An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.