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MMLU-Pro / 11607 / In a diode vacuum tube consisting of a heated, plane metal cathode and a…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

In a diode vacuum tube consisting of a heated, plane metal cathode and a parallel plate, electrons are emitted from the cathode and are accelerated toward the plate. In the region between the two tube elements there is a cloud of electrons called a space charge. The potential function is given by V = V_0 (x/a)^4/3, where V_0 is the potential of the plate, x is the coordinate distance from the cathode, and a is the distance of the plate from the cathode. Assuming that the electrons are emitted with negligible initial velocity, find the velocity of the electrons at any point x and the time of flight from cathode to plate.

category

engineering

options

  1. time of flight = 6.5(10^-9) sec, velocity at plate = 4.93 (10^6) m per sec
  2. time of flight = 7.5(10^-9) sec, velocity at plate = 3.93 (10^6) m per sec
  3. time of flight = 5.5(10^-9) sec, velocity at plate = 5.93 (10^6) m per sec
  4. time of flight = 4.5(10^-9) sec, velocity at plate = 7.93 (10^6) m per sec
  5. time of flight = 4.8(10^-9) sec, velocity at plate = 7.00 (10^6) m per sec
  6. time of flight = 3.5(10^-9) sec, velocity at plate = 6.93 (10^6) m per sec
  7. time of flight = 5.2(10^-9) sec, velocity at plate = 5.50 (10^6) m per sec
  8. time of flight = 4.0(10^-9) sec, velocity at plate = 9.93 (10^6) m per sec
  9. time of flight = 6.0(10^-9) sec, velocity at plate = 6.53 (10^6) m per sec
  10. time of flight = 5.0(10^-9) sec, velocity at plate = 8.93 (10^6) m per sec

src

stemez-Electromagnetics

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Source and history

upstream_id / Original problem ID
11607
task_id
fbbe6290-b3cd-5e01-85e6-4cc1d39e9f11
task_key
default--test--11607
task_revision_id
1
config / split
default / test

Official source

initial import