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I recently read a research paper on the effects of a magnetic field on redox potential of water (Magnetic Field Effects on Redox Potential of Reduction and Oxidation Agents), but the paper didn't include any of the equations related to the internal energy of the system.

Another paper (Magnetohydrodynamic Propulsion for the Classroom) stated magnetohydrodynamic (MHD) force (on water) as F = qv x B, where qv = (qnAL)v. The n is the number of charges per volume and A and L are the cross-sectional area and length of the channel or container. The quantity qnAv will define the current I. The paper stated "This leads to the statement for the force imparted on a current in the presence of a magnetic field", which redefines the equation for force as F = LI x B, with B as the magnetic field.

The work for the electrolysis of water is calculated as W = PΔV. Considering the listed equations, is there an equation to calculate the work done to the system within a magnetic field? Any help is greatly appreciated.

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# Magnetic Field and Water Electrolysis Work

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