📢Tensor Derivation and Verification of Spherical Divergence

The derivation of the divergence in spherical coordinates begins with the general tensor calculus formula. The crucial geometric factor for this coordinate system is the square root of the metric determinant. Substituting this into the formula and simplifying yields the divergence in terms of the contravariant components. To verify this result against the standard physics expression, the contravariant components were converted to the physical components using the relationship, which introduces specific scaling factors, confirming the tensor-based derivation is consistent with the traditional vector analysis formula.

Divergence in Spherical Coordinates Derivation and Verification | Proof and Derivationviadean on Notion