Concept explainers
An electron is accelerated from rest through a potential difference of 800 V. It then moves perpendicularly to a magnetic field of 30 G. Find the radius of its orbit and its orbital frequency.
The radius and orbital frequency of the electronthat is accelerated from rest through a potential difference of
Answer to Problem 35SP
Solution:
Explanation of Solution
Given data:
The electric potential difference is
The magnitude of the magnetic field acting on the electron is
Formula used:
The radius of a circular path of a charged particle moving along in a magnetic field is given as
Here,
The velocity of a charged particle moving due an electric potential difference is given as
Here,
The expression for orbital frequency of an object is given as
Here,
Explanation:
Consider the expression for radius of the circular path of an electron:
Here,
Consider the expression for the velocity of an electronmoving due to an electric potential difference:
From equation (1) and (2)
Keep in mind that
Substitute
Consider the expression for the velocity of an electron moving due to an electric potential difference:
Substitute
Consider the expression for the orbital frequency of the electron:
Here,
Substitute
Conclusion:
Therefore, the radius and the orbital frequency of the electron orbit are
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Chapter 30 Solutions
College Physics
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