I How Does a Vibrating Sample Magnetometer Calculate Magnetic Moment?

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A Vibrating Sample Magnetometer (VSM) calculates magnetic moment by measuring the induced voltage in a coil as the sample oscillates in a magnetic field. The relationship between induced electromotive force (emf) and magnetic moment is derived from the equation emf = -dPhi/dt, where dPhi/dz is proportional to the magnetic moment. This proportionality is based on the assumption of small amplitude oscillations, leading to a linear dependence of magnetic flux on the displacement z. The discussion highlights confusion around this relationship and the mechanics of the VSM, which involves a vibrating sample creating a measurable signal in a stationary coil. Understanding these principles is crucial for accurate magnetic moment calculations using VSM technology.
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How do you find the change in flux with respect to position
In descriptions of a VSM, the induced voltage in a coil is shown to be emf = -dPhi/dt = - (dPhi/dz)(dz/dt). From here, everyone seem to jump to a solution of emf = 2*Pi*A*f*m*sin(2*Pi*f*t).
That makes some sense: in this case, you can define z = A*cos(2*Pi*f*t) so (dz/dt) = 2*Pi*A*f*sin(2*Pi*f*t). I'm confused why (dPhi/dz) turns out to be equal to or proportional to m (the magnetic moment). Is it an approximation that assumes a small amplitude of oscillation and so a linear dependence of the magnetic flux on z? I am having trouble picturing this. Can someone help?
 
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What is a "VSM"? Is it a rotating coil in a magnetic field?
 
vanhees71 said:
What is a "VSM"? Is it a rotating coil in a magnetic field?
I guess it's his Vibrating Sample Magnetometer -- a quick search of Google Images turns up this:

1666717336498.png


https://en.wikipedia.org/wiki/Vibrating-sample_magnetometer
 

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Thread 'Inducing EMF Through a Coil: Understanding Flux'

Thread 'Inducing EMF Through a Coil: Understanding Flux'

Thank you for reading my post. I can understand why a change in magnetic flux through a conducting surface would induce an emf, but how does this work when inducing an emf through a coil? How does the flux through the empty space between the wires have an effect on the electrons in the wire itself? In the image below is a coil with a magnetic field going through the space between the wires but not necessarily through the wires themselves. Thank you.
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Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. In the page 196, in the first paragraph, the author argues as follows ...
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