Magnetic Vector-Potential Gauge

In classical electromagnetism, the magnetic field B is defined as the curl of the magnetic vector potential A, i.e., B = ∇ × A. Because the curl of a gradient is always zero, we can add the gradient of any scalar field χ to the vector potential without changing the observable magnetic field: A' = A + ∇ χ. This flexibility is known as gauge freedom.

Experiment

In the interactive module, you can select different gauges and observe how the vector field arrows change. You can configure:

1. Gauge: Choose between Symmetric, Cross gradient, or Radial gradient gauges.
2. Uniform B: Set the strength of the uniform magnetic field B_z.
3. Point x, y: Set the target coordinate to see the exact vector potential calculated there.
4. Loop radius: Change the size of the integration loop to verify that the circulation ∮ A · dl remains invariant across different gauges for the same magnetic field.