Question

Why is there a negative sign in emf= `-(Delta Phi)/ (Delta t)`?

Faraday's law?

Answer 1

If I remember correctly is a consequence of Lenz's Law.

Explanation:

It is quite curious but the emf or current generated by a varying magnetic field (that will produce a change in the flux `Phi`) will oppose the cause of this variation.

So if the flux increases the emf tends to reduce this action while if it decreases it will tend to support/sustain this variation. So the result of change in flux will be an "antagonist" emf.

As a very simplicistic example imagine you are a runner; when you ara good and full of energy you have to drag another person that tries to slow you down while when you are tired and slowing down this person pushes you helping to keep on running....

Hope it helps.