Difference between $ \ F^{\mu\nu}$ and $\tilde F_{\rho\sigma}$

Question

$ \ F^{\mu\nu}$ and the Hodge dual $\tilde F_{\rho\sigma}$ these are two tensors, related by $\epsilon_{\rho\sigma\mu\nu }$. My question is, is there any physical difference between them( I am aware their matrix form)?

Answer 1

They're related via the electromagnetic duality transformation ${\bf E} \to {\bf B},\ {\bf B} \to -{\bf E}$.