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Magnetic Vector Potential

Magnetic Vector Potential

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...

Magnetostatic Boundary Conditions

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...

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Related Experiment Video

Updated: Aug 10, 2025

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Published on: July 20, 2022

Edge-Machine-Learning-Assisted Robust Magnetometer Based on Randomly Oriented NV-Ensembles in Diamond.

Jonas Homrighausen¹, Ludwig Horsthemke², Jens Pogorzelski²

¹Department of Engineering Physics, Münster University of Applied Sciences, Stegerwaldstraße 39, 48565 Steinfurt, Germany.

Sensors (Basel, Switzerland)

|February 11, 2023

Summary

This summary is machine-generated.

This study introduces a low-cost quantum magnetometer using nitrogen vacancy centers and edge machine learning for precise magnetic field sensing. The system utilizes an ESP32 microcontroller for real-time data analysis and magnetic field deduction.

Keywords:

NV center in diamond edge machine learning magnetometry microcontroller neural networks optically detected magnetic resonance quantum sensing

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Area of Science:

Quantum sensing
Materials science
Machine learning

Background:

Optically detected magnetic resonance (ODMR) of nitrogen vacancy (NV) centers in diamonds offers high precision for magnetic field sensing.
Existing quantum magnetometers can be complex and costly, limiting widespread adoption.

Purpose of the Study:

To develop a low-cost, stand-alone quantum magnetometer using NV centers and edge machine learning.
To demonstrate the feasibility of using an embedded microcontroller for real-time magnetic field measurement.

Main Methods:

A continuous-wave ODMR setup was used to acquire data for training an artificial neural network.
An ESP32 microcontroller was employed for controlling data acquisition and performing network inference (edge machine learning).
The trained neural network was deployed on the ESP32 to deduce magnetic field strength from ODMR spectra.

Main Results:

The developed sensor setup successfully measured magnetic fields with high precision.
The edge machine learning approach enabled real-time magnetic field deduction on a low-power embedded device.
Proof-of-concept demonstrated the system's capability across a wide measuring range.

Conclusions:

The proposed low-cost quantum magnetometer with edge machine learning is a viable and accessible solution for precise magnetic field sensing.
This technology has the potential to enable robust and widespread sensor applications.
Further development could lead to portable and cost-effective magnetic field measurement tools.