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We use right hand thumb rule to relate $dS$ and $dl$ like if $dS$ points in the direction of thumb then direction of $dl$ is taken in the direction of fingers but if we use left hand thumb rule to relate $dS$ and $dl$ then there is no need of negative sign in the equation? $$\oint\vec{E'}\cdot\vec{dl'}=-\frac{d\phi_B}{dt} $$

Akshat Sharma
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Manik Singh
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No, this isn't directly due to the right-hand rule as far as I know.

It is because of Lenz's law. Lenz's law states that a change in electric field will oppose whatever is driving the change.

For example, if a magnetic flux is changing in one way, Lenz's law asserts that the electric field created by this changing flux will be in such a direction to induce another magnetic field which will try to cancel the change in initial field.

Fundamentally, this is derived from the conservation of energy - the alternative is an exponentially growing magnetic field which keeps increasing its own magnitude, thus creating energy from nothing!

Going back to your equation, the minus sign is simply the statement of this opposition of changing magnetic field and induced electric field.

user19642323
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  • How do you know that negative sign signifies that opposition – Manik Singh May 29 '21 at 11:34
  • I am saying mathematically what negative sign signifies is a coincidence because of using right hand thumb rule. – Manik Singh May 29 '21 at 11:37
  • Like if I tell you, you said that it hand nothing to do with right hand thumb rule then that means we can also use left hand thumb rule , integral E•dl is always true and it always gives correct value of emf with correct sign – Manik Singh May 29 '21 at 11:39
  • I understand what you're saying. My intuition is that there should also be a minus sign even if you use the left-hand coordinate system, but I can't quite think exactly why. Let me chew it over and I'll get back to you. – user19642323 May 29 '21 at 11:42
  • I am pretty much not able to understand what it actually means everyone has a different answer regarding that. – Manik Singh May 29 '21 at 11:44
  • But I believe that it's just a part of mathematics and it's not physics and we alter the things so that they are more sensible to us and more intuitive but that doesn't actually means that they are correct – Manik Singh May 29 '21 at 11:45
  • Yes intuitively we tend to say that if there is something opposing then relate negative sign with that and that's not wrong because it satisfies our intuition but we also have to change things mathematically so that both , our intuition and mathematics are satisfied – Manik Singh May 29 '21 at 11:49
  • Consider the classic example of Faraday's law - a wire moving in a uniform B field. In a left-hand coordinate system, you would find the EMF induced in the opposite direction to a right-hand one. However, this would then produce a force on the wire in the same direction in both coordinate systems since you again use the RH/LH rule to work out in which direction the force due to the current from the EMF (i.e. $\vec{F} = \vec{B}\times\vec{l} I$) pushes the wire, I think. – user19642323 May 29 '21 at 11:54
  • I am not saying that to say about a fact we can change conventions – Manik Singh May 29 '21 at 12:01
  • Sorry, I don't quite know what you mean. Could you elaborate? – user19642323 May 29 '21 at 12:02
  • Let us continue this discussion in chat. – user19642323 May 29 '21 at 12:02
  • You can't use left hand thumb rule for finding direction of magnetic field due current carring wire because it's direction is a fact – Manik Singh May 29 '21 at 12:02
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Whatever rule we use to relate the sense of the flux produced by a current circulating in the loop in a given sense, we must use the same rule when relating the emf (which has a circulation sense) to the flux change that produces it. Then to comply with Lenz's law we need the minus sign!

This works with either a left hand rule or a right hand rule.

Philip Wood
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  • I understand that what you are trying to say is the rule which we use in finding the direction of magnetic field produced in a current carring wire that rule we have to use in relating dS and dl? Is that correct – Manik Singh May 29 '21 at 12:25
  • If What I am saying is actually what you are trying to explain then why we have to do that – Manik Singh May 29 '21 at 12:27
  • But why, to define a fact we use a particular rule which agrees with the actual fact, but relation between direction of dS and dl is our creation it's not natural fact then why we can't relate it by our willing so that mathematics is satisfied and facts are also satisfied – Manik Singh May 29 '21 at 12:43
  • Your first comment... No; for one thing, my answer involved induced emf. Yours doesn't seem to. Your last comment... I find it hard to follow, but my basic point is that whatever rule we use to associate a circulation direction around a loop with direction of flux through it, we must apply it consistently. – Philip Wood May 29 '21 at 13:33
  • I am not associating direction of dl with direction of flux but I am associating direction of dl with direction of dS and dS is not fixed – Manik Singh May 29 '21 at 14:01
  • And what do you mean by "circulation direction"? – Manik Singh May 29 '21 at 14:02
  • Clockwise or anticlockwise (when viewing loop from an agree viewpoint). – Philip Wood May 29 '21 at 14:07
  • Please explain by using notations instead of terms – Manik Singh May 29 '21 at 14:14
  • You are saying to use LHR or RHR but to determine the direction of flux produced by current circulating in a particular direction in rotational sense we have to use RHR because for particular direction of circulation of current there is fixed direction of flux produced so it's fact it's not choice("Whatever rule we use to relate the sense of the flux produced by a current circulating in the loop in a given sense"). – Manik Singh May 29 '21 at 14:19
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In principle we could use opposite orientations for the line and surface integral and the negative sign would vanish but (by convention) we use the direction as given by the right hand rule.

Suppose you know the electric field at all points in space. In absence of a convention there would always be a sign ambiguity and you wouldn't know whether Faraday's law says the flux is increasing or decreasing as the surface integral could be calculated using either of the two orientations.

Akshat Sharma
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The right hand rule is related to the convention that the positive sense of rotation is the anti-clockwise from the point of view of who is looking to the plane.

Maybe it is related to the convention that the North is "up", and if we imagine looking at the earth from "above", it is rotating anti-clockwise. Old arabic maps depicted the Europe below Africa, so it is just a convention.

But anyway, once a convention is agreed, it must be followed. In the case of Maxwell equations, if we get rid of the minus sign in the Faraday Law by changing convention, it is moved to the Ampere's Law.

Claudio Saspinski
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Yes, using right hand thumb rule is the reason why there is negative sign in equation of faraday's law. If we use left hand rule then instead of using negative sign we have to replace it by positive for consistency of equation. So, that means conventions are changing sign and so particularly there is no physical significance of negative sign in equation of faraday's law. People usually relate negative sign with some opposition intuitively which in this case is induced emf opposing change in magnetic flux. So, to satisfy their intuition they somehow find negative sign to be the contributor for the reason of opposition. In that case if we use left hand rule then we can also say that positive sign is contributor for opposition of change in flux because equation is still following Lenz law if we have to find out what thing in the equation is doing that opposition thing. I feel many things in the equation are more or less responsible for that opposition behaviour.

Manik Singh
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