Effect of magnetism on dissolved Na+ and Cl- ions in water
There are a couple of issues: first, a uniform magnetic field doesn't exert a force on stationary charges and secondly, when the charges are moving the force is at right angles to the magnetic field. There are a few ways to get the charges moving. You could have an electric current flow from the bottom of your figure to the top. The $\text{Na}^+$ ions would move with the current, up the page and since the magnetic field points to the left in your figure, the $\text{Na}^+$ ions would be pushed towards the reader by the right hand rule resulting in higher electric potential near the reader. This is called a positive Hall effect. The $\text{Cl}^-$ ions would move against the current, down the page and paradoxically would be pushed towards the reader again by the right hand rule, this time resulting in a lower electric potential near the reader: a negative Hall effect.
Another way is to have the electric current directed out of the page. Positive $\text{Na}^+$ ions move towards the reader and then are pushed down the page by the magnetic field according to the right hand rule. Negative $\text{Cl}^-$ ions move away from the reader and are also pushed down the page by the magnetic field via the right hand rule. This is the principle of magnetohydrodynamic propulsion.
Another way is to have the brine flowing up the page which forces $\text{Na}^+$ charges towards the reader and $\text{Cl}^-$ charges away from the reader by the right hand rule, both resulting in higher electrostatic potential on the near side of the stream. This would be magnetohydrodynamic propulsion in reverse operating as a generator.