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Building on general formulas obtained from the approximate renormalizedeffective action, the approximate stress-energy tensor of the quantized massivescalar field with arbitrary curvature coupling in the spacetime of chargedblack hole being a solution of coupled equations of nonlinear electrodynamicsand general relativity is constructed and analysed. It is shown that in a fewlimiting cases, the analytical expressions relating obtained tensor to thegeneral renormalized stress-energy tensor evaluated in the geometry of theReissner-Nordstr\"{o}m black hole could be derived. A detailed numericalanalysis with special emphasis put on the minimal coupling is presented and theresults are compared with those obtained earlier for the conformally coupledfield. Some novel features of the renormalized stress-energy tensor arediscussed

Vacuum polarization in the spacetime of a charged nonlinear black hole