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Solved: Inductance of a Solenoid. (a) A long, straight
Chapter 30, Problem 15E(choose chapter or problem)
Problem 15E
Inductance of a Solenoid. (a) A long, straight solenoid has N turns, uniform cross-sectional area A, and length l. Show that the inductance of this solenoid is given by the equation L = µ0AN2/l. Assume that the magnetic field is uniform inside the solenoid and zero outside. (Your answer is approximate because B is actually smaller at the ends than at the center. For this reason, your answer is actually an upper limit on the inductance.) (b) A metallic laboratory spring is typically 5.00 cm long and 0.150 cm in diameter and has 50 coils. If you connect such a spring in an electric circuit, how much self-inductance must you include for it if you model it as an ideal solenoid?
Questions & Answers
QUESTION:
Problem 15E
Inductance of a Solenoid. (a) A long, straight solenoid has N turns, uniform cross-sectional area A, and length l. Show that the inductance of this solenoid is given by the equation L = µ0AN2/l. Assume that the magnetic field is uniform inside the solenoid and zero outside. (Your answer is approximate because B is actually smaller at the ends than at the center. For this reason, your answer is actually an upper limit on the inductance.) (b) A metallic laboratory spring is typically 5.00 cm long and 0.150 cm in diameter and has 50 coils. If you connect such a spring in an electric circuit, how much self-inductance must you include for it if you model it as an ideal solenoid?
ANSWER:
Solution 15E
Step 1 :
Introduction :
In this question, we need to show inductance of the coil is given by
In the second part, we need to find the amount if self inductance must be included if we consider this as ideal solenoid
Data given
Length of metallic spring
Diameter
Radius
Number of coils