- #1
patric44
- 296
- 39
- Homework Statement
- find the current between the plates of a vacuum tube ?
- Relevant Equations
- J = ρv = -J_{CL}
hi guys
i have an assigment of deriving the current between the plates of a vacuum tube as a function of the potential bias applied on the upper plate
from what i had found this relation is called Child-Langmuir law and states that :
$$I = K V_{d}^{3/2}$$
from what i find online i can derive it from poisson equation ##\nabla^{2}\phi = \frac{-\rho}{\epsilon_{o}}## but i don't get the intuition behind it , i kinda have a sloppy argument not sure if it is true or not : we try to find the potential in the regions between the plates related to current density ##\rho## that comes directly from the heated filament . but then some question in head asks what about the charge density in the two plates ?! did it come directly from the current density ##j## that was released from the filament or it has nothing to do with my solution .
my understanding is a little bit shaky i want some one to explain it a little further .
1) another question :
a paper i read online about Child-Langmuir law states at the top of the page that ##J = \rho v = -J_{CL}## what is that mean! and shouldn't the child-Langmuir current moves that same way as the electrons from the negative plate to the positive one ?!
2) another question that i have no answer to : how the electrons from the filament moves in the first place overcoming the negative repulsion of the cathode in the vacuum tube ?
i have an assigment of deriving the current between the plates of a vacuum tube as a function of the potential bias applied on the upper plate
from what i had found this relation is called Child-Langmuir law and states that :
$$I = K V_{d}^{3/2}$$
from what i find online i can derive it from poisson equation ##\nabla^{2}\phi = \frac{-\rho}{\epsilon_{o}}## but i don't get the intuition behind it , i kinda have a sloppy argument not sure if it is true or not : we try to find the potential in the regions between the plates related to current density ##\rho## that comes directly from the heated filament . but then some question in head asks what about the charge density in the two plates ?! did it come directly from the current density ##j## that was released from the filament or it has nothing to do with my solution .
my understanding is a little bit shaky i want some one to explain it a little further .
1) another question :
a paper i read online about Child-Langmuir law states at the top of the page that ##J = \rho v = -J_{CL}## what is that mean! and shouldn't the child-Langmuir current moves that same way as the electrons from the negative plate to the positive one ?!
2) another question that i have no answer to : how the electrons from the filament moves in the first place overcoming the negative repulsion of the cathode in the vacuum tube ?