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Related Concept Videos

Potential Due to a Magnetized Object01:24

Potential Due to a Magnetized Object

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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.
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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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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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Related Experiment Video

Updated: Jul 23, 2025

Magnetic Adjustment of Afterload in Engineered Heart Tissues
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Exact and Computationally Robust Solutions for Cylindrical Magnets Systems with Programmable Magnetization.

Federico Masiero1,2, Edoardo Sinibaldi3

  • 1Biorobotics Institute, Scuola Superiore Sant'Anna, viale Rinaldo Piaggio 34, Pontedera, 56025, Italy.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|July 17, 2023
PubMed
Summary

Researchers developed exact analytical solutions for magnetic fields and forces from cylindrical magnets, overcoming dipole approximation limitations. These findings offer significant computational savings for micro/millirobotics and biomedical applications.

Keywords:
cylindrical magnets systemsexact analytical solutionmagnetic actuationmagnetic field and gradientmagnetic force and torqueprogrammable magnetization

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Area of Science:

  • Physics
  • Engineering
  • Materials Science

Background:

  • Permanent magnets are crucial for micro/millirobotics and biomedical applications.
  • Analytical solutions for magnetic systems are lacking, hindering computational efficiency.
  • The dipole approximation is often used but has limitations for precise calculations.

Purpose of the Study:

  • To derive exact analytical solutions for the magnetic field and gradient of cylindrical magnets.
  • To develop computationally robust solutions for forces and torques between coaxial magnets.
  • To provide alternatives to the dipole approximation and numerical simulations.

Main Methods:

  • Derivation of exact analytical solutions for magnetic fields and gradients of uniformly magnetized cylinders.
  • Extension of solutions to systems of arbitrary complexity.
  • Calculation of exact forces and torques between coaxial magnets.

Main Results:

  • Exact analytical solutions for magnetic field and gradient of cylindrical magnets are presented.
  • Exact and computationally robust solutions for forces and torques between coaxial magnets are unveiled.
  • Computational gains of up to 10^6 compared to numerical simulations were achieved.

Conclusions:

  • The developed analytical solutions overcome the limitations of the dipole approximation.
  • These solutions offer significant computational advantages for designing magnetic systems.
  • The findings enable advancements in biomedical tools through programmable magnetization patterns for targeted applications.