r, where E, is a constant. Find an expression for
%3D
CH
67.
CH
%3D
the electrostatic energy stored within the region.
55. A sphere of radius R carries total charge Q distributed uniformly
over its surface. Show that the energy stored in its electric field
is U = kQ²/2R.
56. We live inside a giant capacitor! Its plates are Earth's surface
and the ionosphere, a conducting layer of the atmosphere begin-
ning about 60 km up. (a) Find the capacitance of this system,
68.
CH
Transcribed Image Text:approximating it as a parallel-plate capacitor. (This is justified
because the atmosphere is so thin compared with Earth's radius;
however, your answer is an underestimate because the atmo-
spheric electric field isn't uniform.) (b) The potential difference
between Earth's surface and the ionosphere is about 400 kV (this
is maintained by the action of thunderstorms). Estimate the total
energy stored in the planetary capacitor.
. Two widely separated 4.0-mm-diameter water drops each carry
15 nC. Assuming all charge resides on the drops' surfaces, find
the change in electrostatic potential energy if they're brought to-
gether to form a single spherical drop.in lanoioal
. A 2.1-mm-diameter wire carries a uniform line charge density
1 = 28 µC/m. Find the electric energy stored in a region 1.0 m
long within one wire diameter of the wire surface.
. A typical lightning flash transfers 30 C across a potential differ-
ence of 30 MV. Assuming such flashes occur every 5 s in the
thunderstorm of Example 23.4, roughly how long would the
%3D
otorm loat if :t
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