We investigate effects of the modified $f(R, mathcal{T})$ gravity on the charged strange quark stars with the standard choice of $f(R, mathcal{T})=R+2chi mathcal{T}$. Those types of stars are supposed to be made of strange quark matter (SQM) whose distribution is governed by the phenomenological MIT bag EOS as $p=frac{1}{3}(rho-4B)$, where $B$ is the bag constant, while the form of charge distribution is chosen to be $qleft(rright)=Qleft(r/Rright)^3=alpha r^3$ with $alpha$ as a constant. We derive the values of the unknown parameters by matching the interior spacetime to the exterior Reissner-Nordstr{o}m metric followed by the appropriate choice of the values of the parameters $chi$ and $alpha$. Our study reveals that besides SQM, a new kind of matter distribution originates due to the interaction between the matter and the extra geometric term, while the modification of the Tolman-Oppenheimer-Volkoff (TOV) equation invokes the presence of a new force $F_c$. The accumulation of the electric charge distribution reaches its maximum at the surface, and the predicted values of the corresponding electric charge and electric field are of the order of $10^{19-20}$ C and $10^{21-22}$ V/cm, respectively. To examine the physical validity of our solutions, we perform several tests and find that the proposed $f(R, mathcal{T})$ model survives all these critical tests. Therefore, our model can describe the non-singular charged strange stars and justify the supermassive compact stellar objects having their masses beyond the maximum mass limit for the compact stars in the standard scenario. Our model also supports the existence of several exotic astrophysical objects like super-Chandrasekhar white dwarfs, massive pulsars, and even magnetars, which remain unexplained in the framework of General Relativity (GR).
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