Bound on the time variation of the fine structure constant driven by quintessence

The bound on the time variation of the fine structure constant ($\alpha$) driven by the dynamics of quintessence scalar field which is coupled to electromagnetism is discussed using phenomenological quintessential models constrained by SNIa and CMB observations. We find that those models allowing early quintessence give the largest variation $\mathrm{\Delta }\alpha$ at the decoupling epoch. Furthermore, the fifth force experiments imply that $\mathrm{\Delta }\alpha \mathrm{/}\alpha$ is less than about 0.1%.