Concept explainers
In a long, .straight, vertical lightning stroke, electrons move downward and positive ions move upward and constitute a current of magnitude 20.0 kA. At a location 50.0 m east of the middle of the stroke, a free electron drifts through the air toward the west with a speed of 300 m/s. (a) Make a sketch showing the various vectors involved. Ignore the effect of the Earth's magnetic field. (b) Find the vector force the lightning stroke exerts on the electron. (c) Find the radius of the electron’s path. (d) Is it a good approximation to model the electron as moving in a uniform field? Explain your answer. (e) If it does not collide with any obstacles, how many revolutions will the electron complete during the 60.0-µs duration of the lightning stroke?
(a)
To draw: The various vectors involved to represent the lightning stroke of the electron and the positive ions.
Answer to Problem 30.16P
The various vectors involved to represent the lightning stroke of the electron and the positive ions as shown below,
Explanation of Solution
Given info: The electrons move downward and the positive ions move upwards. The magnitude of the uniform current is
According to the Ampere’s right hand thumb rule, the index finger represents the direction of the velocity vector
Write the expression for the magnetic field.
Here,
Substitute
Write the expression for the direction of the magnetic field according to the ampere’s law of the magnetic field.
Write the expression for the velocity vector pointed towards the west.
Write the expression for the force vector on the electron,
Here,
Substitute
From the result of the force vector, field vector and velocity vector the as shown below,
Figure (1)
(b)
The vector force lightning stroke exert on the electron.
Answer to Problem 30.16P
The vector force lightning stroke exert on the electron is
Explanation of Solution
Given info: The electrons move downward and the positive ions move upwards. The magnitude of the uniform current is
From the part (a), the vector force on the electron.
Conclusion:
Therefore, the vector force lightning stroke exert on the electron is
(c)
The radius of the electron path.
Answer to Problem 30.16P
The radius of the electron path is
Explanation of Solution
Given info: The electrons move downward and the positive ions move upwards. The magnitude of the uniform current is
Write the expression for the radius of the electron path.
Here,
Substitute
Conclusion:
Therefore, the radius of the electron path is
(d)
Whether it is a good approximation to model the electron as moving in a uniform field.
Answer to Problem 30.16P
The electron was not moving in a uniform field cause of the magnetic field is varies from the location of the lightning stroke.
Explanation of Solution
Given info: The electrons move downward and the positive ions move upwards. The magnitude of the uniform current is
From the figure (1) of the part (a), the magnitude of the magnetic field is varies with the distance of the light stroke towards the positive
Conclusion:
Therefore, the electron was not moving in a uniform field cause of the magnetic field is varies from the location of the lightning stroke.
(e)
The number of the revolutions will the electron complete during the
Answer to Problem 30.16P
The number of the revolutions will the electron complete during
Explanation of Solution
Given info: The electrons move downward and the positive ions move upwards. The magnitude of the uniform current is
From the part (c) the radius of the electron path,
Write the expression for the number of the revolution complete by the electron.
Here,
Substitute
Conclusion:
Therefore, the number of the revolutions will the electron complete during
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Chapter 30 Solutions
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