📢Using the Metric Tensor to Convert Contravariant to Covariant Components

In non-Cartesian coordinate systems, the basis vectors are not of unit length, causing the components to behave differently. The process uses the metric tensor as a conversion tool, which accounts for the varying scale of the coordinate system. The result shows that while the initial contravariant component depends on the radial distance from the wire, the final covariant component is constant, directly representing the physical field strength after accounting for the basis vector's length.

Finding the Covariant Components of a Magnetic Field | Proof and Derivationviadean on Notion