Why does a larger DNA gel box require a higher voltage to move DNA at the same speed?
It's actually a physics question. The speed of the particle in the gel is proportional to the force that acts on it. The force that acts on the charged particle is proportional to the strength of the electric field $E$. The strength of the electric field is proportional to the voltage $U$ and inverse proportional to the length of the gel $d$.

$$E = \frac{U}{d}$$

So if you want to have the same strength of the electric field you have to double the voltage if you double the length of the gel.