I've seen derivations for c=E/B and c=1/√μ0ε0, but I don't seem to get the directions right. i.e. I end up with a negative sign in one of the equations. The derivations I've seen do not use vector calculus. One derivation I've seen is in this video. But in this video I don't know how the direction of integration is determined, as that would solve my problem; it seems to contradict Lenz's law. Any help would be grateful!