At time t0, an electron is moving on the negative z-axis with unknown speed vo in the positive z-direction and may be considered force-free at this time (the gravitational pull in the negative y-direction shall be neglected in this problem). When the particle reaches the origin, it experiences a uniform and con- stant electric field Ẽ = E^ and a uniform and constant magnetic field B = Bŷ in the half- space> 0, as indicated in the schematic. = voz x 818181 (i) [5pts] Suppose you observe that the electron stays on its straight trajectory along the z-axis after it enters the electromagnetic fields. - Determine the unknown original speed vo. - Does the electron speed remain constant at z> 0? (Yes/No) - Would the trajectory of a positively charged particle with the same initial velocity be different? (Yes / No) (ii) [4pts] Consider the scenario in which only the E-field is present at z > 0. What can you say about the magnitude and direction of the electron velocity a long time after the electron enters the E-field? = vož For t→ ∞, บ: v : (iii) [4pts] Now consider the scenario in which only the B-field is present at z > 0. What can you say about the magnitude and direction of the electron velocity a long time after the electron enters the B-field? For t∞, v: v : = v02 x 11 E 11
At time t0, an electron is moving on the negative z-axis with unknown speed vo in the positive z-direction and may be considered force-free at this time (the gravitational pull in the negative y-direction shall be neglected in this problem). When the particle reaches the origin, it experiences a uniform and con- stant electric field Ẽ = E^ and a uniform and constant magnetic field B = Bŷ in the half- space> 0, as indicated in the schematic. = voz x 818181 (i) [5pts] Suppose you observe that the electron stays on its straight trajectory along the z-axis after it enters the electromagnetic fields. - Determine the unknown original speed vo. - Does the electron speed remain constant at z> 0? (Yes/No) - Would the trajectory of a positively charged particle with the same initial velocity be different? (Yes / No) (ii) [4pts] Consider the scenario in which only the E-field is present at z > 0. What can you say about the magnitude and direction of the electron velocity a long time after the electron enters the E-field? = vož For t→ ∞, บ: v : (iii) [4pts] Now consider the scenario in which only the B-field is present at z > 0. What can you say about the magnitude and direction of the electron velocity a long time after the electron enters the B-field? For t∞, v: v : = v02 x 11 E 11
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Chapter1: Units, Trigonometry. And Vectors
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Please help. I don't get this.
![At time t0, an electron is moving on the
negative z-axis with unknown speed vo in the
positive z-direction and may be considered
force-free at this time (the gravitational pull
in the negative y-direction shall be neglected
in this problem). When the particle reaches
the origin, it experiences a uniform and con-
stant electric field Ẽ = E^ and a uniform and
constant magnetic field B = Bŷ in the half-
space> 0, as indicated in the schematic.
=
voz
x
818181
(i) [5pts] Suppose you observe that the electron stays on its straight trajectory along the z-axis after it enters
the electromagnetic fields.
- Determine the unknown original speed vo.
- Does the electron speed remain constant at z> 0? (Yes/No)
- Would the trajectory of a positively charged particle with the same initial velocity be different? (Yes / No)
(ii) [4pts] Consider the scenario in which only
the E-field is present at z > 0.
What can you say about the magnitude and
direction of the electron velocity a long time
after the electron enters the E-field?
= vož
For t→ ∞,
บ:
v :
(iii) [4pts] Now consider the scenario in which
only the B-field is present at z > 0.
What can you say about the magnitude and
direction of the electron velocity a long time
after the electron enters the B-field?
For t∞,
v:
v :
= v02
x
11
E
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d1ae07f-bdb5-47a8-9afa-ea5a04bdf9c8%2Fb0962b10-32c8-421e-a673-64f065483166%2F7tzn8kr_processed.png&w=3840&q=75)
Transcribed Image Text:At time t0, an electron is moving on the
negative z-axis with unknown speed vo in the
positive z-direction and may be considered
force-free at this time (the gravitational pull
in the negative y-direction shall be neglected
in this problem). When the particle reaches
the origin, it experiences a uniform and con-
stant electric field Ẽ = E^ and a uniform and
constant magnetic field B = Bŷ in the half-
space> 0, as indicated in the schematic.
=
voz
x
818181
(i) [5pts] Suppose you observe that the electron stays on its straight trajectory along the z-axis after it enters
the electromagnetic fields.
- Determine the unknown original speed vo.
- Does the electron speed remain constant at z> 0? (Yes/No)
- Would the trajectory of a positively charged particle with the same initial velocity be different? (Yes / No)
(ii) [4pts] Consider the scenario in which only
the E-field is present at z > 0.
What can you say about the magnitude and
direction of the electron velocity a long time
after the electron enters the E-field?
= vož
For t→ ∞,
บ:
v :
(iii) [4pts] Now consider the scenario in which
only the B-field is present at z > 0.
What can you say about the magnitude and
direction of the electron velocity a long time
after the electron enters the B-field?
For t∞,
v:
v :
= v02
x
11
E
11
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