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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...

Divergence and Curl of Magnetic Field

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:

Potential Due to a Magnetized Object

Potential Due to a Magnetized Object

Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...

Biot-Savart Law

Biot-Savart Law

The Biot-Savart law gives the magnitude and direction of the magnetic field produced by a current. This empirical law was named in honor of two scientists, Jean-Baptiste Biot and Félix Savart, who investigated the interaction between a straight, current-carrying wire and a permanent magnet.
A current-carrying wire creates a magnetic field in its vicinity. Consider an infinitesimal current element dl in a wire. The direction of vector dl is along the direction of the current. The total magnetic...

Magnetic Force On A Current-Carrying Conductor

Magnetic Force On A Current-Carrying Conductor

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor carrying a current creates a magnetic field around it.
Consider a compass placed near a current-carrying wire. The wire experiences a force that aligns the needle of the compass tangentially around the wire. Thus, the current-carrying wire produces concentric circular loops of magnetic field. The magnetic field generated by a wire can be...

Magnetic Field Of A Current Loop

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.

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A Vectorial Current Density Imaging Method Based on Magnetic Gradient Tensor.

Yangjing Wu¹, Mingji Zhang¹, Chengyuan Peng¹

¹Sino-German College of Intelligent Manufacturing, Shenzhen Technology University, Shenzhen 518118, China.

Sensors (Basel, Switzerland)

|July 14, 2023

Summary

This summary is machine-generated.

This study introduces a new vectorial current density imaging method. It accurately visualizes both the magnitude and direction of electrical currents in devices, overcoming limitations of previous techniques.

Keywords:

closed-form inversion current density inversion magnetic current imaging magnetic gradient tensor nondestructive testing

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Area of Science:

Electrical Engineering
Non-invasive Inspection Techniques
Materials Science

Background:

Magnetic current imaging is an emerging technique for visualizing electrical currents in electronic devices.
Existing methods, like Fourier Transform back-evolution, are limited to imaging current density magnitude and are prone to noise.
There is a need for advanced techniques capable of vectorial current density imaging for comprehensive device analysis.

Purpose of the Study:

To develop a novel vectorial current density imaging method.
To overcome the limitations of existing mono-functional magnetic current imaging techniques.
To enable simultaneous imaging of both magnitude and direction of current density in electronic devices.

Main Methods:

Developed a vectorial current density imaging method based on detecting magnetic field gradients from current-carrying conductors.
Derived and numerically verified a closed-form solution for current density inversion.
Employed a tri-axial fluxgate sensor for scanning over various electrical wire shapes.

Main Results:

Achieved a current density resolution of 24.15 mA/mm².
Demonstrated a probe-to-sample separation of 2 mm and a spatial resolution of 0.69 mm.
Successfully imaged both magnitude and direction of current density over a 300 mm × 300 mm area.

Conclusions:

The novel vectorial current density imaging method successfully images both magnitude and direction of current density.
This technique offers improved performance over existing methods, with high resolution and minimal noise distortion.
It presents a promising solution for in situ, non-invasive inspection in the power electronics and semiconductor industries.