Relationship between paramagnetic fields and distance

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The discussion focuses on understanding how the strength of a magnetic field generated by a paramagnetic substance, specifically gadolinium above its Curie point, diminishes with distance from the source. The original poster seeks to determine the theoretical strength of paramagnetism at various distances and questions whether existing formulas for diamagnetic materials apply to paramagnetic substances. There is clarification that the paramagnetic field is internal to the material, while the external auxiliary magnetic field may be distorted by the presence of the gadolinium. The conversation emphasizes the need to establish proximity between the gadolinium and the sensor to accurately detect these magnetic effects. Overall, the thread explores the complexities of measuring paramagnetic fields in a nano-scale context.
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Summary: What is the relationship between paramagnetic field strength at a given distance from the source?

Apologies if I have put this in the wrong topic. And apologies if the question is unclear, I am a biologist by background attempting to do some physics here!

Basically I am looking to define how a magnetic field generated by a paramagnetic substance (gadolinium above curie point) in the presence of an auxiliary magnetic field would deteriorate over distance. I have calculated the magnetisation of the gadolinium, and now want to work out the theoretical strength of the paramagnetism at a given distance from the source? I think I have found formulae for calculating this with regards to diamagnetic materials, but does this hold true for paramagnetism?

Experimental Background: I have developed a magnetometer system (cannot discuss due to IP) but essentially want to see where the sensor is sensing only the auxiliary magnetic field and areas where the sensor is picking up extra magnetism of the gadolinium. What I am trying to establish is how close the gadolinium needs to be to the sensor in order for me to sense these effects? (this is all being done on the nano-scale)
 
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Welcome to the PF. :smile:

I have a basic understanding of magnetic fields, but I'm no expert. I'm not sure it's correct to talk about an external "paramagnetic field". The paramagnetic field is internal to the paramagnetic matierial, I believe. The external field (that you call the auxiliary field) will be somewhat distorted due to the presence of the paramagnetic material. Is that what you are calling the "paramagnetic field"?

https://en.wikipedia.org/wiki/Paramagnetism
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