• Support PF! Buy your school textbooks, materials and every day products Here!

Electrion moving between two parallel plates

  • #1
516
19

Homework Statement


At what angle will the electrons in the image leave the uniform electric field at the end of the parallel plates (point P) ? Assume the plates are .049 m long, E = 5x10^3 N/C and v0 = 1x10^7 m/s. Ignore fringing of the field.
GIANCOLI.ch21.p59.jpg

Homework Equations


E = kQ/r^2
F=ma
F= kQ1Q2/r^2

The Attempt at a Solution


I am having difficulty figuring out how to get started. I know the equation for the motion of the electron is
y= -(eEx^2)/(2mv0^2) but I don't know if this helps me. I think they want the angle the path of the electron makes with the x axis, but I am not sure. Can someone get me started or give me a hint on how to relate the angle to everything else please?
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,396
2,836
The angle at which the electron is moving is given by the direction of the velocity vector of the electron. So, try to figure out the x and y components of the velocity at point P.

Note: Two out of the three equations that you listed under "relevant equations" are not actually relevant to this problem. Can you spot them?
 
  • #3
516
19
I tried plugging in .049 m for x into the equation of motion as well as the mass of an electron for m and all the other given information and got
y = - [(1.602x10^-19)(5x10^3)(.049)^2]/[2(9.1x10^-31)(1x10^7)^2] = -.011 m
which is how far below the x axis it is so the angle would be tan^-1(-.011/.049) = -13 degrees?
 
  • #4
516
19
I guess F= ma is the relevant one?
 
  • #5
TSny
Homework Helper
Gold Member
12,396
2,836
I guess F= ma is the relevant one?
Right. But you'll need some other equations, too.
 
  • #6
516
19
ok so to find the velocity vector at point P ... there is no x component of acceleration, so vx= v0
vy = vy0 - at
vy0 = 0 so
vy = - at
a = F/m = qE/m = -eE/m
so
vy = eEt/m ... am i on the right track?
 
  • #7
TSny
Homework Helper
Gold Member
12,396
2,836
ok so to find the velocity vector at point P ... there is no x component of acceleration, so vx= v0
vy = vy0 - at
vy0 = 0 so
vy = - at
a = F/m = qE/m = -eE/m
so
vy = eEt/m ... am i on the right track?
Yes, you are!
 
  • #8
516
19
I think I am now stuck though because I dont have any information for t
 
  • #9
TSny
Homework Helper
Gold Member
12,396
2,836
Any way to use the information about the length of the plates?
 
  • #10
516
19
ah thank you! so it constantly travels 1x10^7 m/s in the x direction for the length of .049 m.
v = d/t so t= d/v = .049 m / 1x10^7 m/s = 4.9 x 10 ^-9 s
so
vy = eEt/m = (1.602x10^-19)(5x10^3)(4.9x10^-9)/(9.1x10^-31) = 4313077 m/s right?
 
  • #11
TSny
Homework Helper
Gold Member
12,396
2,836
That looks right. I haven't actually grabbed a calculator and checked your numbers.
 
  • #12
516
19
ok so that means theta = tan^-1(4313077/(1x10^7)) = 23.3 degrees but -23.3 degrees because it is going clockwise from the x axis
 
  • #13
TSny
Homework Helper
Gold Member
12,396
2,836
Yes. Or you can just say 23.3o below the horizontal. (That way, whoever sees your answer doesn't have to decipher the meaning of the negative sign.) But, if you are having to plug your answer into some sort of grading program, then you might need to include the sign.
 
  • #14
516
19
thank you so much!
 

Related Threads on Electrion moving between two parallel plates

Replies
0
Views
2K
Replies
2
Views
4K
Replies
1
Views
991
Replies
5
Views
51K
Replies
1
Views
8K
Replies
26
Views
3K
Replies
1
Views
3K
Replies
6
Views
999
Replies
4
Views
4K
Replies
1
Views
2K
Top