What is significance of negative sign in Maxwell's third equation?

Question

Is that explanation actually correct? Can we take sign conventions according to our preference which satisfies equation and also predict direction?

Answer 1

The article is right about the Lenz law not being a good explanation of the minus sign in the Faraday Law. In order to a good understanding, we must know first the convention of which is the B-vector direction.

Take a magnet and check which side is the North pole and which is the South pole. It can be made, putting the magnet in a floating device on water and verifying the alignment with the earth North-South. The side pointing to North is the North pole of the magnet.

By convention, the B-field has the direction North to South pole of the magnet.

Now, take a long wire, make some loops around a circular area, and connect each end to the terminals of a voltimeter. Put the magnet inside the area, with the North pole upward. Wait for the voltimeter stabilizes.

Now flip suddenly the magnet, while looking to the display of the voltimeter. What you are doing is increasing the B-field in the up-direction, because it was downward (North to South) and becomes upward.

Using the right hand rule, with thumb up (direction of increase of B-field), your fingers will indicate a direction in the wire

You will see that the sign of the voltage in the display shows that it tends to force a current flow in the opposite direction of your fingers.

Translating in mathematical language: the curl of the E-field is proportional to the change of the B-field, but in the opposite direction. That is the meaning of the minus sign.