eli5: Why in Faraday’s Law do we put a negative sign on the variation of magnetic flux, while in Ampere’s Law the variation of electric flux is taken as positive?


In the Maxwell-Ampere’s law.

In: 2

They have to be opposites. Otherwise you would get a runaway effect.

Amperes law states a wire with current creates a magnetic field, Faraday’s law states that a changing magnetic field will create a voltage (aka induce current) in the opposite direction with the same magnet. If they were both the same sign, what would happen is the wire would create a magnetic field which would increase the current in the wire which would create a stronger magnetic field which would increase the current in the wire further and so on, this would be an exponential runaway effect.

Instead we have that faraday’s law resists changes in current, because increasing current increases magnetic field which resists current, and current finds a nice little equilibrium to rise because of induction.

Which equation has the minus sign is kinda arbitrary, we decided a magnetic field is considered “positive” facing one direction and our equations ended up with the negative on faraday’s equation. What really matters is that they are opposites.