The emphasis placed on there being no induced e.m.f. in the Lewin Clock voltmeter leads is important. However, in my opinion it leaves us somewhat uncertain as to the underlying purpose of the inclusion of this feature in the apparatus ‘design’. Why is it important that there be no induction in the voltmeter leads? It should be noted from the outset, that the absence of any induction in the voltmeter leads does not imply the absence of induction in the Lewin Clock measurement path as a whole. After all, irrespective of what I define as the closed measurement path, that path encloses a fraction of the total time-varying magnetic flux. Faraday induction is integral and essential to what the Lewin Clock indicates. The relevance of induction in the voltmeter leads is of interest when interpreting the indication observed, where the voltmeter and its test leads are positioned external to the loop boundary. It is often proposed that a non-zero induction in the voltmeter test lead wires produces a misleading indication, which is not the ‘true’ voltage between the probed points. What do we mean by the ‘true’ voltage? The externally connected voltmeter indicates something. In this configuration, it correctly indicates the Ohmic voltage difference between the two points being probed. It is often suggested that the true voltage is the scalar potential difference (PD) between the two probed points. This is the position taken by Dr Kirk McDonald in his discussion paper on the so-called “Lewin Paradox” (see link below). I note that Dr McDonald’s view concerning the definition of voltage in this particular example, is at odds with the International Electrotechnical Commission’s definition (see IEC 60050 section 121 Electromagnetism - electropedia.org). Nevertheless, a scalar PD can be attributed only to the line integral of whatever purely conservative electric field strength is encountered in a traversal of the loop conductor path segment between the probed points. In that aforementioned measurement configuration, we cannot differentiate between the individual contribution of either the non-conservative or conservative electric field strengths responsible for current flow, in the loop segment being probed. Only the net effect (or superposition) of those different field components along the loop segment is observed with that voltmeter location. The net effect is the correct indication of the Ohmic voltage difference. Many people fail to understand the point, that with Faraday induction, the underlying induced loop e.m.f. appears exclusively as the accumulated Ohmic (IR) voltage differences established around the closed loop. In contrast to what an externally connected voltmeter indicates, Prof Cullwick was looking to measure something different with his setup. Prof Cullwick’s aim with his apparatus design, was to obtain a measurement of the purely conservative scalar PD between any two arbitrary points on the homogeneous resistive loop. The actual (Ohmic) voltage difference between any two points along the loop is given by the line integral of the singular longitudinal electric field strength, encountered in a traversal of the particular path taken between those two points. There is but one resultant field at any location which can account for the uniform current flow. In the homogeneous resistive loop case, the electric field at any location along the loop will be uniform and subject to the constitutive relationship we call the generalised form of Ohm's Law. The Ohmic voltage difference between any two points on the loop is also path dependent, whereas the scalar PD is not. We may generally regard the electric field strength at any location to be the superposition of both non-conservative and conservative electric field components. It is rarely the case that the two don't conceptually co-exist. In this present situation, the non-conservative electric field component at any location arises from Faraday induction. The line integral of just the Faraday induced electric field strength encountered in a traversal of the probed loop segment, may or may not, be the same as the line integral of the singular electric field strength present along that same segment. Under certain conditions there could well be a discrepancy between the two. Any discrepancy can only be reconciled by proposing the existence of conservative electric fields that are established by surface charge density gradients. These surface charge gradients arise spontaneously as necessary, to set up electric fields which, together with the non-conservative induced electric fields, ensure uniform current flow is established at any location along the closed loop path. Prof Cullwick's apparatus ‘determines’ any difference between the two aforementioned line integrals, by nulling out the non-conservative induced field component in the measurement path. In the apparatus, the closed measurement path comprises the voltmeter mechanism, the voltmeter leads and either of the loop segment paths between the probed points. The time-varying magnetic flux enclosed by either of the two traceable measurement loops, gives rise to the required nullifying component. By virtue of the apparatus topology, no Faraday induction arises in the voltmeter leads, meaning the induction component in the loop segment is nullified. The resulting voltmeter indication is thus the line integral of the purely conservative electric field strength along either path between the probed points. The value of that line integral is path independent. Being a purely conservative term, that line integral equates to the difference in scalar potential between the probed points. Link to Dr McDonald's paper: www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=www.physicsforums.com/insights/wp-content/uploads/2018/06/k-t-mcdonald-lewin.pdf&ved=2ahUKEwilnpP4xciHAxXbU2wGHbbCAVgQFnoECBEQAQ&usg=AOvVaw2T58AsZMYnDrzacjaOFygt
This topic was so interesting to me when I first saw the classroom demonstration from Professor Walter Lewin many years ago. I was completely perplexed at the time. I some how came across your channel and for some reason I remembered you had much more content on this issue. I'm actually pleased you covered Jesse's Lewin clock which I admit was a novel name for the device he built. Your considerable expertise has not gone unappreciated from me.
Hi Trevor Well detailed video. Why did you divide the conductive ring into two segments and assign the voltmeter to the smaller segment. Time stamp starting at 2:06 .
@@trevorkearney3088 The voltmeter is in the path OPQO around the orange area , and it is also in the path OQYXPQ around the Green area. You chose OPQO and not OQYXPQ. The reasoning you applied also applies to OQYXPO. Consider Professor Gullwick wrote - "The lines of force of the electric field induced by the alternating magnetic field are thus circles, concentric with the axis, which cut the straight portions of the leads at right angles. No e.m.f., therefore, is induced in the leads." end quote. That would also apply inside the circumference of the solenoid. Is that how you view the arrangement.
It doesn't matter which closed path is used. The indicated scalar potential difference is of necessity path invariant, since it is subject exclusively to electrostatic fields arising from surface charge density gradients. If I consider the alternative path enclosing the green coloured area, I get the same result. Presumably, you realise the result in the symmetrical case shown is zero - as Prof Cullwick noted in his article submitted to the SQJ. There is no PD between any two points along the loop path. This means there cannot be any surface charge gradients arising in this situation. I cover the symmetrical case in more detail from about time 29:00 to 31:11.
@@trevorkearney3088 Can you expand on your explanation regarding induced emf that states it is present in loop OPQO and not present in the leads O to P and O to Q.
@@woodcoast5026 Thanks for the question. If you refer to Prof Cullwick's original description, he states, with respect to obtaining a measure of the scalar PD between any two points on his resistive loop, that "All that is necessary is to devise an arrangement in which no e.m.f. is induced by the alternating magnetic flux in the leads to the voltmeter." The notion of there being an e.m.f. induced along a particular fraction of any closed path is somewhat misleading, if we focus our attention solely on the enclosed time-varying magnetic flux. There is a subtle distinction between the e.m.f. and the induced electric field. On page 268 of the third edition of his text, “The Fundamentals of Electro-Magnetism”, Prof Cullwick states: “In dealing with the induction of e.m.f. by a changing magnetic field, we make use of Faraday’s law of induction in the form e=-d(phi)/dt=closed path integral of vector E dot dl. Now this equation gives us no information about the value of the electric field, E, at any point, but only the value of the line-integral of E around a closed path, so that the usefulness of the magnetic-field concept is limited after all.” Prof Cullwick then proceeds to introduce the concept of what he terms, “the vector potential of the electric current”, designated A. He then relates the vector potential A to the Maxwell-Faraday induced electric field E. In other words, he allows us the means of deducing the E field at a particular location. The existence of the vector potential was originally proposed by Maxwell. I introduce this concept at time interval 11:35 to 12:07 in the video. The key point to note is that the induced E field in either of the radial leads OP and OQ is notionally orthogonal (fully transverse) to the lead paths OP and OQ and no induced e.m.f. can be attributed to them. The line integral of E along either path OP or OQ must be notionally zero. The only possible effect of the transverse field E on the meter leads is that a charge redistribution will arise on the lead surfaces, giving rise to a transverse electrostatic field which exactly counters the induced transverse field within the conductor material.
Good to see another video citing actual physics and electromagnetic textbooks and trying to undo the damage done by certain TH-cam 'influencers'. Let's hope one day the actual physics will prevail upon that sort of entertainment.
Thanks. I noticed from another post, you're planning to upload some videos on clarifying some of the key issues relevant to the physics. I look forward to it. These things require a lot of time and effort to produce. Hopefully, it provides other open minded viewers with well reasoned and informed perspectives. Regarding the use of good reference texts on electromagnetic theory - it seems there is a curious reluctance to exercise the discipline required to read and understand these valuable resources. A sign of the times, perhaps.
@@trevorkearney3088 yeah, I have just finished the audio voiceover and now I have dozens of formulas to convert to SVG. The funny thing is that what in my mind should have been a five minute video turned into three half an hour videos. The one I'm about to publish this week has about eight minutes of me slapping books on my desk ;-). One of them is Panofski & Phillips.
I understand your dilemma. It's easy to state something which is wrong or a half-truth without offering any explanation or rigorous justification. One can also demonstrate a measurement and state it proves an argument - even though it does not. There are some classics in this category. As one text on electromagnetic theory notes, "For instance, nobody in his right mind would wrap the leads of a voltmeter around the core of a transformer in determining the voltage between two points in a circuit". I've seen this done in a couple of TH-cam videos and nobody scratches their head as to the flawed reasoning underpinning the conclusions drawn from such observations.
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The emphasis placed on there being no induced e.m.f. in the Lewin Clock voltmeter leads is important. However, in my opinion it leaves us somewhat uncertain as to the underlying purpose of the inclusion of this feature in the apparatus ‘design’. Why is it important that there be no induction in the voltmeter leads? It should be noted from the outset, that the absence of any induction in the voltmeter leads does not imply the absence of induction in the Lewin Clock measurement path as a whole. After all, irrespective of what I define as the closed measurement path, that path encloses a fraction of the total time-varying magnetic flux. Faraday induction is integral and essential to what the Lewin Clock indicates.
The relevance of induction in the voltmeter leads is of interest when interpreting the indication observed, where the voltmeter and its test leads are positioned external to the loop boundary. It is often proposed that a non-zero induction in the voltmeter test lead wires produces a misleading indication, which is not the ‘true’ voltage between the probed points. What do we mean by the ‘true’ voltage? The externally connected voltmeter indicates something. In this configuration, it correctly indicates the Ohmic voltage difference between the two points being probed. It is often suggested that the true voltage is the scalar potential difference (PD) between the two probed points. This is the position taken by Dr Kirk McDonald in his discussion paper on the so-called “Lewin Paradox” (see link below). I note that Dr McDonald’s view concerning the definition of voltage in this particular example, is at odds with the International Electrotechnical Commission’s definition (see IEC 60050 section 121 Electromagnetism - electropedia.org). Nevertheless, a scalar PD can be attributed only to the line integral of whatever purely conservative electric field strength is encountered in a traversal of the loop conductor path segment between the probed points. In that aforementioned measurement configuration, we cannot differentiate between the individual contribution of either the non-conservative or conservative electric field strengths responsible for current flow, in the loop segment being probed. Only the net effect (or superposition) of those different field components along the loop segment is observed with that voltmeter location. The net effect is the correct indication of the Ohmic voltage difference. Many people fail to understand the point, that with Faraday induction, the underlying induced loop e.m.f. appears exclusively as the accumulated Ohmic (IR) voltage differences established around the closed loop.
In contrast to what an externally connected voltmeter indicates, Prof Cullwick was looking to measure something different with his setup. Prof Cullwick’s aim with his apparatus design, was to obtain a measurement of the purely conservative scalar PD between any two arbitrary points on the homogeneous resistive loop. The actual (Ohmic) voltage difference between any two points along the loop is given by the line integral of the singular longitudinal electric field strength, encountered in a traversal of the particular path taken between those two points. There is but one resultant field at any location which can account for the uniform current flow. In the homogeneous resistive loop case, the electric field at any location along the loop will be uniform and subject to the constitutive relationship we call the generalised form of Ohm's Law. The Ohmic voltage difference between any two points on the loop is also path dependent, whereas the scalar PD is not.
We may generally regard the electric field strength at any location to be the superposition of both non-conservative and conservative electric field components. It is rarely the case that the two don't conceptually co-exist. In this present situation, the non-conservative electric field component at any location arises from Faraday induction. The line integral of just the Faraday induced electric field strength encountered in a traversal of the probed loop segment, may or may not, be the same as the line integral of the singular electric field strength present along that same segment. Under certain conditions there could well be a discrepancy between the two. Any discrepancy can only be reconciled by proposing the existence of conservative electric fields that are established by surface charge density gradients. These surface charge gradients arise spontaneously as necessary, to set up electric fields which, together with the non-conservative induced electric fields, ensure uniform current flow is established at any location along the closed loop path.
Prof Cullwick's apparatus ‘determines’ any difference between the two aforementioned line integrals, by nulling out the non-conservative induced field component in the measurement path. In the apparatus, the closed measurement path comprises the voltmeter mechanism, the voltmeter leads and either of the loop segment paths between the probed points. The time-varying magnetic flux enclosed by either of the two traceable measurement loops, gives rise to the required nullifying component. By virtue of the apparatus topology, no Faraday induction arises in the voltmeter leads, meaning the induction component in the loop segment is nullified. The resulting voltmeter indication is thus the line integral of the purely conservative electric field strength along either path between the probed points. The value of that line integral is path independent. Being a purely conservative term, that line integral equates to the difference in scalar potential between the probed points.
Link to Dr McDonald's paper:
www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=www.physicsforums.com/insights/wp-content/uploads/2018/06/k-t-mcdonald-lewin.pdf&ved=2ahUKEwilnpP4xciHAxXbU2wGHbbCAVgQFnoECBEQAQ&usg=AOvVaw2T58AsZMYnDrzacjaOFygt
This topic was so interesting to me when I first saw the classroom demonstration from Professor Walter Lewin many years ago. I was completely perplexed at the time. I some how came across your channel and for some reason I remembered you had much more content on this issue. I'm actually pleased you covered Jesse's Lewin clock which I admit was a novel name for the device he built. Your considerable expertise has not gone unappreciated from me.
Thanks for sharing!
Hi Trevor
Well detailed video. Why did you divide the conductive ring into two segments and assign the voltmeter to the smaller segment. Time stamp starting at 2:06 .
A purely arbitrary placement of the "clock hands". What would the clock voltmeter indicate for such an arrangement?
@@trevorkearney3088
The voltmeter is in the path OPQO around the orange area , and it is also in the path OQYXPQ around the Green area. You chose OPQO and not OQYXPQ. The reasoning you applied also applies to OQYXPO.
Consider Professor Gullwick wrote -
"The lines of force of the electric field induced by the alternating magnetic field are thus circles, concentric with the axis, which cut the straight portions of the leads at right angles. No e.m.f., therefore, is induced in the leads." end quote.
That would also apply inside the circumference of the solenoid.
Is that how you view the arrangement.
It doesn't matter which closed path is used. The indicated scalar potential difference is of necessity path invariant, since it is subject exclusively to electrostatic fields arising from surface charge density gradients. If I consider the alternative path enclosing the green coloured area, I get the same result. Presumably, you realise the result in the symmetrical case shown is zero - as Prof Cullwick noted in his article submitted to the SQJ. There is no PD between any two points along the loop path. This means there cannot be any surface charge gradients arising in this situation.
I cover the symmetrical case in more detail from about time 29:00 to 31:11.
@@trevorkearney3088 Can you expand on your explanation regarding induced emf that states it is present in loop OPQO and not present in the leads O to P and O to Q.
@@woodcoast5026
Thanks for the question.
If you refer to Prof Cullwick's original description, he states, with respect to obtaining a measure of the scalar PD between any two points on his resistive loop, that "All that is necessary is to devise an arrangement in which no e.m.f. is induced by the alternating magnetic flux in the leads to the voltmeter."
The notion of there being an e.m.f. induced along a particular fraction of any closed path is somewhat misleading, if we focus our attention solely on the enclosed time-varying magnetic flux. There is a subtle distinction between the e.m.f. and the induced electric field. On page 268 of the third edition of his text, “The Fundamentals of Electro-Magnetism”, Prof Cullwick states:
“In dealing with the induction of e.m.f. by a changing magnetic field, we make use of Faraday’s law of induction in the form e=-d(phi)/dt=closed path integral of vector E dot dl. Now this equation gives us no information about the value of the electric field, E, at any point, but only the value of the line-integral of E around a closed path, so that the usefulness of the magnetic-field concept is limited after all.”
Prof Cullwick then proceeds to introduce the concept of what he terms, “the vector potential of the electric current”, designated A. He then relates the vector potential A to the Maxwell-Faraday induced electric field E. In other words, he allows us the means of deducing the E field at a particular location. The existence of the vector potential was originally proposed by Maxwell.
I introduce this concept at time interval 11:35 to 12:07 in the video.
The key point to note is that the induced E field in either of the radial leads OP and OQ is notionally orthogonal (fully transverse) to the lead paths OP and OQ and no induced e.m.f. can be attributed to them. The line integral of E along either path OP or OQ must be notionally zero. The only possible effect of the transverse field E on the meter leads is that a charge redistribution will arise on the lead surfaces, giving rise to a transverse electrostatic field which exactly counters the induced transverse field within the conductor material.
Good to see another video citing actual physics and electromagnetic textbooks and trying to undo the damage done by certain TH-cam 'influencers'.
Let's hope one day the actual physics will prevail upon that sort of entertainment.
Thanks. I noticed from another post, you're planning to upload some videos on clarifying some of the key issues relevant to the physics. I look forward to it. These things require a lot of time and effort to produce. Hopefully, it provides other open minded viewers with well reasoned and informed perspectives. Regarding the use of good reference texts on electromagnetic theory - it seems there is a curious reluctance to exercise the discipline required to read and understand these valuable resources. A sign of the times, perhaps.
@@trevorkearney3088 yeah, I have just finished the audio voiceover and now I have dozens of formulas to convert to SVG. The funny thing is that what in my mind should have been a five minute video turned into three half an hour videos. The one I'm about to publish this week has about eight minutes of me slapping books on my desk ;-). One of them is Panofski & Phillips.
I understand your dilemma. It's easy to state something which is wrong or a half-truth without offering any explanation or rigorous justification. One can also demonstrate a measurement and state it proves an argument - even though it does not. There are some classics in this category. As one text on electromagnetic theory notes, "For instance, nobody in his right
mind would wrap the leads of a voltmeter around the core of a transformer in determining the voltage between two points in a circuit". I've seen this done in a couple of TH-cam videos and nobody scratches their head as to the flawed reasoning underpinning the conclusions drawn from such observations.
@@trevorkearney3088 hey, that's the quote from Fano I have in my future video "what a voltmeter measures"!!!
@@copernicofelinis
Yep - thanks for the reminder.