(a)
The electron would be in equilibrium at centre and if displaced would experience a restoring force.
(a)
Answer to Problem 24.62CP
The electron would be in equilibrium at centre and if displaced would experience a restoring force of magnitude
Explanation of Solution
Given info:
Consider the field distance
Write the expression of Guass’s law.
Here,
Write the expression for area of sphere.
Here,
Substitute
Write the expression for electric charge.
Here,
Substitute
Write the expression for volume of sphere.
Write the expression for density of sphere.
Here,
Substitute
Substitute
So,
The above electric field is directed outward.
The expression for the force is,
Substitute
Conclusion:
Therefore, the electron would be in equilibrium at centre and if displaced would experience a restoring force of magnitude
(b)
To show: The constant
(b)
Answer to Problem 24.62CP
The constant
Explanation of Solution
Given info:
Write the expression for spring force.
Here,
Also, the field force is,
Equate the above two force equations.
Substitute
Conclusion:
Therefore, the constant
(c)
The expression for the frequency
(c)
Answer to Problem 24.62CP
The expression for the frequency
Explanation of Solution
Given info:
According to Newton’s second law of motion,
Here,
Also, the field force is,
Equate the above two force equations.
Rearrange the above equation to get
Compare the above equation with the simple harmonic wave equation which is,
Equate the above two acceleration equations.
From the above equation
Write the general expression for frequency of
Substitute
Substitute
Conclusion:
Therefore, the expression for the frequency
(d)
The value of radius of orbit.
(d)
Answer to Problem 24.62CP
The value for
Explanation of Solution
Given info:
Write the expression for frequency
Rearrange the above equation to get
Substitute
Conclusion:
Therefore, the value for
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Chapter 24 Solutions
Physics for Scientists and Engineers, Volume 1
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