Solution
Force Balance:
For the fluid pressure at the bottom to vanish, the upward magnetic force must balance the total weight of the fluid. Let current flow along the length $l$.
$$ F_m = Mg $$ $$ I l B = (\rho_m l b h) g $$ $$ I = \frac{\rho_m b h g}{B} $$Potential Difference:
The potential difference required is $V = IR$. The resistance of the fluid block for current flowing along length $l$ (cross-section $bh$) is:
$$ R = \rho_e \frac{l}{A} = \rho_e \frac{l}{bh} $$Substituting $I$:
$$ V = \left( \frac{\rho_m b h g}{B} \right) \left( \rho_e \frac{l}{bh} \right) $$
$$ V = \frac{\rho_m \rho_e g l}{B} $$