That’s correct if you are not imposing an external magnetic field. The electric potential method solves the electric potential equation (see Sec. 22.3. Electric Potential Method of the Theory Guide), which is then used to calculate current j. The electric potential approach does not solve for the magnetic field. The Lorentz force is given by: F = j x B, which will be zero unless an external magnetic field is prescribed, hence no effect of the electric potential on the fluid. The electric potential will have an effect on charged DPM particles, however.
You should consider the magnetic induction method which will calculate induced magnetic field and give a non-zero Lorentz force.
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