A positive charge Q is uniformly distributed on a thin-walled spherical plastic shell (hollow sphere) with radius R, centered at point 1 in the origin of our coordinate system. A uniformly charged solid plastic sphere with the same radius and the op- posite total charge, -Q, is centered in point 4 on the positive x-axis at a distance L from the ori- gin. Point 2 on the outer surface of the positively charged hollow shell and point 3 on the surface of the negatively charged solid sphere face each other and mark the closest separation between the two plastic objects as shown in the schematic. +Q y 1 2 R L -Q 3 4 R x 1. [6pts] What is the potential difference (V4 - V₁) between points 1 and 4 due to the positively charged shell alone? 2. [6pts] Which of the following graphs best describes the electric potential V+(x) between points 1 and 4 due to the positively charged shell alone, assuming the convention that the potential is zero infinitely far from the charge? (Circle the letter A-F associated with the graph you choose.) V+ V+ A V+ C 3 x+ 2 * * 1 2 3 4 1 2 V+ 1 2 E 3 4 x B D * x 3 4 * * 3 4 x V+ F: none of A-E, but this: (sketch correct curve below) 1 2 * 3 4 * +Q L Next, find the potential difference (V4 - Vi) between points 1 and 4 due to the negatively charged sphere alone. Note that the electric field inside a solid sphere with uniformly distributed charge Q is [12pts] +Q Ein =k Qr Απερ L Finally, consider the scenario where a proton with mass mp is placed in the location of point 2 and released. What speed will it have when crashing into the negatively charged sphere?
A positive charge Q is uniformly distributed on a thin-walled spherical plastic shell (hollow sphere) with radius R, centered at point 1 in the origin of our coordinate system. A uniformly charged solid plastic sphere with the same radius and the op- posite total charge, -Q, is centered in point 4 on the positive x-axis at a distance L from the ori- gin. Point 2 on the outer surface of the positively charged hollow shell and point 3 on the surface of the negatively charged solid sphere face each other and mark the closest separation between the two plastic objects as shown in the schematic. +Q y 1 2 R L -Q 3 4 R x 1. [6pts] What is the potential difference (V4 - V₁) between points 1 and 4 due to the positively charged shell alone? 2. [6pts] Which of the following graphs best describes the electric potential V+(x) between points 1 and 4 due to the positively charged shell alone, assuming the convention that the potential is zero infinitely far from the charge? (Circle the letter A-F associated with the graph you choose.) V+ V+ A V+ C 3 x+ 2 * * 1 2 3 4 1 2 V+ 1 2 E 3 4 x B D * x 3 4 * * 3 4 x V+ F: none of A-E, but this: (sketch correct curve below) 1 2 * 3 4 * +Q L Next, find the potential difference (V4 - Vi) between points 1 and 4 due to the negatively charged sphere alone. Note that the electric field inside a solid sphere with uniformly distributed charge Q is [12pts] +Q Ein =k Qr Απερ L Finally, consider the scenario where a proton with mass mp is placed in the location of point 2 and released. What speed will it have when crashing into the negatively charged sphere?
Chapter6: Gauss's Law
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![A positive charge Q is uniformly distributed on a
thin-walled spherical plastic shell (hollow sphere)
with radius R, centered at point 1 in the origin of
our coordinate system. A uniformly charged solid
plastic sphere with the same radius and the op-
posite total charge, -Q, is centered in point 4 on
the positive x-axis at a distance L from the ori-
gin. Point 2 on the outer surface of the positively
charged hollow shell and point 3 on the surface of
the negatively charged solid sphere face each other
and mark the closest separation between the two
plastic objects as shown in the schematic.
+Q
y
1
2
R
L
-Q
3
4
R
x
1. [6pts] What is the potential difference (V4 - V₁) between points 1 and 4 due to the positively charged shell
alone?
2. [6pts] Which of the following graphs best describes the electric potential V+(x) between points 1 and 4 due
to the positively charged shell alone, assuming the convention that the potential is zero infinitely far from
the charge? (Circle the letter A-F associated with the graph you choose.)
V+
V+
A
V+
C
3
x+
2
*
*
1 2
3 4
1 2
V+
1 2
E
3
4
x
B
D
*
x
3
4
* *
3 4
x
V+
F: none of A-E, but this:
(sketch correct curve below)
1
2
*
3
4
*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fbb0be9ed-b802-4439-8f6c-80b8407c0f81%2Fp959023_processed.png&w=3840&q=75)
Transcribed Image Text:A positive charge Q is uniformly distributed on a
thin-walled spherical plastic shell (hollow sphere)
with radius R, centered at point 1 in the origin of
our coordinate system. A uniformly charged solid
plastic sphere with the same radius and the op-
posite total charge, -Q, is centered in point 4 on
the positive x-axis at a distance L from the ori-
gin. Point 2 on the outer surface of the positively
charged hollow shell and point 3 on the surface of
the negatively charged solid sphere face each other
and mark the closest separation between the two
plastic objects as shown in the schematic.
+Q
y
1
2
R
L
-Q
3
4
R
x
1. [6pts] What is the potential difference (V4 - V₁) between points 1 and 4 due to the positively charged shell
alone?
2. [6pts] Which of the following graphs best describes the electric potential V+(x) between points 1 and 4 due
to the positively charged shell alone, assuming the convention that the potential is zero infinitely far from
the charge? (Circle the letter A-F associated with the graph you choose.)
V+
V+
A
V+
C
3
x+
2
*
*
1 2
3 4
1 2
V+
1 2
E
3
4
x
B
D
*
x
3
4
* *
3 4
x
V+
F: none of A-E, but this:
(sketch correct curve below)
1
2
*
3
4
*
![+Q
L
Next, find the potential difference (V4 - Vi) between points 1 and 4 due to the negatively charged sphere
alone. Note that the electric field inside a solid sphere with uniformly distributed charge Q is
[12pts]
+Q
Ein
=k
Qr
Απερ
L
Finally, consider the scenario where a proton with mass mp is placed in the location of point 2 and released.
What speed will it have when crashing into the negatively charged sphere?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fbb0be9ed-b802-4439-8f6c-80b8407c0f81%2Fsuo62e_processed.png&w=3840&q=75)
Transcribed Image Text:+Q
L
Next, find the potential difference (V4 - Vi) between points 1 and 4 due to the negatively charged sphere
alone. Note that the electric field inside a solid sphere with uniformly distributed charge Q is
[12pts]
+Q
Ein
=k
Qr
Απερ
L
Finally, consider the scenario where a proton with mass mp is placed in the location of point 2 and released.
What speed will it have when crashing into the negatively charged sphere?
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