Answer to Question #133115 in Physics for sabi

Question

Explain with proper figures (in detail): In the Faraday’s electromagnetic equation (also known as Maxwell’s 3rd equation), why the sign of the time derivative is negative but the curl part (of electric field) is positive.
Also explain in detail (with proper figures): if the sign ‘were’ positive, what would happen!

Answer 1

Faraday’s electromagnetic equation:

$$E=-N\frac{\text{d}\Phi}{\text{d}t}.$$

We see that the induced electromotive force (EMF) is directly proportional to the decrease of flux change over time and the number of turns.

The negative sign tells us that the induced EMF is always opposite the flux varying with time (following Lenz's law). If the sign ‘were’ positive, the increase of flux would increase the magnitude of EMF turning this into a positive feedback loop., which would cause everlasting increase of EMF, which contradicts the second law of thermodynamics.