Concept explainers
(a)
The magnitude and direction of the electric field in the wire.
(a)
Answer to Problem 27.67AP
Explanation of Solution
Given information: Length of the cylindrical wire is
Explanation:
Formula to calculate the magnitude of the electric field in the wire.
Here,
Substitute
Thus, the magnitude and direction of the electric field in the wire is
Conclusion:
Therefore, the magnitude and direction of the electric field in the wire is
(b)
The resistance of the wire.
(b)
Answer to Problem 27.67AP
Explanation of Solution
Given information: Length of the cylindrical wire is
Explanation:
Write the expression for the area of cross section of the cylindrical wire.
Here,
Substitute
Thus, the area of cross section of the cylindrical wire is
Formula to calculate the resistance of the wire.
Here,
Substitute
Thus, the resistance of the wire is
Conclusion:
Therefore, the resistance of the wire is
(c)
The magnitude and direction of the electric current in the wire.
(c)
Answer to Problem 27.67AP
Explanation of Solution
Given information: Length of the cylindrical wire is
Explanation:
Formula to calculate the magnitude of the electric current in the wire.
Here,
Substitute
Thus, the magnitude and direction of the electric current in the wire is
Conclusion:
Therefore, the magnitude and direction of the electric current in the wire is
(d)
The current density in the wire.
(d)
Answer to Problem 27.67AP
Explanation of Solution
Given information: Length of the cylindrical wire is
Explanation:
Formula to calculate the current density in the wire.
Here,
Substitute
Thus, the current density in the wire is
Conclusion:
Therefore, the current density in the wire is
(e)
To show: The expression for electric field in the wire is given by
(e)
Answer to Problem 27.67AP
Explanation of Solution
Given information: Length of the cylindrical wire is
Explanation:
From equation (1), write the expression for the electric field in the wire.
Multiply by
From equation (5), formula to calculate the current density in the wire.
From equation (4), formula to calculate the magnitude of the electric current in the wire.
Substitute
From equation (3), formula to calculate the resistance of the wire.
Substitute
Substitute
Thus, the expression for electric field in the wire is given by
Conclusion:
Therefore, the expression for electric field in the wire is given by
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Chapter 27 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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