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

[Caroline Stuart]

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 ?

 

[phyzguy]

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?

 

[Caroline Stuart]

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.

 

[Caroline Stuart]

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.

 

[phyzguy]

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?

 

[Caroline Stuart]

t(squared)=2ms/(-eE), E is either -V2/d or 2ms/(-et(squared))

 

[phyzguy]

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.

 

[phyzguy]

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}

 

[Caroline Stuart]

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

 

[Caroline Stuart]

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?

 

[phyzguy]

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.

 

[Caroline Stuart]

so what is correct formula for t squared?

 

[phyzguy]

so what is correct formula for t squared?

Do what I said in post #8 and tell me what you get.

 

[Caroline Stuart]

sorry didnt see your reply at post 8, I am new to it, i see it now

 

[Caroline Stuart]

what is z exactly, is a coordinate axis?

 

[phyzguy]

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.

 

[Caroline Stuart]

t=z/v; if v equals square root of (2eV/m) then t equals (z*square root of m)/(square root of 2eV)

 

[Caroline Stuart]

what do i do then?

 

[phyzguy]

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)?

 

[Caroline Stuart]

t squared is 2eV1 over m;

 

[Caroline Stuart]

s=(-2e^2V1V2)/(2dm^2)

 

[phyzguy]

t squared is 2eV1 over m;

No. Try again. If t = z\sqrt{\frac{m}{2e V_1}}, what is t^2?

 

[Caroline Stuart]

its (z^2)*m/(2eV1)

 

[phyzguy]

its (z^2)*m/(2eV1)

Good! Now plug that and your exprssion for E into equation (1). What do you get for s?

 

[Caroline Stuart]

but how have you deduced that t= z times square root m/(2eV1) ?

 

[phyzguy]

but how have you deduced that t= z times square root m/(2eV1) ?

You told me that in post #17!

 

[Caroline Stuart]

s=(-eV2t^2)/(2dm) for post 24

 

[Caroline Stuart]

post 27 is wrong it should be: s=(-e^2V1V2)/(dm^2) for post 24

 

[Caroline Stuart]

I got it eventually Thank you, ur Genius.

 

[phyzguy]

Glad I could help. Good luck!