Finding EMF - why we ignore the negative sign in Faraday's law

[ncstebb]

Hi all,

I've been using Faraday's law to find the EMF in a coil of wire in a changing magnetic field.

EMF = -N (change in mag flux/change in time) for N loops​

I'm finding that the EMF is always positive regardless of whether the change in flux is positive or negative. I'm wondering at what point we choose to ignore the negative sign and why?

What I've been considering...

• I was thinking it could be a vector/scalar issue. But scalars can be negative.
• I think that the sign of the change in flux is important (Lenz's law etc).
• I understand that conservation of energy requires the induced EMF to oppose the change in flux. So the negative sign is important in the law.
• So is the sign of the EMF not important for some reason?

Thanks for your help.

 

[marcusl]

The sign in the equation is correct, as required to satisfy Lenz's Law (you are completely right about that). If you always see the same sign, then you aren't doing your experiment correctly or aren't interpreting your results correctly.

 

[jtbell]

The minus sign has to do with the direction of the emf: whether it is in one direction or the other, going around the coil, which in turn determines the direction of the induced current. Usually, in an introductory course, we figure out the direction of the emf or current non-mathematically, using a right-hand rule, in which case the minus sign in Faraday's Law is irrelevant as far as calculating the magnitude of the emf or current is concerned. When I teach Faraday's Law at that level, I always write it in terms of magnitudes, using absolute-values, and omit the minus sign.

In intermediate or advanced classes, we write out the emf and the flux as integrals:

$$\int {\vec E \cdot d \vec l} = - \frac{d}{dt} \int {\vec B \cdot d \vec a}$$

where the first integral is a line integral around the loop (coil), and the second integral is a surface integral over a surface bounded by the loop. Without the minus sign, the direction of integration around the loop is related to the orientation of the surface (direction of $d \vec a$) by the right-hand rule. To make things come out right physically, we need to include the minus sign.

 

[ncstebb]

Thanks for the reply marcusl. This is not from an experiment, it is from questions in a textbook and the textbook always gives the EMF as positive regardless of the sign of the change in magnetic flux.

If I understand jtbell correctly this is because they are only interested in the magnitude of the EMF (even though they don't state it).

I think I'll need to understand more about how the direction of the change in flux relates to the direction of the EMF before I'll really be comfortable with this.

Thanks again for the help.

 

[marcusl]

You can determine the polarity of EMF from Lenz's law in the following way. Let the magnetic flux within a loop of wire be increasing, say. Imagine inserting a voltmeter into the loop at a point so you can measure the polarity of the emf. The emf induces a current in the loop (due to ohm's law) which must oppose or reduce the flux change in the loop. Why? If it reinforced the flux change, then the emf would increase due to Faraday's law which would increase the current, which creates energy from nothing, which is a violation of the 2nd law of thermodynamics. So the emf must have a polarity that generates a current and flux that act to reduce the flux change.

The diagrams here might be helpful:

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