Electron deflected via magnetic field

In summary, an electron is accelerated through a potential difference from 0V to N kV, then ejected through a slit and deflected 10 degrees over a distance of 2 cm. To find B, v_f, and t, the equations qdelta V = 1/2Me v_f^2 and M(v/r) = qBsin\theta can be used, where r is the distance traveled by the electron after passing through the slit. By correctly applying the formula for impulse and considering the change in momentum, the time taken for the electron to travel the 2 cm distance can be determined.
  • #1
Frostfire
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Homework Statement



an electron is accelerated through a potential difference from 0v to N kv. It is then ejected through a slit and deflected 10* over a distance r of 2 cm.

find B ,v_f, and t(time)



Homework Equations



qdelta V = 1/2Me v_f^2 (solved for vf)

M(v/r)= qBsin[tex]\theta[/tex] solved for B

The Attempt at a Solution



As listed above I solved for the variables listed (assuming I did it right, please correct me if I am wrong)
but what is the relation of t to this, is it a kinematic or a break down of db/dt?
 
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  • #2
You have done the first part correctly.

However, for the second part you seem to be using the formula for centripetal force, which is not correct. r is not the radius of curvature. r is the distance the electron travels from the slit opening, over which distance it is deflected 10 degrees.

So this part concerns a deflection of 10 degrees over a distance of 2 cm. after accelerating through the potential difference. How long did it take for the electron to travel that 2 cm.? That is the time that you need to find.

The force (Lorentz force) multiplied by the time over which it acts gives you the impulse received by the electron (after passing through the slit).

The change in velocity after passing through the slit is easy to calculate. So you can determine that change in momentum.

How is change in momentum related to impulse? That will give you the correct answer.

AM
 
Last edited:

1. How does a magnetic field deflect an electron?

When an electron moves through a magnetic field, it experiences a force due to its negative charge. This force causes the electron to move in a circular path perpendicular to the direction of the magnetic field.

2. What is the relationship between the strength of the magnetic field and the amount of deflection of the electron?

The amount of deflection of an electron depends on the strength of the magnetic field and the velocity of the electron. The stronger the magnetic field, the greater the force on the electron and the larger the deflection.

3. Can an electron be deflected in the absence of a magnetic field?

No, an electron cannot be deflected without the presence of a magnetic field. This is because the force on the electron is directly proportional to the strength of the magnetic field.

4. What factors affect the direction of deflection of an electron in a magnetic field?

The direction of deflection of an electron in a magnetic field is determined by the direction of the magnetic field, the direction of the electron's velocity, and the orientation of the electron's spin relative to the magnetic field.

5. How is the deflection of an electron used in scientific research?

The deflection of electrons in a magnetic field is a fundamental principle used in many scientific research techniques, such as particle accelerators, mass spectrometry, and electron microscopy. By controlling the strength and direction of the magnetic field, scientists can manipulate the path of electrons to study various phenomena and obtain valuable information about the properties of matter.

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