Uncertainty Relations for Two Dimensional Quantized Electromagnetic Potential

The canonical quantization of flux is performed. It is shown that according to the canonical flux quantization there must be a new uncertainty relation: $e \Delta A_m . \Delta x_m \geq \hbar$ where $A_m$ and $\Delta x_m \geq l_B$ are the electromagnetic gauge potential, the position uncertainty and the magnetic length, respectively. Other arguments in favour of this uncertainty relation are also discussed.