Physical meaning of minus in Faraday's law of induction

  • Thread starter yoran
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  • #1
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Main Question or Discussion Point

Hi,

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.
 

Answers and Replies

  • #2
Doc Al
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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?
 
  • #3
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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.
 
  • #4
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I just think of the minus sign as a reminder to apply Lenz's Law when dealing with an induced emf.
 
  • #5
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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.
 
  • #6
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Yeah, that seems right.
 

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