Question

If the minus sign were not in Faraday's law it would lead to a violation of the law of conservation of energy. True or False?

Answer 1

Answer: True  

Faraday's Law (also known as Faraday's Law of Electromagnetic Induction) was formulated from the experiments made by him and states that:  

The voltage induced in a closed circuit is directly proportional to the speed with which the magnetic flux that crosses any surface with the circuit as edge changes in time

$\oint\limits_C {\vec{E}}\,d\vec{l}=-\frac{d}{dt} \int\limits_S {\vec{B}} \, d\vec{A}$

where:  

$\vec{E}$ is the Electric Field  

$d\vec{l}$ is the infinitesimal element of the C contour  

$\vec{B}$ is the magnetic field density  

$S$ is an arbitrary surface, whose edge is C  

The negative sign indicates the direction of the induced current and refers to the opposition between the fields induced by the magnetic flux and the electromotive force. In addition, its consequences are also expressed in the Lenz law, which states that the induced electricity will be in a direction such that it opposes the variation of the magnetic flux that produced it as a consequence of the principle of conservation of energy.  

Therefore:

If he minus sign were not in Faraday's law it would lead to a violation of the law of conservation of energy