Is that explanation actually correct? Can we take sign conventions according to our preference which satisfies equation and also predict direction?
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1$\begingroup$ Does this answer your question? Why negative sign is used in Maxwell's third equation? $\endgroup$– BrickMay 29, 2021 at 0:26
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4$\begingroup$ You asked this question earlier and had it closed. Best case, you should have edited that one with the new information. But you still really haven't asked a question that's appropriate to this format and you've probably violated the copyright of the article that you've now posted here. $\endgroup$– BrickMay 29, 2021 at 0:28
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6$\begingroup$ Please do not repost closed questions, but edit them instead. Also, please do not post images of texts you want to quote, but type it out instead so it is readable for all users and so that it can be indexed by search engines. For formulae, use MathJax instead. $\endgroup$– ACuriousMind ♦May 29, 2021 at 13:25
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1 Answer
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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.
answered May 29, 2021 at 0:40
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$\begingroup$ If we change convention for relation dS and dl then there is no need to use negative sign like we relate dS and dl by right hand thumb rule if we take dS as thumb then our fingers represent direction of dl but if we use left hand thumb rule for relating dS and dl then all things are changed and there is no need of negative sign in equation $\endgroup$ May 29, 2021 at 10:57
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$\begingroup$ @ManikSingh If we change the right hand rule convention, we need to change it everywhere in all physics formulas containing cross products and then the sign in the other Maxwell equation would change ;-) It does not help with anything. $\endgroup$ Jun 24, 2021 at 12:01