# Physical meaning of minus in Faraday's law of induction

## Main Question or Discussion Point

Hi,

I'm having some troubles with Faraday's law of induction:
$$\mathcal{E} = - {{d\Phi_B} \over dt}$$

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.

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right hand rule

To interpret the minus sign, use the right hand rule. Here's an example. Imagine a circular loop in the x-y plan and centered at the origin. Let's say we define the flux to be positive when the B field is pointing in the +z direction. If Faraday's law tells you that the sign of the EMF is positive, the right hand rule* will tell you that the EMF is counterclockwise (as viewed from the +z axis looked down towards the origin); if negative, then clockwise.

*If the thumb of your right hand points parallel or anti-parallel to +z axis (depending upon the sign of the EMF given by Faraday's law), the curl of your fingers will give you the orientation of the EMF.

Make sense?

Faraday's law of induction itself is confusing to me. Consider that the force x distance energy of pushing a coil against magnetism; converts to magnetic energy in the coil.

Force x distance relationships are independent of rate of movement through the force. Consider that in a demonstration related to the Meissner effect, a magnet placed above a superconductor is levitated. I suspect the levitation height is independent of magnet velocity before levitation.

I just think of the minus sign as a reminder to apply Lenz's Law when dealing with an induced emf.

Thanks guys I understand it now. So basically you have to define a reference direction in order to give a meaning to the minus sign.

Yeah, that seems right.