Hi Dan, Thanks for the video! I’m slightly confused on the section where you consider self inductance of the wire (15:47). I’ve seen alternative derivations for internal inductance which use the same relationship between flux and flux linkage, when considering a single wire which doesn’t concur with the idea of encirclement of the current within that area. Moreover, in this derivation, assuming 1&3 are circular, how would this account for the region of d_r which is outside of the core ie on the other side? Many thanks
Dear Drn Yelverton, The flux linkage inside the wire is quite clear. Thank you. As for the space "between" the wires, you are really talking about the two (intersecring) cylinders each is centered on its respective wire centre and excluding the wires themselves. But there is also a space outside these two cylinders in which the B flux from each wire add but do not cancel. Is the flux in this space being neglected for simplicity? For your Phi2, could you have integrated from a to infinity rather to d-a? Does this use of upper limit blow up Phi2?
Thanks for watching, glad it was helpful. There is indeed a nonzero flux through the region outside the wires, but it's only the flux in the central region between the wires that's relevant, because according to Faraday's law, it's only changes in flux through the circuit itself that induce an EMF. So ignoring the outside region is not just a simplification, it wouldn't be correct to include it and it would indeed give an infinite inductance!
Hmm.. software / digital electronics techy here.. branching out into analog.. And just appreciating how few people there are that can communicate how things work in each are of speciality. Thanks for sharing what you have learnt with others.
Thank you so much for this, was very helpful. Do you have any videos on Taylor series expansion? It would be great to see a video on practical applications/knowing how to identify a problem that is best suited for Taylor series.
Glad it was helpful! I don't have a video on Taylor series in general, but do apply them a lot in my videos. From a physicist's perspective, they're useful whenver things can't be solved exactly and an approximation is good enough. Off the top of my head, this video is probably one of the ones where Taylor series feature most prominently: ua-cam.com/video/NG6nV5u2oBg/v-deo.html
Hi Dan! Thank you for this! In the final formula L, seems that if d is infinite, ln(d/a) is also infinite. Is there a limit to distance d in the formula?
The inductance can be arbitrarily large because more distance always increases the area between the wires and therefore always increases the flux. There's no specific limit on d, though we're assuming that the two wires are part of the same circuit, and in reality we can't have an infinitely big circuit!
Thank you for the video. Can you please explain why the distance "d" is selected at the center of each wire? Why do we not integrate all the way to the ends of each wire? Thanks in advance.
Measuring d between the centres is purely a matter of convenience, you could redefine it to be the distance between the far ends of the wires and your result would be the same in the limit of a
@@DrBenYelverton Thank you for the clarification. Do you know where I can find a derivation for integrating from the outer ends of the wire? I am assuming someone had to have done it both ways to prove they yield equivalent results. Unfortunately, I am not seeing how it is equivalent because it seems to me there would still be some current contribution cancellation up until the outside boundary of the opposite conductor. In other words, only when "both" conductors are encircled by an Amperian loop, does the flux totally cancel. Am I missing something? By the way, what is the significance of the limit of a
Wonderful! Cleared my misconception. Thanks alot for this.
Excellent, good to hear!
Very good, more videos on em, please !
Thanks, I will try to cover some more EM topics in the future!
Superb!
Sincerely thank you for this video!
Hi Dan, Thanks for the video! I’m slightly confused on the section where you consider self inductance of the wire (15:47). I’ve seen alternative derivations for internal inductance which use the same relationship between flux and flux linkage, when considering a single wire which doesn’t concur with the idea of encirclement of the current within that area. Moreover, in this derivation, assuming 1&3 are circular, how would this account for the region of d_r which is outside of the core ie on the other side?
Many thanks
Dear Drn Yelverton, The flux linkage inside the wire is quite clear. Thank you.
As for the space "between" the wires, you are really talking about the two (intersecring) cylinders each is centered on its respective wire centre and excluding the wires themselves.
But there is also a space outside these two cylinders in which the B flux from each wire add but do not cancel. Is the flux in this space being neglected for simplicity?
For your Phi2, could you have integrated from a to infinity rather to d-a? Does this use of upper limit blow up Phi2?
Thanks for watching, glad it was helpful. There is indeed a nonzero flux through the region outside the wires, but it's only the flux in the central region between the wires that's relevant, because according to Faraday's law, it's only changes in flux through the circuit itself that induce an EMF. So ignoring the outside region is not just a simplification, it wouldn't be correct to include it and it would indeed give an infinite inductance!
Hmm.. software / digital electronics techy here.. branching out into analog.. And just appreciating how few people there are that can communicate how things work in each are of speciality. Thanks for sharing what you have learnt with others.
Happy to help! I appreciate your kind words.
Thank you so much for this, was very helpful. Do you have any videos on Taylor series expansion? It would be great to see a video on practical applications/knowing how to identify a problem that is best suited for Taylor series.
Glad it was helpful! I don't have a video on Taylor series in general, but do apply them a lot in my videos. From a physicist's perspective, they're useful whenver things can't be solved exactly and an approximation is good enough. Off the top of my head, this video is probably one of the ones where Taylor series feature most prominently: ua-cam.com/video/NG6nV5u2oBg/v-deo.html
Thank you this is amazing
Hi Dan! Thank you for this! In the final formula L, seems that if d is infinite, ln(d/a) is also infinite. Is there a limit to distance d in the formula?
The inductance can be arbitrarily large because more distance always increases the area between the wires and therefore always increases the flux. There's no specific limit on d, though we're assuming that the two wires are part of the same circuit, and in reality we can't have an infinitely big circuit!
Thank you for the video. Can you please explain why the distance "d" is selected at the center of each wire? Why do we not integrate all the way to the ends of each wire? Thanks in advance.
Measuring d between the centres is purely a matter of convenience, you could redefine it to be the distance between the far ends of the wires and your result would be the same in the limit of a
@@DrBenYelverton Thank you for the clarification. Do you know where I can find a derivation for integrating from the outer ends of the wire? I am assuming someone had to have done it both ways to prove they yield equivalent results. Unfortunately, I am not seeing how it is equivalent because it seems to me there would still be some current contribution cancellation up until the outside boundary of the opposite conductor. In other words, only when "both" conductors are encircled by an Amperian loop, does the flux totally cancel. Am I missing something?
By the way, what is the significance of the limit of a
How we need to calculate four parallel wire inductance
I was realy confused about this , thank you this helped so much
I'm glad it helped!