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

AI Thread Summary
When an electron is accelerated through a potential difference V, its kinetic energy is directly related to that potential. Tripling the potential to 3V increases the electron's velocity, which affects the radius of its circular path in a magnetic field. The relationship between the velocity of the electron and the radius of the circular arc indicates that the radius increases with the square root of the potential difference. Consequently, when the potential is tripled, the radius of the circular arc becomes √3 times the original radius R. Understanding these relationships is crucial for solving the problem effectively.
googlyeyes
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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



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The Attempt at a Solution



The answer is √3 R, just not sure how to get there
 
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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.
 

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