Concept explainers
(a)
The speed of the proton as it leaves region 1 and enters region 2.
(a)
Answer to Problem 42P
The speed of the proton as it leaves region 1 and enters region 2 is
Explanation of Solution
The potential difference in region 1 is
As the proton passes out of region 1, the potential energy due to the potential difference is converted into kinetic energy.
Here,
Re-write the above equation to get an expression for
Conclusion:
Substitute
The speed of the proton as it leaves region 1 and enters region 2 is
(b)
The magnitude and direction of the electric field in region 2 if the proton moves in straight line in region 2.
(b)
Answer to Problem 42P
The magnitude of the electric field is
Explanation of Solution
The potential difference in region 1 is
If the proton moves in straight line in region 2, the magnetic force is balanced by the electric force.
Here,
Re-write the above equation to get an expression for
The direction of the magnetic force is determined by right hand rule. The magnetic field is directed upward, the velocity of the proton is east ward. Thus by right hand rule the magnetic force will be towards south direction.
Conclusion:
Substitute
To cancel the magnetic force, the electric field has to be in the opposite direction of the magnetic force. Thus the direction of the electric field is towards north.
The magnitude of the electric field is
(c)
The path of the proton in region 3.
(c)
Answer to Problem 42P
In region 3 the proton follows the path 2.
Explanation of Solution
The potential difference in region 1 is
The direction of the magnetic force is determined by right hand rule. The magnetic field is directed upward, the velocity of the proton is east ward. Thus by right hand rule the magnetic force will be towards south direction.
In region 3 there is only magnetic field. Thus the force on the proton is only the magnetic force. Thus the force on the proton is directed in south direction so it follows the path 2.
Conclusion:
In region 3 the proton follows the path 2.
(d)
The radius of the circular path in region 3.
(d)
Answer to Problem 42P
The radius of the circular path in region 3 is
Explanation of Solution
The potential difference in region 1 is
The magnetic force makes the proton move in circular path. Thus the magnetic force is equal to the
Here,
Re-write the above equation to get an expression for
Conclusion:
Substitute
The radius of the circular path in region 3 is
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