Understanding the Negative Sign in Lenz's Law: A Geometric Interpretation

[stfz]

Homework Statement

I'm trying to see the relationship between the negative sign (Lenz's Law) in Faraday's law. It states that EMF is equal to negative flux change. I understand how to use Lenz's Law to find direction of current and hence EMF, but I am not seeing the relation between the neg sign and the EMF directly, that is, I understand it qualitatively, but not quantitatively in the context of the formula.

Flux and voltage are both scalar quantities, and they measure different things. So how can I geometrically interpret the negative in the formula? What would that mean?

Homework Equations

$$V= -\frac{d\Phi}{dt}$$

The Attempt at a Solution

If I draw up a diagram, and flux change is positive, then I know that EMF is negative in the loop. But how do I know which direction it is in? EMF could be measured both ways!

So I'm wondering whether or not the negative sign in Lenz's law simply serves a "qualitative" function, i.e. to let the reader know that it produces a current that opposes the flux change, rather than any computational significance? :P

 

[ash64449]

The statement of Lenz' law is like this:

Whenever the magnetic flux associated with a closed coil changes, an EMF is induced in the loop, And the direction of the induced EMF is in such a manner that it tends to produce a current that opposes the change in magnetic flux produced it.

-ve sigh in mathematical equation corresponds to this statement.

I think the statement of Lenz's law solves your problem. By that statement you can find what direction current is and hence direction of EMF.