Two point charges are located in the x-y-plane: 91 = 1 nC at position < 4, -3,0> m, and 92 = -4 nC at position < 8, 6,0> m. You are tasked with positioning an electric dipole on the positive z-axis such that the resulting net electric field in the origin is zero. The dipole at your disposal consists of two point charges with opposite sign and magnitude dip = 6μC, separated by a distance s = 1 mm. The following steps will guide you toward finding the unknown location and orientation you need to give your dipole in order to solve your task. 1. [6pts] In the diagram of the x-y-plane add two arrows in the origin that roughly indicate for this location the direction and relative magnitude of the electric fields E1 and E2 created by the two charges. 6 92 5 4. 2 1 -3 -2 -1 1 2 3 4 -1 -2. 5 6 91 7 8 9 2. [12pts] Calculate the total electric field Ē₁+2 in the origin due to the charges q₁ and 92. Your result should have the unit of Newtons per Coulomb. [Hint: You are allowed to use a calculator, but it is possible and maybe even faster to do this calculation without a calculator (and without the risk of rounding errors) by expressing all numbers as integers or ratios of integers.] 3. [6pts] In the 3D diagram on the right, add arrows indicating the field E1+2 from part 2, the compensating dipole field Edip needed to ensure zero net field in the origin, and the dipole moment p associated with the dipole at < 0, 0, d>. (If you were not able to find Ē1+2 in part 2, then guess a vector in the x-y-plane, label it Ē1+2, in the diagram, and proceed as instructed.) guess Z y x 4. [4pts] Based on your previous results and the information given, write down the dipole moment p of the properly oriented dipole (in units of Cm). p = 5. [12pts] Calculate the distance d along the z-axis where the dipole needs to be.
Two point charges are located in the x-y-plane: 91 = 1 nC at position < 4, -3,0> m, and 92 = -4 nC at position < 8, 6,0> m. You are tasked with positioning an electric dipole on the positive z-axis such that the resulting net electric field in the origin is zero. The dipole at your disposal consists of two point charges with opposite sign and magnitude dip = 6μC, separated by a distance s = 1 mm. The following steps will guide you toward finding the unknown location and orientation you need to give your dipole in order to solve your task. 1. [6pts] In the diagram of the x-y-plane add two arrows in the origin that roughly indicate for this location the direction and relative magnitude of the electric fields E1 and E2 created by the two charges. 6 92 5 4. 2 1 -3 -2 -1 1 2 3 4 -1 -2. 5 6 91 7 8 9 2. [12pts] Calculate the total electric field Ē₁+2 in the origin due to the charges q₁ and 92. Your result should have the unit of Newtons per Coulomb. [Hint: You are allowed to use a calculator, but it is possible and maybe even faster to do this calculation without a calculator (and without the risk of rounding errors) by expressing all numbers as integers or ratios of integers.] 3. [6pts] In the 3D diagram on the right, add arrows indicating the field E1+2 from part 2, the compensating dipole field Edip needed to ensure zero net field in the origin, and the dipole moment p associated with the dipole at < 0, 0, d>. (If you were not able to find Ē1+2 in part 2, then guess a vector in the x-y-plane, label it Ē1+2, in the diagram, and proceed as instructed.) guess Z y x 4. [4pts] Based on your previous results and the information given, write down the dipole moment p of the properly oriented dipole (in units of Cm). p = 5. [12pts] Calculate the distance d along the z-axis where the dipole needs to be.
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter24: Electric Fields
Section: Chapter Questions
Problem 14PQ: A particle with charge q on the negative x axis and a second particle with charge 2q on the positive...
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Question
Please answer questions 3, 4, and 5
![Two point charges are located in the x-y-plane: 91 = 1 nC at position < 4, -3,0> m, and 92 = -4 nC at position
< 8, 6,0> m. You are tasked with positioning an electric dipole on the positive z-axis such that the resulting net
electric field in the origin is zero. The dipole at your disposal consists of two point charges with opposite sign and
magnitude dip = 6μC, separated by a distance s = 1 mm. The following steps will guide you toward finding the
unknown location and orientation you need to give your dipole in order to solve your task.
1. [6pts]
In the diagram of the x-y-plane add two arrows in
the origin that roughly indicate for this location the
direction and relative magnitude of the electric fields
E1 and E2 created by the two charges.
6
92
5
4.
2
1
-3 -2 -1
1
2
3
4
-1
-2.
5
6
91
7
8 9
2. [12pts] Calculate the total electric field Ē₁+2 in the origin due to the charges q₁ and 92. Your result should
have the unit of Newtons per Coulomb. [Hint: You are allowed to use a calculator, but it is possible and
maybe even faster to do this calculation without a calculator (and without the risk of rounding errors) by
expressing all numbers as integers or ratios of integers.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fa25896fc-8749-4aa2-9763-b50fdac49f5d%2F9ujw9ek_processed.png&w=3840&q=75)
Transcribed Image Text:Two point charges are located in the x-y-plane: 91 = 1 nC at position < 4, -3,0> m, and 92 = -4 nC at position
< 8, 6,0> m. You are tasked with positioning an electric dipole on the positive z-axis such that the resulting net
electric field in the origin is zero. The dipole at your disposal consists of two point charges with opposite sign and
magnitude dip = 6μC, separated by a distance s = 1 mm. The following steps will guide you toward finding the
unknown location and orientation you need to give your dipole in order to solve your task.
1. [6pts]
In the diagram of the x-y-plane add two arrows in
the origin that roughly indicate for this location the
direction and relative magnitude of the electric fields
E1 and E2 created by the two charges.
6
92
5
4.
2
1
-3 -2 -1
1
2
3
4
-1
-2.
5
6
91
7
8 9
2. [12pts] Calculate the total electric field Ē₁+2 in the origin due to the charges q₁ and 92. Your result should
have the unit of Newtons per Coulomb. [Hint: You are allowed to use a calculator, but it is possible and
maybe even faster to do this calculation without a calculator (and without the risk of rounding errors) by
expressing all numbers as integers or ratios of integers.]
![3. [6pts]
In the 3D diagram on the right, add arrows indicating
the field E1+2 from part 2, the compensating dipole
field Edip needed to ensure zero net field in the origin,
and the dipole moment p associated with the dipole at
< 0, 0, d>. (If you were not able to find Ē1+2 in part 2,
then guess a vector in the x-y-plane, label it Ē1+2,
in the diagram, and proceed as instructed.)
guess
Z
y
x
4. [4pts] Based on your previous results and the information given, write down the dipole moment p of the
properly oriented dipole (in units of Cm).
p =
5. [12pts] Calculate the distance d along the z-axis where the dipole needs to be.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fa25896fc-8749-4aa2-9763-b50fdac49f5d%2Fvrdke6f_processed.png&w=3840&q=75)
Transcribed Image Text:3. [6pts]
In the 3D diagram on the right, add arrows indicating
the field E1+2 from part 2, the compensating dipole
field Edip needed to ensure zero net field in the origin,
and the dipole moment p associated with the dipole at
< 0, 0, d>. (If you were not able to find Ē1+2 in part 2,
then guess a vector in the x-y-plane, label it Ē1+2,
in the diagram, and proceed as instructed.)
guess
Z
y
x
4. [4pts] Based on your previous results and the information given, write down the dipole moment p of the
properly oriented dipole (in units of Cm).
p =
5. [12pts] Calculate the distance d along the z-axis where the dipole needs to be.
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