An object with height h, mass m, and a uniform cross-sectional area a floats upright in a liquid with density ρ.

Support the vertical distance = y

Object's density = M/(A*h) (since A*h = volume)

By applying the condition, 

(M/(Ah))/ρ = y/h

M/(ρAh) = y/h

y = M/(ρA)  

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explanation:

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it