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Magnetic Field Due to Two Straight Wires01:18

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the magnetic field at a point "P2", midway between the wires. Also, evaluate the magnetic field when the direction of the current is reversed in the second wire.
Magnetic Field Of A Current Loop01:16

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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.
Magnetic Field Due To A Thin Straight Wire01:27

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Second Uniqueness Theorem01:16

Second Uniqueness Theorem

Consider a region consisting of several individual conductors with a definite charge density in the region between these conductors. The second uniqueness theorem states that if the total charge on each conductor and the charge density in the in-between region are known, then the electric field can be uniquely determined.
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Magnetic Field of a Solenoid01:18

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Related Experiment Video

Updated: Jul 2, 2026

Frequency Mixing Magnetic Detection Scanner for Imaging Magnetic Particles in Planar Samples
07:01

Frequency Mixing Magnetic Detection Scanner for Imaging Magnetic Particles in Planar Samples

Published on: June 9, 2016

Uniformity condition for a rectangular field coil with a split winding.

T N Casselman1, R B Fryer, F N Simon

  • 1Honeywell Corporate Material Sciences Center, Bloomington, Minnesota 55420.

The Review of Scientific Instruments
|January 1, 1978
PubMed
Summary
This summary is machine-generated.

Researchers derived a generalized Helmholtz condition for magnetic field uniformity in multilayer rectangular coils. This finding aids in designing coils for precise field generation, crucial for various scientific applications.

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Area of Science:

  • Physics
  • Electromagnetism
  • Coil Design

Background:

  • Achieving uniform magnetic fields is critical for many scientific and technological applications.
  • Existing methods for designing magnetic coils often rely on approximations or empirical data.
  • A precise theoretical condition for field uniformity in rectangular coils is needed.

Purpose of the Study:

  • To derive a generalized Helmholtz condition for field uniformity in multilayer rectangular coil pairs.
  • To establish the relationship among coil dimensions that satisfy this uniformity condition.
  • To compare theoretical predictions with experimental measurements.

Main Methods:

  • Derivation of a closed-form solution for the magnetic field of a multilayer rectangular coil pair.
  • Analysis of the solution to establish a generalized Helmholtz condition.
  • Parametric plotting of the dimension relations for single and multilayer coils.
  • Experimental validation of the derived condition.

Main Results:

  • A generalized Helmholtz condition for field uniformity was successfully derived.
  • Parametric plots illustrate the relationship between coil dimensions for achieving uniformity.
  • For small-aspect-ratio square coils, gap separation approaches half the coil radius.
  • Experimental comparisons showed agreement within 6% deviation for +/-5% field tolerances.

Conclusions:

  • The derived generalized Helmholtz condition provides a theoretical basis for designing uniform magnetic fields in rectangular coils.
  • The findings are applicable to both single-layer and multilayer coil configurations.
  • Experimental validation confirms the accuracy and practical utility of the derived condition.