Physics 46 Maxwell's Equations (5 of 30) Faraday's Law of Induction

Visit ilectureonline.com for more math and science lectures!
In this video I will explain and calculate Faraday's Law of induction.

[@alexlim20]

wow.. this takes me to a new level of understanding Lenz' Law and Faraday's Law. Thank you so much Professor Michel!

[@MichelvanBiezen]

Glad it was helpful!

[@shayangfkk7948]

Great teaching by professor , he is SO underrated . and another example of math elegancy and power and beauty .

[@MichelvanBiezen]

Wow, thank you!

[@oneinabillion654]

My talent is in classical mech, but not in the field of E and M theory. The way you explained the negative sign in Faraday's induction law by drawing an analogy to F=-kx (reactionary force) is brilliant. Cleared my doubts on the negative sign.

[@Live4Christ4ever100]

Amazing! Thank you so much Professor Michel. You are a wonderful teacher!

[@MichelvanBiezen]

Andrew, Thanks for the comment. Much appreciated.

[@Live4Christ4ever100]

I'm sharing your video's with all my friends. This is the first time in a long time that I've learned from a teacher and not from just reading a text book. i feel like im in a class room because of the environment that you have set up. Keep it up.

[@MichelvanBiezen]

Marcela, If you switch the direction of the magnetic field, the effects will also be in reverse. If you change the angle, the flux through the loop will be a factor of the cosine of the angle between the magnetic field and the normal to the plane. The direction of the EMF can be found using Lenz's law. (See my video in the playlist: PHYSICS 45 ELECTROMAGNETIC INDUCTION

[@manniman82]

Sir, I have a a couple of questions in regards to induced electric fields like in this example. First, are the electric field lines a circle (the shape of the loop)? And if so, where do they begin or end? I thought that electric field lines always begin and end at a charge, or is that only for electrostatic fields? Second, Gauss's Law says that the line integral of the electric field times the area is equal to the net charge enclosed divided by the electric constant: In the case of induced electric fields like in this example, if we draw a Gaussian surface around the loop so that it encloses all of it, is the net charge enclosed equal to the sum of the moving charges that make up the induced current ... Or maybe it's zero since there would be no potential difference (emf) if it wasn't for the magnetic field? But if it's zero how can there be an electric field that has a non-zero value? (These are just guesses) Or maybe it's something else?

[@zuhairalsaffar7001]

Sir really l don't know how to thank you you are more than amazing person all the best for you

[@chronicsnail6675]

i have no high knowledge of maths yet i still understand, this is amazing

[@CatsBirds2010]

Beautifully done

[@zakirhussain-js9ku]

Change in magnetic flux is associated with motion of flux. Increasing current expands or moves M-flux outward & decreasing current contracts or moves M-flux inward. Similarly if a conductor of constant length cuts across constant magnetic field at constant velocity an emf is induced in the conductor. While in later case flux is constant it is in motion relative to conductor. In both cases motion of flux relative to conductor is common factor. Why we don't say motion of magnetic flux induces electric flux & vice versa. This query is just to clear my understanding.

[@valeriereid2337]

Thanks so much for this amazing lecture.

[@MichelvanBiezen]

You're very welcome! You appear to be enjoying Maxwell's equations. 🙂

[@MrAngrybox]

Great video and explanation! Thank you very much

[@jennifertheodora3961]

Hi Prof, at 9.37 can we write the magnetic flux as πR² (2 - 0.1t)? By the way, I'm super super grateful I found this channel! You are amazing prof.

[@karthikmaheshrao6021]

The induced voltage in the wire loop produces a current in its loop that is due to mutual inductance from the magnetic field lines of one active conductor onto another inactive conductor(wire loop). This induced current is known as Eddy currents. Am I right, Prof?

[@MichelvanBiezen]

Eddie currents are currents inside a single conductor induced by a changing magnetic field perpendicular to the loops of current.

[@curtpiazza1688]

Powerful stuff! Thanx!

[@MichelvanBiezen]

Glad you liked it. 🙂

[@endritmargjeka8460]

Thanks a lot, very nice content. I just can not comprehend why you are using ds and not s. Is it because you are talking about a change in space rather than the space in itsself?

[@MichelvanBiezen]

We must use ds (and not s) because it is in an integral format. It represents an infinitesimal section around the loop. (Standard calculus practice)

[@marcemercadolm]

Hi Professor, first, you're great at teaching, thanks for the lessons, I have an specific question: Does it matter the direction the Magnetic field is respect to the conductor loop? what about if the axis of he loop is perpendicular to B?, and also, how can I determine the direction of the EMF produced? thank you very much!

[@tag_of_frank]

Do you have any videos explaining transmission line equation for circuit analysis? At the moment, I can only find videos from India explaining it.

[@MichelvanBiezen]

We haven't reached that material yet.

[@OswaldChisala]

Womderful video, professor Michel! I would like to ask a minor question: what happens if the loop dimensions change, for example that as the flux through the loop changes with time, so does the area of the loop. Assuming all changes to be continuous, would it make sense to generate time-dependent path and surface functions for the various limits of Faraday's law? A simple thought experiment would be a U-shaped rectangular loop with a sliding conductor making up the fourth side of the rectangle, and moving at constant velocity along the rails prescribed by the loop. In such a situation, how would one calculate the emf that is generated?

[@MichelvanBiezen]

Take a look at video # 6 in this playlist: PHYSICS 45 ELECTROMAGNETIC INDUCTION kzbin.infoplaylists?sort=dd&view=50&shelf_id=10 You will find that exact example.

[@OswaldChisala]

Thank you, I watched videos in that playlist, and came across the example I had in mind. I have a follow up question posted in the comment section of the video you recommended.

[@Hally96]

What is the potential difference across? If the loop is a closed loop it doesn't make sense for there to be a 'battery' at one arbitrary point.

[@MichelvanBiezen]

+Jack Hall Exactly, it doesn't make sense, yet there is a current as if there is an invisible battery driving current around the loop. That is why it is called "induced" Emf. And it is the change of magnetic flux through the loop that causes that phenomena.

[@spencershabshab3241]

Thanks for a great lecture. I have always wondered: Are we assuming in your example that the total NET flux through the coil is changing at the specified rate? That is, when we say that the B field decreases at a rate of 0.1T/s, are we including the induced flux of the resultant coil current?

[@MichelvanBiezen]

No, we are only considering the B-field that initiates the changes.

[@spencershabshab3241]

OK, so the current in the coil will react to the 0.1T/s change even though the total flux is changing at a slower rate? Thanks for your reply!

[@MichelvanBiezen]

Correct.

[@waqarali9166]

yes that really make sense :) amazing

[@surendrakverma555]

Very good 🙏🙏🙏🙏

[@MichelvanBiezen]

Thank you! Cheers!

[@Sam-dc9bg]

Thanks for the lesson.

[@zakirhussain-js9ku]

A moving magnet induces electric field in space around it. Magnet has no electric field of its own. What is source of electric field which appears in space around it.

[@MichelvanBiezen]

Not exactly. A moving magnet causes a change of the magnetic field, and a changing magnetic field causes forces to be exerted on any charges inside that changing magnetic field.

[@zakirhussain-js9ku]

​@@MichelvanBiezen Yes, a moving magnet changes magnetic flux in space around it, which would exert force on charge falling within changing flux. My question was not about force on charge. My question was about source of electric field which would appear around changing magnetic flux even in free space where there are no charges within changing magnetic flux. In free space only charges present are in the atoms of magnet it self unless they have any role.

[@MichelvanBiezen]

A moving magnet causes a changing magnetic field, which causes the magnetic flux to change. If the changing magnetic flux is within a closed conductor loop, the the changing magnetic flux will induce an EMF which will then push the charges around the loop. Only charge produces an electric field and oscillating (or accelerating) charges produce an E&M wave.

[@MichelvanBiezen]

A moving magnet causes a changing magnetic field, which causes the magnetic flux to change. If the changing magnetic flux is within a closed conductor loop, the the changing magnetic flux will induce an EMF which will then push the charges around the loop. Only charge produces an electric field and oscillating (or accelerating) charges produce an E&M wave.

[@zakirhussain-js9ku]

​@@MichelvanBiezen Changing magnetic field induces circulating electric field even in free space w/o any conducting loop. I am curious about source of circulating electric field around the magnet as magnet its is electrically neutral.

[@WillyGhillie]

Thank you! Great video :)

[@nikhilwardrobe]

professor at 9:37 how did you got the 5% change?

[@MichelvanBiezen]

+nikhil monarch The change in the magnetic flux per unit time = change in the B-field x Area The change in the B field is given as 0.1 T/sec and the area is pi*R^2

[@jake31609]

Therefore wouldn't it be .1*(2*Pi*r^2) db/dt = .1 --> dflux/dt= bd(*A)/dt =.1*(2*Pi*r^2)/1 Is it not the actual change in flux not the percentage change in flux. Eg Using percentages the same EMF would be produced if it went from 1000Wb to 500Wb in a second as if it went from .01Wb to .05Wb. edit: a=dv/dt we do not measure acceleration as a percentage. Going from 1 to 100ms in a seconds is greater acceleration than going from .1 to 10 m/s

[@MustafaYlmaz-ri6qv]

@@MichelvanBiezen it is already given change in the B field as -0,1 T/sec, we can use this directly in equation and so no need to use initial value of B and the value 0,05 since it is confusing.

[@KFE2016]

another way look at it is, how long time does it take to change the full B (2T) to 0. That is 2(T)/0.1(T/sec) => 20 sec. so dt = 20sec 1/dt = 1/20 = 0.05, which then you can multiply dFlux.

[@Mortgageman145]

Wait, doesn’t Maxwell’s second law state the magnetic flux should always be zero? What’s going on here? If I were to guess, Maxwells’ second law has to do with net flux not independent flux

[@MichelvanBiezen]

To describe Maxwell's second law, we must state it more precisely. "The magnetic flux THROUGH ANY CLOSED SURFACE is zero" Which implies that a magenetic monopole doesn't exist.

[@Mortgageman145]

@@MichelvanBiezen Thanks for clarifying, thought it has something to do with that

[@Bruc32]

Great Video! What happen if i add a small gap in the loop? Do you still get an emf across the gap? The Ohm law is still valid in this context? I mean, in order to calculate the current may i still apply the Ohm law after computing the emf? Thanks!

[@MichelvanBiezen]

In order to have a current you must have a complete loop. When there is a gap, there cannot be a current.

[@diegobadillo3335]

how do you know the direction of ds?

[@sipkagergo2353]

Can we move the test charge right to the + plane? I mean, can they touch each other? Since they're both of the same charges then is it possible to bring them together?

[@MichelvanBiezen]

Remember that like charges do repel, so it will require force and/or energy

[@ShreyasRavibighero6]

Why is the magnetic flux not zero as per gauss' law for magnetism?

[@MichelvanBiezen]

I think you may be mixing up 2 different and independent concepts. If there is an existing magnetic field and we place a loop in the field you will have magnetic flux through the loop. If you place a volume in the field, the flux entering the volume will equal the flux leaving the volume.

[@douglasstrother6584]

Gauss' Law applies to a closed surface. The surface is open in this case.

[@Arkantosi]

Should it not be E dot dl? It's a line element, not a surface element.

[@MichelvanBiezen]

The letter "s" is used for displacement and for arc length, therefore ds has the exact same meaning as dl.

[@Arkantosi]

@@MichelvanBiezen Ah, then it's just a matter of notation. My book uses dl, ds and dv to specify line, surface and volume element, thus my confusion. Thanks!

[@MichelvanBiezen]

Yes, different authors use different symbols :)

[@ryantom5265]

Just wanted to let you know that in your playlist this video shows up as the 4th one and Gauss' Law for Magnetism shows up as the 5th.

[@ryantom5265]

Love your videos btw

[@MichelvanBiezen]

Just fixed it. Thanks for letting me know.

[@leejy2]

how did you get the 5%?

[@jks2389]

+leejy2 I realize its a bit late, but its simply the ratio of change: 0.1T is 5% of 2T (0.1/2=0.05).

[@dattatreymaity3196]

but I wanted continuity equation of time varying field

[@mhdmouazawad8464]

how diff of flux come

[@richardjohnston3370]

Maybe if you were to talk even faster, you could make your videos shorter, then those of us who are really trying to understand the material can fail more quickly.

[@ronniemacdonald2768]

Did you make this rude and needless comment before or after youtube introduced the ability to slow videos down?

[@curtpiazza1688]

Powerful stuff! Thanx!

[@MichelvanBiezen]

Glad you liked it. 🙂