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Divergence and Curl of Magnetic Field01:26

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:
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A superconductor is a substance that offers zero resistance to the electric current when it drops below a critical temperature. Zero resistance is not the only interesting phenomenon as materials reach their transition temperatures. A second effect is the exclusion of magnetic fields. This is known as the Meissner effect. A light, permanent magnet placed over a superconducting sample will levitate in a stable position above the superconductor. High-speed trains that levitate on strong...
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Magnetic Field due to Moving Charges

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Related Experiment Video

Updated: May 11, 2026

Scanning SQUID Study of Vortex Manipulation by Local Contact
06:53

Scanning SQUID Study of Vortex Manipulation by Local Contact

Published on: February 1, 2017

Vortex kinks in superconducting films with periodically modulated thickness.

Jorge I Facio1, Anabella Abate, J Guimpel

  • 1Instituto Balseiro, Comisión Nacional de Energía Atómica and Universidad Nacional de Cuyo, Centro Atómico Bariloche, 8400 Bariloche, Argentina. facioj@ib.cnea.gov.ar

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 31, 2013
PubMed
Summary

We studied how magnetic fields affect niobium (Nb) films with patterned surfaces. These patterns control superconducting vortices, leading to predictable changes in electrical resistance, especially at specific magnetic field strengths.

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Last Updated: May 11, 2026

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Area of Science:

  • Superconductivity
  • Condensed Matter Physics
  • Materials Science

Background:

  • Superconducting vortices are quantized magnetic flux lines within a superconductor.
  • Vortex behavior is crucial for understanding superconductivity in applied magnetic fields.
  • Periodic pinning potentials can significantly alter vortex dynamics.

Purpose of the Study:

  • To investigate the magnetoresistance of niobium (Nb) films with periodic thickness modulations.
  • To understand how patterned structures influence superconducting vortex flow.
  • To correlate vortex-flow regimes with observed magnetoresistance features.

Main Methods:

  • Magnetoresistance measurements were performed on Nb films with square lattice thickness modulations.
  • Varying magnetic fields (B) were applied perpendicular to the film surface.
  • Numerical simulations were used to model vortex dynamics and flow regimes.

Main Results:

  • Resistivity (ρ) showed approximately piecewise linear dependence on magnetic field (B) at low currents.
  • Slope changes in ρ-B characteristics occurred at matching fields, related to vortex density.
  • Simulations identified different vortex-flow regimes, including those dominated by discommensuration propagation.

Conclusions:

  • Periodic thickness modulations create effective repulsive potentials for superconducting vortices.
  • Magnetoresistance measurements reveal distinct vortex-flow regimes governed by the pinning landscape.
  • The study provides insights into vortex matter control using engineered pinning sites.