The binding energy of a tuned quantum dot (QD) under an external magnetic field have been theoretically investigated. For this goal, the Schrödinger equation is analytically solved without and with considering the impurity term and the energy eigenvalues and eigenfunctions are analytically derived. Then, the binding of the tuned QD was studied considering the various parameters. We found that (i) the binding energy decrease with rising the potential range. (ii) The binding energy reduces with enhancing the potential depth. The depth and stretching range of the confinement potential have important effects on the binding energy of the tuned QD.The binding energy of a tuned quantum dot (QD) under an external magnetic field have been theoretically investigated. For this goal, the Schrödinger equation is analytically solved without and with considering the impurity term and the energy eigenvalues and eigenfunctions are analytically derived. Then, the binding of the tuned QD was studied considering the various parameters. We found that (i) the binding energy decrease with rising the potential range. (ii) The binding energy reduces with enhancing the potential depth. The depth and stretching range of the confinement potential have important effects on the binding energy of the tuned QD. Manuscript profile