While deriving the formula for motional emf, we consider an equilibrium point where the force on the electron due to the magnetic field (Lorentz force) is equal to the force of electric field.

Hence f_m=f_e

ie. evB•sin 90 = eE (e is electronic charge)

this would give vB= E

Isn't electric field equal to - Delta V/length? Wouldn't that result in emf to be negative, which is obviously not the case? What am I missing here?

While deriving the formula for motional emf, we consider an equilibrium point where the force on the electron due to the magnetic field (Lorentz force) is equal to the force of electric field.

Hence $f_m$=$f_e$

ie. evB•sin 90 = eE (e is electronic charge)

this would give vB= E

Isn't electric field equal to - $\Delta$ $\frac Vl$?Wouldn't that result in $\epsilon$ to be negative (ie. - Bvl), which is obviously not the case? What am I missing here?