(a)
The magnitude and direction of the magnetic force on the electrons in the conductor shown in Figure 19.37.
(a)
Answer to Problem 33E
The magnitude of the force is
Explanation of Solution
The magnitude of magnetic force experienced on a moving charge can be written as,
Here,
Let
Conclusion:
Substitute
Direction of force will be in the direction of the cross product
Therefore, the magnitude of the force is
(b)
The magnitude and direction of the electric field that would exert an equal but opposite force on the electrons.
(b)
Answer to Problem 33E
The magnitude of electric field that would exert an equal but opposite force on the electrons is
Explanation of Solution
Write the expression to find the force on a charge in an electric field.
Here,
Rewrite equation (III) to find
For an electron,
Substitute equation (II) in part (a) in (V) to find
The direction of electric force will be same as that of the force. That is upward.
Conclusion:
Therefore, the magnitude of electric field that would exert an equal but opposite force on the electrons is
(c)
The potential difference across the conductor to produce the electric field.
(c)
Answer to Problem 33E
Potential difference across the conductor to produce the electric field is
Explanation of Solution
Write the expression to find the work done on a charge in a potential difference.
Here,
Write the expression to find the work done.
Here,
Substitute equations (III) and (VI) in (VII) to and solve for
Conclusion:
From part (a) it is found that the magnitude of electric field that would exert an equal but opposite force on the electrons is
Substitute
Therefore, potential difference across the conductor to produce the electric field is
(d)
The potential difference when no external electric field is applied.
(d)
Answer to Problem 33E
The potential difference when no external electric field is applied is
Explanation of Solution
The establishment of a potential difference across a conductor in a magnetic field is called Hall effect.
Write the expression to find the hall voltage.
Here,
Conclusion:
Substitute
Therefore, the potential difference when no external electric field is applied is
(e)
The Hall potential difference of the circuit.
(e)
Answer to Problem 33E
The Hall potential difference is
Explanation of Solution
The establishment of a potential difference across a conductor in a magnetic field is called Hall effect. Use equation (X) in part (d) to find the Hall potential difference.
Conclusion:
Substitute
Therefore, the Hall potential difference is
(f)
The direction of current in the circuit in Figure 19.37.
(f)
Answer to Problem 33E
The direction of the current is out of the page.
Explanation of Solution
Figure 1 represents the direction of the current in the circuit. Since the drift velocity of electrons is into the page the direction of current will be opposite to that. That is out of the page.
Conclusion:
Therefore, the direction of the current is out of the page.
(g)
To check whether the Hall potential difference be the same when the carriers are negative.
(g)
Answer to Problem 33E
The Hall potential difference will be opposite in sign for a given current direction.
Explanation of Solution
Hall Effect is a
Conclusion:
Therefore, the Hall potential difference will be opposite in sign for a given current direction.
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Chapter 19 Solutions
General Physics, 2nd Edition
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