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Introductory Physics Homework Help
Magnetization of the core of a long solenoid
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[QUOTE="prodo123, post: 6028574, member: 644550"] [h2]Homework Statement [/h2] A long solenoid of 60 turns/cm carries a current of 0.15 A. It wraps a steel core with relative permeability ##\mu_r=5200##. Find the magnitude of the magnetization of the core. [h2]Homework Equations[/h2] ##N=\lambda L## ##\chi = \mu_r-1## ##\mu = \mu_r\mu_0## ##\vec{M}=\chi\vec{H}## where ##\vec{H}## is the external magnetic field applied to the core and ##\vec{M}## is the magnetization of the core. This equation never showed up on the textbook for some reason. ##\vec{B_m}=\mu_0\vec{M}## where ##\vec{B_m}## is the additional magnetic field in the core induced by the external field ##\vec{H}##.Constants for the problem: ##\lambda=6000## (60 turns/cm = 6000 turns/m) ##I=0.15## [h2]The Attempt at a Solution[/h2] The magnetic field induced by the solenoid is the external magnetic field ##\vec{H}## applied to the core. Ampere's Law finds the induced magnetic field of the solenoid along the center axis as: ##\int \vec{H}\cdot d\vec{l} = \mu_0 N I## ##HL=\mu_0 \lambda L I## ##H=\mu_0 \lambda I## ##H = 1.13 \text{ mT}## ##\chi=\mu_r-1=\frac{M}{H}## ##M = H(\mu_r-1)## ##M = 5.88\text{ A/m}## The textbook has a completely different answer: ##M = \mu_r \lambda I## ##M = 4.68\text{ MA/m}## which I assume took the following steps: ##H=\mu_0 \lambda I## ##B_m=\mu\lambda I = \mu_0 M## ##M = \frac{\mu}{\mu_0}\lambda I## ##M = \mu_r \lambda I## Which is the right approach and why? [/QUOTE]
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Magnetization of the core of a long solenoid
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