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We calculate the $\delta f$ correction to the one particle distributionfunction in presence of magnetic field and non-zero shear viscosity within therelaxation time approximation. The $\delta f$ correction is found to beelectric charge dependent. Subsequently, we also calculate one longitudinal andfour transverse shear viscous coefficients as a function of dimensionless Hallparameter $\chi_{H}$ in presence of the magnetic field. We find that a properlinear combination of the shear viscous coefficients calculated in this workscales with the result obtained from Grad's moment method in\cite{Denicol:2018rbw}. Calculation of invariant yield of $\pi^{-}$ in a simpleBjorken expansion with cylindrical symmetry shows no noticeable change inspectra due to the $\delta f$ correction for realistic values of the magneticfield and relaxation time. However, when transverse expansion is taken intoaccount using a blast wave type flow field we found noticeable change inspectra and elliptic flow coefficients due to the $\delta f$ correction. The$\delta f$ is also found to be very sensitive on the magnitude of magneticfield. Hence we think it is important to take into account the $\delta f$correction in more realistic numerical magnetohydrodynamics simulations.

One particle distribution function and shear viscosity in magnetic field: a relaxation time approach