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I'm having some troubles with Faraday's law of induction:

[tex]\mathcal{E} = - {{d\Phi_B} \over dt}[/tex]

I don't understand the meaning of the minus. I do understand that, according to the law of Lenz, the induced current is directed such that it counters the change in magnetic flux. But I don't see how the induced emf can have a direction (positive or negative) because if the magnetic flux is increasing, the induced emf is negative and when the magnetic flux is decreasing, the induced emf is positive. But in a circuit where there is an induced emf, what is the physical meaning of a negative or positive emf?

Thank you.