Assume we have a current carrying conductor of finite-length $l$, carrying a current of $I$ (w/ a negligible cross-sectional area) under the influence of a Magnetic field, whose constant Flux density is $B$ (units ignored) All under a *vacuum*. Now, we know the famous equation,
$$
F = ILB
$$
Where a conductor suffers a Force in the orthogonal direction to the Magnetic field.

Suppose now, we increase the length of this conductor, $l' = kl \, \text{where}\, k\in R^+$.     

Thus, by our equation above, we will get $k$ times more Force than before.

Now, I'm well aware that $\text{Force}\neq\text{Energy}$, But $W=Fs$ where $s\rightarrow \text{displacement}$ and as I said, the entire system is in a *vacuum*. Therefore, after extending my conductor by $k$, We get:

$$
W' = (kF).s = kW
$$

So just by extending the conductor, I've obtained new, $k$ times more energy in the system. This conductor had negligible resistance (But $\neq 0$) so the loss of the current $I$ throughout the conductor would be negligible. $B$ is fixed. Nothing has changed except $l' = kl$, which *shouldn't* introduce new energy in the system at all (After all, we're just introducing free electrons to carry the current - like adding more pans in a conveyor belt waiting to be filled with sauce).

This would violate the conservation of energy, so I'm obviously wrong. But where?