Question

Isn't the inductor equation negative?

Answer 1

Consider this concrete scenario. Let's say that there's a voltage source connected to an inductor (maybe throw in a resistor in series to make it more applicable to a real-world scenario). The voltage source is increasing in time such that it drives an increasing current from point a to point b across the inductor, as you say. We can even do a step in voltage, from 0 to some voltage
.
The inductor will act to counter this flux and hence current, so initially, the voltage at point a must increase rapidly so that the voltage source cannot readily drive more current through it. So this "back EMF" acts to increase the voltage at point a relative to point b . That is consistent with NOT having a negative sign. Your equation implies that the voltage at a is lower than the voltage at point b .

Answer 2

Electronics Tutorial about the Inductor, what are inductors, its Inductance value ... with a positive value indicating an increase in emf and a negative value indicating a decrease in emf.