Helmholtz Rings Magnetic Field Calculator | Biot-Savart Law Calculation

The model is represented as two circular current ribbons carrying currents in the same direction. The rings are positioned along the z-axis and separated symmetrically by a distance of r/2 in the positive and negative directions. Parameters: r — ring radius; w — ribbon width The magnetic field is computed using the Biot–Savart–Laplace law. An elementary current element is a circular ribbon of width dw. The calculation is reduced to a double integral: an integral over the circumference, and an integral over the ribbon width w. One of the integrals has an analytical solution, while the other is evaluated using the Simpson method.

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This calculator computes the magnetic field produced by a pair of coaxial circular coils (Helmholtz configuration). It is useful for analyzing uniform magnetic field regions using the Biot–Savart–Laplace law.

Units: All calculations are performed in the Gaussian (CGS) system.
I/sm
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Even number for Simpson’s rule.
Move the field source
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Observation point
Helmholtz Rings
Two coaxial circular ribbons. The current flows counterclockwise
Helmholtz rings model: two coaxial circular coils producing a uniform field

Two circular ribbons carrying current in the same direction. The configuration produces a highly uniform field near the center.

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