- #1

As an example, the voltage across an inductor might be reported as ##L\frac{di}{dt}## or ##-L\frac{di}{dt}## depending on our choice of sign convention, however the emf is only ever written as ##\mathcal{E} = -L\frac{di}{dt}##. This is because there is a minus sign in Faraday's law. I understand the operational definition of this negative sign (Lenz's law), however don't understand why it needs to be there from a mathematical perspective. Negative with respect to what? In essence, I'm confused as to why there is only ever one correct sign for the emf. Thank you!