Finding charge density

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  • #1
ajith.mk91
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Homework Statement


There is a beam of electrons in the space starting at x=0 and ending at x=20cm. The cross section of the beam is A.The velocity of the electrons is a function of position x and let it be v(x).Now i need to calculate the volume charge density as a function of x.


Homework Equations





The Attempt at a Solution


What i did is this:
I took an imaginary plane perpendicular to the beam.In a small time interval dt the amount of charge crossing the plane of area A is J.So dividing this J with v(x) should give the density. But J is not specified.Is there any other way to solve this?
 

Answers and Replies

  • #2
vela
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I don't think there's enough information to solve the problem. Was that the complete problem as given to you?
 
  • #3
ajith.mk91
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The question has an additional info which i did not mention in my previous post.The current density is given at x=20cm as 10000A/m2(Actually a cathode is placed at x=0 and an anode is placed at x=20cm).But i was asked to find both the volume charge density and current density as a function of x.
 
  • #4
vela
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The equation of continuity

[tex]\nabla\cdot\vec{J}+\frac{\partial\rho}{\partial t} = 0[/tex]

should help you. ρ is the charge density.
 

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