Angle of Deflection of an electron in an magnetic field

In summary, the conversation discussed the deflection angle of electrons in an electron accelerator that first runs through an acceleration voltage before entering a homogeneous magnetic field. Using equations, the velocity and Lorentz force of the electrons were calculated, but the angle was still unknown. It was determined that the trajectory of a charged particle in a magnetic field is circular, but in this case, it would only form an arc due to the short length of the magnetic field. The solution involved determining the radius of the arc and considering the angle between the radius vectors at the entry and exit points of the magnetic field.
  • #1
Lunar_Lander
38
0

Homework Statement



Electrons first run through an accleration voltage of U = 25 kV before entering an homogenous magnetic field which is perpendicular to the electron beam (B=6*10-3 T). The starting velocity of the electrons shall be zero.

What is the deflection angle α, if the magnetic field has a length of 5 cm (This means that the magnetic field stretches out for 5 cm in front of the electron accelerator)?

Homework Equations



0.5*m*v2=e*U can be transformed to give the velocity of the electrons.

q*(v x B) is the Lorentz force. (Or also: FL = q*v*B)

The Attempt at a Solution



From the first equation I know that the velocity of the electron is 9.376*107 m/s. That gives a Lorentz force of 9.001*10-14 N. But how can I get the angle? I read somewhere that the tangent could be important, but I don't know how :(.
 
Physics news on Phys.org
  • #2
What is the shape of the trajectory of a charged particle moving perpendicularly to a magnetic field? (Hint: in what direction does the force act on the particle?)
 
  • #3
If you inject a charged particle into an magnetic field that is perpendicular to it, it will go around in a circle, with the Lorentz Force pointing "inside" the circle.

And in this case, we only get an arc and not a circle because the magnetic field is too "short" to make it go into a circle.

But I am still missing out the final idea on how to solve it, I can imagine some kind of triangle that you can form with one side being the lenghth of the B-Field and the hypotenuse being the arc. Or is that completely wrong?
 
  • #4
Lunar_Lander said:
If you inject a charged particle into an magnetic field that is perpendicular to it, it will go around in a circle, with the Lorentz Force pointing "inside" the circle.

And in this case, we only get an arc and not a circle because the magnetic field is too "short" to make it go into a circle.

But I am still missing out the final idea on how to solve it, I can imagine some kind of triangle that you can form with one side being the lenghth of the B-Field and the hypotenuse being the arc. Or is that completely wrong?

You'll want to determine the radius of the arc that the electron will follow. Take the center of that circle (which the arc is part of) as the center of an x-y coordinate system. You should be able to determine the point where the arc and boundaries of the magnetic field intersect. More importantly, ponder on the angle between the two radius vectors: 1) when the electron first enters the field, and 2) where the electron just leaves the field.

attachment.php?attachmentid=39952&stc=1&d=1318534244.gif
 

Attachments

  • Fig1.gif
    Fig1.gif
    2.2 KB · Views: 4,092
  • #5
I found it, thanks :)!
 

1. What is the angle of deflection of an electron in a magnetic field?

The angle of deflection of an electron in a magnetic field is determined by the strength of the magnetic field, the velocity of the electron, and the charge of the electron. It follows a circular path with the magnitude of the angle depending on these factors.

2. How is the angle of deflection of an electron calculated?

The angle of deflection of an electron can be calculated using the formula θ = qvB/m, where θ is the angle of deflection, q is the charge of the electron, v is the velocity of the electron, B is the magnetic field strength, and m is the mass of the electron.

3. What is the relationship between the angle of deflection and the strength of the magnetic field?

The angle of deflection is directly proportional to the strength of the magnetic field. This means that as the magnetic field strength increases, the angle of deflection also increases. Conversely, if the magnetic field strength decreases, the angle of deflection also decreases.

4. How does the angle of deflection change if the velocity of the electron is increased?

If the velocity of the electron is increased, the angle of deflection will also increase. This is because the force experienced by the electron in the magnetic field is dependent on its velocity, so a higher velocity will result in a larger deflection angle.

5. Can the angle of deflection be controlled or manipulated?

Yes, the angle of deflection can be controlled or manipulated by adjusting the strength of the magnetic field, the velocity of the electron, or the charge of the electron. This principle is used in devices such as cathode ray tubes and particle accelerators.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
697
  • Introductory Physics Homework Help
Replies
31
Views
947
  • Introductory Physics Homework Help
Replies
4
Views
240
  • Introductory Physics Homework Help
Replies
1
Views
198
  • Introductory Physics Homework Help
Replies
18
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
768
  • Introductory Physics Homework Help
Replies
1
Views
928
  • Introductory Physics Homework Help
Replies
3
Views
856
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top