Concept explainers
(a)
The expression for the magnetic field inside the solenoid.
(a)
Answer to Problem 43P
The expression for the magnetic field inside the solenoid is
Explanation of Solution
Write the equation of magnetic field from Ampere’s law.
Here,
Write the equation of the elementary length.
Here,
Write the expression for the number of turns per unit length.
Here,
Conclusion:
Substitute
Thus, the expression for the magnetic field inside the solenoid is
(b)
The expression of magnetic flux through one turn.
(b)
Answer to Problem 43P
The expression of magnetic flux through one turn is
Explanation of Solution
Write the equation of the magnetic flux.
Here,
Write the expression for the area of the loop.
Here,
Conclusion:
Substitute,
Thus, the expression of magnetic flux through one turn is
(c)
The total flux linkage through all turns of the solenoid.
(c)
Answer to Problem 43P
The total flux linkage through all turns of the solenoid is
Explanation of Solution
Considering the total number of turns of the coil is
Write the equation for the total flux.
Here,
Conclusion:
Substitute,
Therefore, the total flux linkage through all turns of the solenoid is
(d)
The expression for the self inductance of the solenoid.
(d)
Answer to Problem 43P
The expression for the self inductance of the solenoid is
Explanation of Solution
Write the equation from definition for the self inductance.
Here,
Conclusion:
Substitute,
Rewrite the equation to find
Therefore, the expression for the self inductance of the solenoid is
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