Can't solve an equation (Deflection of electrons in electrostatic field)

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Homework Help Overview

The discussion revolves around the deflection of electrons in an electrostatic field, specifically focusing on the formulation and understanding of equation (3) related to this phenomenon. Participants are attempting to derive this equation from previously established equations and are grappling with the algebraic manipulations involved.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants are discussing how to combine equations (1) and (2) to arrive at equation (3). There are questions about the relevance of measurements for V2 and the interpretation of variables such as t and z. Some participants express confusion about their calculations and seek clarification on the steps taken.

Discussion Status

The discussion is active, with participants sharing their calculations and questioning each other's reasoning. Some guidance has been offered regarding the relationships between variables, but there is no explicit consensus on the correct approach to derive equation (3). Multiple interpretations of the problem are being explored.

Contextual Notes

Participants mention that certain measurements, such as those for V2, may not be immediately relevant to their understanding of the algebraic derivation needed for equation (3). There is an ongoing examination of the definitions and roles of various variables in the equations being discussed.

Caroline Stuart
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Homework Statement
Hello everyone!
I've tried everything but the equation (3) in "Deflection of electrons in electrostatic field" is impossible. Can someone at least hint me to a a way the composed it ?
Relevant Equations
Relevant equation is in the file
Hello everyone!
I've tried everything but the equation (3) in "Deflection of electrons in electrostatic field" is impossible. Can someone at least hint me to a a way the composed it ?
 

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Equation (3) seems clear enough. What exactly are you trying to do? What do you mean when you say "Can't solve an equation"? Do you have a series of measurements of the deflection at different values of V2?
 
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When i follow the instructions of how to make it s(z) which is equation (3) they say combine equation (1) and equation (2) to make it. My question is how did they do it exactly, can you take me through the steps cause when I attempted it it gave me completely different result.
 
measurements for V2 are irrelevant they are just voltages which deflect path of electron and i would have to record them via measuring length in bubble chamber where electron beam is projected.
 
Caroline Stuart said:
When i follow the instructions of how to make it s(z) which is equation (3) they say combine equation (1) and equation (2) to make it. My question is how did they do it exactly, can you take me through the steps cause when I attempted it it gave me completely different result.

Why don't you show me what you got? What did you get for t^2? What did you get for E?
 
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t(squared)=2ms/(-eE), E is either -V2/d or 2ms/(-et(squared))
 
Caroline Stuart said:
measurements for V2 are irrelevant they are just voltages which deflect path of electron and i would have to record them via measuring length in bubble chamber where electron beam is projected.
Why do you say "measurements for V2 are irrelevant"? You are supposed to measure the value of s for different values of V2.
 
Caroline Stuart said:
t(squared)=2ms/(-eE), E is either -V2/d or 2ms/(-et(squared))
No. It tells you that v= \sqrt{\frac{2 e V_1}{m}} and z=v t. Use those two to calulate t. And you are correct that E = \frac{V_2}{d}
 
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V2 in the formula in the formula doesn't have a numerical value at a given moment - this is why I said its irrelevant, before i proceed to taking measurements i have to understand how to get to formula (3) algebraically
 
  • #10
As i said already did that, i can read, and i got 4meVz/-eEm instead of formula (3) could you please suggest where I've gone wrong?
 
  • #11
Caroline Stuart said:
As i said already did that, i can read, and i got 4meVz/-eEm instead of formula (3) could you please suggest where I've gone wrong?
I'm trying to help. When you did that, what did you get for t^2? In post #6, you said t(squared)=2ms/(-eE), and that's wrong.
 
  • #12
so what is correct formula for t squared?
 
  • #13
Caroline Stuart said:
so what is correct formula for t squared?
Do what I said in post #8 and tell me what you get.
 
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  • #14
sorry didnt see your reply at post 8, I am new to it, i see it now
 
  • #15
what is z exactly, is a coordinate axis?
 
  • #16
z is the distance in the direction the electrons are propagating, right to left in the drawing. s is the distance they get deflected, up or down in the drawing.
 
  • #17
t=z/v; if v equals square root of (2eV/m) then t equals (z*square root of m)/(square root of 2eV)
 
  • #18
what do i do then?
 
  • #19
Caroline Stuart said:
t=z/v; if v equals square root of (2eV/m) then t equals (z*square root of m)/(square root of 2eV)
That's correct. Remeber it is V1, not V. So then what is t^2? And since you correctly said that E=V2/d, what do you get when you plug those into equation (1)?
 
  • #20
t squared is 2eV1 over m;
 
  • #21
s=(-2e^2V1V2)/(2dm^2)
 
  • #22
Caroline Stuart said:
t squared is 2eV1 over m;
No. Try again. If t = z\sqrt{\frac{m}{2e V_1}}, what is t^2?
 
  • #23
its (z^2)*m/(2eV1)
 
  • #24
Caroline Stuart said:
its (z^2)*m/(2eV1)
Good! Now plug that and your exprssion for E into equation (1). What do you get for s?
 
  • #25
but how have you deduced that t= z times square root m/(2eV1) ?
 
  • #26
Caroline Stuart said:
but how have you deduced that t= z times square root m/(2eV1) ?
You told me that in post #17!
 
  • #27
s=(-eV2t^2)/(2dm) for post 24
 
  • #28
post 27 is wrong it should be: s=(-e^2V1V2)/(dm^2) for post 24
 
  • #29
I got it eventually Thank you, ur Genius.
 
  • #30
Glad I could help. Good luck!
 
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