Concept explainers
A particle with electric charge q moves along a straight line in a uniform electric field
(b) Discuss the significance of the dependence of the acceleration on the speed. (c) What If? If the particle starts from rest it x = 0 at t = 0, how would you proceed to find the speed of the particle and its position at time t?
(a)
To show: The acceleration of the particle in the
Answer to Problem 54CP
Explanation of Solution
The formula to calculate the relative momentum is,
Here,
The formula to calculate the force on the electric charge is,
Here,
The formula to calculate the Force due to motion is,
The force on the electric charge due to motion must be equal to that of the force due to electric field.
Substitute
Substitute
Further solve the above equation.
The formula to calculate the acceleration is,
Substitute
Conclusion
Therefore, the acceleration of the particle in the
(b)
Answer to Problem 54CP
Explanation of Solution
The formula to calculate the acceleration of the charge is,
As the speed of charge approaches to the speed of light, the acceleration approaches to zero.
When the speed of the charge is very small as compared to that of the speed of the light the above equation can be transformed.
So the relative expression is transformed to the classical expression when the speed of the charge is very small as compared to that of the speed of the light.
Conclusion
Therefore, the significance of the dependence of the acceleration on the speed is that when the speed of the charge is very small as compared to that of the speed of light the relative expression is transformed to the classical expression.
(c)
Answer to Problem 54CP
Explanation of Solution
The formula to calculate the acceleration of the charge is,
Integrate the above equation from velocity
Thus the speed of the particle at time
The formula to calculate the position of the particle is,
Substitute
Integrate the above equation from position
Conclusion
Therefore, the speed of the charge particle at time
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Chapter 38 Solutions
Physics for Scientists and Engineers
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