Why is there no negative sign in the Faraday's Law stated here

[eognvoi]

Summary:: Figure b also shows that there is no negative sign in Faraday's Law. How do I know when to include the negative sign?

 

[berkeman]

Welcome to PF.

What book or link is that from? Wikipedia and Hyperphysics agree that there should be a minus sign (Lentz' Law):

https://en.wikipedia.org/wiki/Faraday's_law_of_induction

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

 

[kuruman]

I was under the impression that the term "voltage" is used exclusively to denote the absolute value of the electric potential difference which can be positive of negative. For example, when we say that "the voltage across a capacitor is charge divided by capacitance", all three quantities are positive. In my mind, voltage is to potential difference as distance is to displacement.

I agree that the negative sign in Faraday's law is put there for Lenz's law. It indicates that the induced potential difference is such that it gives rise to an induced current that opposes the proposed change in magnetic flux. I view it as analogous to the negative sign in Hooke's law that indicates that the direction of the force exerted by the spring opposes the proposed deformation of the spring. The direction of an arrow in a free body diagram says it all and a minus sign is not needed. In fact, it would be wrong to label an arrow representing the force due to a spring by "-kx". Similarly, the direction of the induced current in a circuit says it all and a minus sign is not needed.

I remember having this conversation about voltage here at PF a number of years ago, but I could not find the link.

 

[dlgoff]

I remember having this conversation about voltage here at PF a number of years ago, but I could not find the link.

Is this the "conversation" you were thinking of?
Faraday law of electromagnetic induction

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[vanhees71]

I was under the impression that the term "voltage" is used exclusively to denote the absolute value of the electric potential difference which can be positive of negative. For example, when we say that "the voltage across a capacitor is charge divided by capacitance", all three quantities are positive. In my mind, voltage is to potential difference as distance is to displacement.

I agree that the negative sign in Faraday's law is put there for Lenz's law. It indicates that the induced potential difference is such that it gives rise to an induced current that opposes the proposed change in magnetic flux. I view it as analogous to the negative sign in Hooke's law that indicates that the direction of the force exerted by the spring opposes the proposed deformation of the spring. The direction of an arrow in a free body diagram says it all and a minus sign is not needed. In fact, it would be wrong to label an arrow representing the force due to a spring by "-kx". Similarly, the direction of the induced current in a circuit says it all and a minus sign is not needed.

I remember having this conversation about voltage here at PF a number of years ago, but I could not find the link.

Just don't use the word "voltage" in connection with Faraday's law, because it's a contradiction in itself. There is no potential when time-varying magnetic fields are present due to Faraday's law:
$$\vec{\nabla} \times \vec{E}=-\partial_t \vec{B},$$
and the minus-sign is of course crucial for the entire consistency of electromagnetic theory.