Appropriate Language when Discussing Faraday's Law

[tzonehunter]

Quick question, when discussing induce emf, would you state:

"An emf is induced in the coil..."
or

"An emf is induced across the coil..."

The reason I ask is that grammatically, it sounds proper to state "An electromotive force is induced in..." (something). However, an emf is a potential difference, which would occur across two points.

 

[gleem]

"An emf is induced in the coil..."

Definitely. Some people use the term electromotance since emf is not a force and is measured in volts. The result of the Faraday Law is to create a current. This does imply the existence of an electric force which implies the existence of a potential difference. However in a closed good conducting loop having no definite beginning or end you cannot put a voltmeter across any part of it and get the same reading unless the length of the arc subtended is the same. One can think of the situation as being a distributed potential difference i.e., potential difference per unit length that exists around the entire loop.

 

[Mister T]

"An emf is induced in the coil..."

That's the way I see it used.

However, an emf is a potential difference, which would occur across two points.

No, that is true only in the electrostatic case. If you review an introductory calculus-based physics textbook, you will see the explanation for why the induced EMF is not a potential difference. In short, to have a potential difference you need two potentials so you can subtract them, and since you do not have a conservative force you cannot define an electrostatic potential.

 

[metastable]

"An emf is induced in the coil..."
or

"An emf is induced across the coil..."

I thought perhaps this would be a useful illustration here... a photo I took of the innards of an electric skateboard hub motor (84mm tire diameter) with exposed stator core consisting of 12 wound coils/solenoids...

 

[rude man]

That's the way I see it used.

No, that is true only in the electrostatic case. If you review an introductory calculus-based physics textbook, you will see the explanation for why the induced EMF is not a potential difference. In short, to have a potential difference you need two potentials so you can subtract them, and since you do not have a conservative force you cannot define an electrostatic potential.

Good one @Mister T.

It should further be pointed out that a voltmeter does not always indicate the voltage across its two probe tips. In the aforementioned case of a coil of resistance r surrounding a time-changing B field, if the probes are placed across some arc section θ of the coil, and if there is no B-dot field within the meter circuit (coil section θ, the meter and its probe wiring), the voltmeter will read rθI/2π, I = current. This is often mistaken as the voltage across the coil section θ but in reality that voltage is zero. The reason is that the meter wiring itself forms an alternate arc for coil section θ of the closed path. Furthermore, the voltmeter itself always reads actual voltage across itself assuming it forms a negligible length of the meter circuit. Cf. my Insight article on Dr Lewin's conundrum.