What is the radius of the circular arc if the accelerating potential is tripled?

In summary, the conversation discusses the acceleration of an electron through a potential difference V and its subsequent deflection into a circular arc by a perpendicular magnetic field. It poses questions about the relationship between electric field and potential difference, the force on the electron, the velocity of the electron in relation to the potential difference and the radius of the circular arc. The answer to the question regarding the radius of the circular arc when the potential difference is tripled is √3 R, but the method to obtain this answer is not known.
  • #1
googlyeyes
17
0

Homework Statement



An electron is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?

Homework Equations



?

The Attempt at a Solution



The answer is √3 R, just not sure how to get there
 
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  • #2
googlyeyes said:
The answer is √3 R, just not sure how to get there

1. What is the relationship between Electric field and potential difference V ?
2. What is the force on the electron as it moves through the region of potential difference V?
3. Find the relationship between the velocity of the electron just as it is about to enter the magnetic field , and the potential difference V ?
4.Find the relationship between the velocity of the electron in the magnetic field , and the radius of the circular arc.
 

FAQ: What is the radius of the circular arc if the accelerating potential is tripled?

1. What is the role of a magnetic field in the behavior of an electron?

The magnetic field affects the motion of an electron by exerting a force on it. This force can change the direction and speed of the electron's movement.

2. How does an electron behave in a uniform magnetic field?

In a uniform magnetic field, an electron will experience a force that is perpendicular to both its velocity and the magnetic field. This results in the electron moving in a circular motion.

3. What is the relationship between the strength of a magnetic field and the force on an electron?

The force on an electron in a magnetic field is directly proportional to the strength of the magnetic field. This means that a stronger magnetic field will result in a greater force on the electron.

4. Can an electron's spin be affected by a magnetic field?

Yes, a magnetic field can affect an electron's spin. In a uniform magnetic field, the electron's spin will align with the magnetic field, resulting in a different energy state for the electron.

5. How is the motion of an electron in a magnetic field different from its motion in an electric field?

The motion of an electron in a magnetic field is different from its motion in an electric field because the force exerted by a magnetic field is perpendicular to the electron's motion, while the force exerted by an electric field is in the same direction as the electron's motion.

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