This Equation Explains Electricity (and Other Electromagnetic Phenomena) - Parth G Electromagnetism
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- čas přidán 20. 05. 2024
- What do the symbols in the Lorentz Force Equation mean? And exactly how do Electric and Magnetic Fields influence Charged Particles placed within them?
Hey everyone, Parth here again with another equation explanation video. Today, we're looking at the Lorentz Force equation. This equation describes the forces exerted by both electric and magnetic fields on a charge particle found within these fields.
Named after Hendrik Lorentz, the equation can simply be split up into two parts. The force exerted by electric fields, and the force exerted by magnetic fields on charged particles.
In this video, we begin by seeing how electric and magnetic field lines are useful descriptions of how charges and magnets respectively interact with fields. Both can be described as vector fields, meaning we can assign a vector to each point in space. Therefore, we can also represent these fields as vectors in our mathematics.
When a charged particle is placed in an electric field, the field exerts a force on it equal to the charge of the particle multiplied by the electric field strength at that point in space. The direction of the force exerted is the same as the direction of the electric field at that point.
The magnetic component is a bit more complicated. When a charged particle is stationary in a magnetic field, the field does not exert a force on it. However if the particle moves relative to the field, then a force is exerted perpendicular to both the direction of the particle's motion, and the field lines. This is why the magnetic force is given by the particles charge multiplied by the cross product (vector product) between the particle's velocity vector and magnetic field lines.
In this video, we also see how to visualize vector products between two vectors. We see that if the original two vectors are perpendicular, then the cross product between them is maximal in size, but if they are aligned, its size is zero. The vector product is also always perpendicular to both the original vectors.
Additionally, we also see that a particle initially moving with a constant velocity in a constant magnetic field will undergo circular motion because the magnetic field exerts a force perpendicular to its velocity.
Finally, we see that the Lorentz Force equation is just a combination of the electric force and magnetic force experienced by a particle that finds itself in a region where both an electric and a magnetic field exist.
Timestamps:
0:00 - The Lorentz Force Equation, and its relation to Electromagnetism
0:31 - Electric and Magnetic Field Lines to Represent Vector Fields
3:00 - Charged Particles + Electric and Magnetic Parts of Lorentz Force
4:05 - The Force Exerted by the Electric Field on a Charged Particle (qE)
4:48 - The Force Exerted by the Magnetic Field on a Charged Particle (qvxB)
5:36 - Visualizing the Vector Product / Cross Product Between Two Vectors
6:45 - Circular Motion of Moving Charged Particles in Magnetic Fields
8:47 - Putting Everything Together into the Lorentz Force Equation
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Lorentz force, Jack! Nature’s force.
I am an electrical engineer and found your explanation very perfect. I am very proud of young scientists like you.
I found his explanation to be crisp-clear too, as a Physics subject student that needed some clarity, it was so well-done!
great video, just one error: 7:21 this does not mean that the field lines come out of the screen but go into the screen, hence the force should be directed upwards. I remember this imagining an arrow: When the arrow is shot towards you, you see the tip which is like a point in a circle. When it's going away from you, you see the feathers, which are aligned like a cross. Additionally, F_B is at 5:28 indeed into the screen, but the symbol is not the point in a circle but cross.
That's all about taking conventions. You can take whichever convention you may want to, and the ultimate result should come out to be the same. Maybe you are pointing it out because most of the books follow convention opposite to that used in the video.
@@abhishekkumarjaiswal7397 I dunno maybe don't INVERT conventions for no reason? multiple noobs were forever confused by this "choice of representation"
@@orrange911 Yes, I agree. I was confused too.
@@abhishekkumarjaiswal7397they are called convention for a reason... And to be honest i havent seen any other convention thats the opposite of what we normally use. And if he used a convention thats the opposite of what the majority of the world use... Maybe put up a warning. And also no it cant be another convention because if it's, it is contradicting itself
But then the direction of the force in the given example would not make any sense. F would have to be upwards, if the B field were really to be towards the viewer.@@abhishekkumarjaiswal7397
Please complete the Maxwell's equations series and explain the fourth equation
It’s just nature running it’s course
LORENTZ FORCE, GO!!
It’s funny how I got here from watching the Fleming left hand rule.
7:00 the magnetic field B is sketched the wrong way. There should be points • • • not x x x
Good video though!
That's just a man-defined convention, you can take 'CROSS' to denote the magnetic field directed into the page or out of the page. In either way, the laws of nature are not affected.
@@muhammadhussainsarhandi9928 first of all there is a certain logic behind the "cross and point" notation.
Apart from that (I agree it is a convention) I concluded that it points towards the wrong way because of the direction the particle is moving (clockwise. He said that B is pointing outwards).
@@gre81 yes Sir you are right,
@@muhammadhussainsarhandi9928 thank you sir.
@@muhammadhussainsarhandi9928 the Circle-Dot/X convention is meant to represent the vector as an arrow (as in the projectile launched from a bow). The Circle-Dot represents the arrow tip pointing towards you. The X represents the arrow fletchings facing towards you or the arrow tip pointing away from you.
The force @5:30 has to be a cross and the magnetic field @7:00 has to be dots.
Otherwise great video.
Yup, or he has to mention that it's a negative charged particle
Such a nice content presented with simplicity. Thanks man!
Learning this equation in physics class this past semester blew my mind. It always confused me why electricity and magnetism were always lumped together, but it makes so much sense that moving charges produce a magnetic field.
Thanks for the math explainer videos. It fills a gap in the YT "physics explainers". Going over the math, term by term, in declarative form, helps in understanding the precise statement, physics is trying to say.
Hoping this will help me with my lab session tomorrow. Very well explained, thank you!
Thank you Parth, you are such a good teacher
Thank you! A great summary and simple explanation.
Thank you sm!!! THIS WAS SO HELPFUL >.
Hey Parth! Love your videos! Can you make a video explaining the basics of super string theory?
You said all I needed to hear. Liked and subscribed💞.
Amazing!
Just loved it ❤️
You made it so simple!
A clear explanation! Much appreciated!
thank you so much.its really helpful ❤
Do a video on how local symmetry leads to the forces of nature!!!
Really well explained !! Super.
keep making your videos. simple explanations are best
mind-blowing parth
U said ur camera is bit shaky ! But it seems to be tracking ur face 😂!
Great video brother ! 💛
This video was amazingly helpful thank you
This is very useful! I am learning electrodynamics so this helps a lot!
Beautiful content; compelling, comprehensive and yet concise. Thank you! Q: at the very end, does the circular acceleration imparted by the B field when superimposed onto the linear acceleration imparted by the E field, mean the particle would, in effect, tumble from L to R in the plane of the screen; like if we were watching a fixed point on a drum rolling across the floor?
I want more videos from you aspecially on dual nature of atoms and nature and all that stuff for beginners ❤❤
great work sir
6:51
Doesn't cross means magnetic field going into the screen, but you said it comes out.
@Yajur Gupta -- DON'T cross the streams!
@@davep8221 I can't understand what you mean please elaborate 😅
@@TheHumanHades I'm sorry for the confusion. There's a movie called GhostBusters, where one of the ?heroes? says:
“Why worry? Each of us is carrying an unlicensed nuclear accelerator on his back.” They use the beams to catch ghosts.
Sorry to be so verbose, but this stuff is so funny, I have to give it all.
tl;dr
Dr. Egon Spengler : There's something very important I forgot to tell you [about the accelerators].
Dr. Peter Venkman : What?
Dr. Egon Spengler : Don't cross the streams.
Dr. Peter Venkman : Why?
Dr. Egon Spengler : It would be bad.
Dr. Peter Venkman : I'm fuzzy on the whole
good/bad thing. What do you mean, "bad"?
Dr. Egon Spengler : Try to imagine all life
as you know it stopping instantaneously and every molecule in your body exploding at the speed of light.
Dr. Raymond Stantz : Total protonic
reversal.
Dr. Peter Venkman : Right. That's bad. Okay. All right. Important safety tip. Thanks, Egon.
And don't forget the twinkie. For that,
you'll just have to watch the movie.
@@TheHumanHades I'm sorry for the confusion. I'm not the brightest banana in the chandelier.
There's a movie called GhostBusters, where one of the ?heroes? says:
“Why worry? Each of us is carrying an unlicensed nuclear accelerator on his back.” They use the beams to catch ghosts.
Sorry to be so verbose, but this stuff is so funny, I have to give it all.
tl;dr
Dr. Egon Spengler : There's something very important I forgot to tell you [about the accelerators].
Dr. Peter Venkman : What?
Dr. Egon Spengler : Don't cross the streams.
Dr. Peter Venkman : Why?
Dr. Egon Spengler : It would be bad.
Dr. Peter Venkman : I'm fuzzy on the whole
good/bad thing. What do you mean, "bad"?
Dr. Egon Spengler : Try to imagine all life
as you know it stopping instantaneously and every molecule in your body exploding at the speed of light.
Dr. Raymond Stantz : Total protonic
reversal.
Dr. Peter Venkman : Right. That's bad. Okay. All right. Important safety tip. Thanks, Egon.
And don't forget the twinkie. For that,
you'll just have to watch the movie.
BTW, I love your stuff and apologize for making such obtuse and localized comments. It's gotten me into trouble before.
@@davep8221 Ok
Hi, I am in class 10 (15 yrs old) and I have recently learnt Fleming's left hand rule (direction of force experienced by electric charge in magnetic field), and your explanation of vector products really made things click for me.
Love from India!
Isn't he an Indian too?? I assumed him to be an Indian from his name though...
This is a fucking hidden gem of a channel. You're a king for taking your teaching talent to yt
8:40 The radius of the circle is given by the equation:
r = (mv)/(qB)
The momentum divided by qB.
To make the magnetic field part easier to understand, we need to know something about moving charged particles:
That every charged particle that moves in space, will always create a magnetic field around that charged particle. Going back to 2:05 we see that the single North pole will get repilled by the North pole of the magnet and gets attracted by the south pole of the magnet. For a charged particle however, there's no North or south pole in it, so there will not be any attraction or repulsion for that charged particle.
But remember, as I said, if that charged particle moved in space, it will create magnetic field around it, which will create North pole and south pole around it as well, and if that charged particle is inside a magnetic filed of a magnet, and that charged particle is moving, the North pole of that charged particle that is moving inside the magnetic field will get attracted to the south pole of the magnet and repilled by the North pole. Similarly, the south pole of that charged particle that is moving inside a magnetic field will get attracted by the North pole of the magnet and repilled by the south pole of that magnet.
I know this is a lot of text, but I hope it will help you. And thank you Path for making difficult concepts easy for us to understand, and keep going.
congrats, great video !
Great bro nice explaination with clear cut concept 👍👍👍👍
Your videos are just amazing
Great, well explain.
A graphic of the locus followed by the particle would have been icing on the cake :-)
Liking the new set up.
re: single-poles. Rodin coils have been demonstrated to have monopole capability. Also, if you select a cone instead of a cylinder to wire a coil, and if you have less winding as the wide base, and more winding at the apex, you have lots of magnetic strength at the apex and a weak strength at the very wide base of the cone. Also, the speed of light in the wire is less and less as you approach the apex, so there is some complexity to a cone coil. There is a photograph of N. Tesla with a cone coil geometry and this is when he described his so-called "magnifying" effect. Wideband? Relativistic effects? There are many geometries yet to explore I think.
Nice explanation 👌 👍 👏.
Enjoy your videos! What program do you use to make them? Do you know about MASt at Cambridge?
Hello brother Parth. It was a good one to show the Lorenz-force. But I have a request that you could explain also how Catapulte-force is working in magnetic field and could explain the tribunal pressure on a charged partical in a magnetic field what causes the resultant is perpendicular to both its commitments.
Wonderful explanation
I just started 11th grade and understood Lorentz force, thanks to you.
Are u from Uttarakhand ?
@@theimmortalphysicsmaths3962 No, Delhi. I meant I started self-studying 11th grade stuff
@@md.ayaanahmed5152 oh sorry actually there is Ayaan in my class ...ohk u r a 10th grader
fantastic young man
very good explanation
Hi Parth, Its my request that could you please make a vid on Bell’s Theorem/Bell’s Inequality? Its something I really stumble with, and I haven’t found any vid that properly explains it.
Thank you
You are awesome 😍😍😍😍 I love you a lot , bhaiya can you a make video about Dirac relativistic formulation please 🙂🙂🙂
Hi Parth. I am right now with a situation that i am thinking of. I drew two magnets separated , lets say 10cm, and with a laser of 680 nm I point it in order to go through the magnets. So, my question is how would be the interaction between the laser beam , if the force of the magnets can turn the light and change its straight direction.
Parth will you please do a video on how two moving charges supposedly break newtons law and how it inspired Einstein to discover special theory of relativity ✋
6:50 You can determine the direction of the product A x B in this manner. Using your right hand (this is convention) point your fingers in the direction of A, now curl them toward B. Stick out our thumb, it points in the direction of the product A x B., Notice that B x A would point in the opposite direction, so A x B = -(B x A). The length (magnitude or size) of the product is AB sin (angle between the two vectors). When A and B are perpendicular the angle is 90 degrees and the sin = 1, when the point in the same direction, 0 degrees, or opposite directions 180 degrees, sin = 0.
Hi Parth, can you explain how work and energy relates into to this
thank you
Awesome 😎
Lorentz force GO
HAHAHAHHH, WELCOME TO MY UTOPIA OF DEATH
Parth g can u make a video on why center of mass concepts cannot be applied to charged particles
I think it's a silly question but I'm eager to find out the reason
That was beautifully explained as always.
Question: With the contribution of both electric and magnetic fields, how the particles behaves? I mean, the movement of the particle inside such fields?
Thanks.
The exact direction and motion is highly dependent on the fields, the two can cancel eachother out or amplify eachouther. To calculate it exactly you can probably work with classical mechanics (i.e. Newtons laws applied to the specific problem with modern math tricks) and build a model that correspond with the equations of motion.
@@davidurban528 oww Thanks for that.
Just one more thing I’d like to see explained: a charged particle undergoing acceleration is supposed to radiate energy away. As a result, it loses energy. So a charged particle moving perpendicular to a magnetic field wouldn’t undergo circular motion but would spiral inward. How does the Lorentz force account for this, or how can the Lorentz force equation be used to account for this?
I’m no physicist, but my instinct is that this behavior actually can’t be explained by Maxwell’s equations, which assume that the charge on any particle is stationary over time.
@@TheBasikShow The electric field accelerates the charged particle. The curvature will depend upon the strengths of the fields. If there is no E field then the particle would spiral in
GREAT. Melodious explanationSend me the list of all your videos explained in this fashion. Do not just read this & ignore it, will U?
Lovely video. Even I managed to understand it from here. But I have a question:
Say you make a simple AC generator. A coil inside which you spin a permanent magnet as a rotor. Nothing fancy. So the coil is the stator, and the magnet is the rotor. Now when you start drawing power, Lorentz force will push... on the coil, cause the charges are travelling thru the winding. But the stator is ...stationary. How does the Lorentz force slow it down when you draw power, since it pushes on the stator ?
According to Thomas Bearden, the Heaviside simplification of the Maxwell Equations relies on symmetry. Yet nature also has systems that are NOT symmetric. For example, you could make a coil of wire that follows the golden ratio. That is NOT symmetric. Geomerites can be non-symmetric. Next, the simplification throws out potentials, and yet nature can have huge potentials that could be harvested such as charges that have built up over time on a metal surface that is not grounded due to incoming particles from the cosmos. Bearden has a pretty good list of the various things wrong with EM theory, including that it hasn't kept up with modern physics, and requires the ether. But also, just in terms of math, Quaternion math, now used by PC game developers for a better physics model, doesn't suffer gimbal lock or divide-by-zero special casing like vector math. We have had space craft and jets crash because of these math errors. It seems "rotation" is something that needs to be correct when considering electro-magnetism.
What is the Lorentz-O mentioned in Stan Deyo's anti-gravity talk on youtube? He describes a toroidal coil (in a flying saucer) that has an air gap and is pulsed with DC in order to keep the spin direction the same. The equations to work out with respect to Lorentz require this sort of geometry where the magnetic and electric fields are in a state of rotation (not back and forth), but rotating more like Tesla's "Egg of Columbas" can do. Tesla created a rotating field using 4 coils and two phases or 6 coils and 3 phases. But another way is via this pulsed DC approach. In the Leedskalnin Perpetual Motion Holder (PMH), the magnetic field is held in the device for years w/o weakening. Explain that with equations.
Hey parth pls pls make a video on standard model plssss
Nice vid!
LORENTZ FORCE, GO!
im curious as to what the direction of movement would be when both magn. and elc. fields are at play, if anyone knows please lemme kno
Hey can you make a video on tensors??
bhaiya, as we know velocity is frame-dependent and if I make sure that the charge in a magnetic field is at rest and the observer moving with respect to charge then the observer, observes any force due to the magnetic field on the charge? (and the electric field is zero)
in this case, charge have some relative velocity with respect to the observer but with respect ground (maybe or coordinate axes) is zero
9:51 I don't know what country he lives in, but the convention is that x represents vectors pointing away from the viewer (INTO the screen) like the tail of an arrow where the feathers are located. Dots represent vectors pointing toward the viewer (out of the screen) like the pointed tip of an arrow coming AT you. it is simple to remember using a arrow. you see the pointed tip (dot) of the arrow as it flies toward you. You see the x pattern of the feathers at the back of the arrow as it flies away from you.
I remembered that x means into the page is that the case?
Velocity is referenced to the observer not the magnetic field.
What software is used to create the animations?
If a charged particle is travelling north away from the centre/source.. It is rotated by the EM field to its anti position (south), still travelling north, but back towards the centre/source. There will be 2 sets of poles as suggested in the video because it is symmetrical. The path of the particle (-electron/+proton) would be spiral in nature.
Can a beam of light change the motion of a charged particle if it is in its path since it has electric and magnetic components
what about the pointing vector. pls, explain then your electro-magnetism playlist will be completed.
Lorentz force go !
There is one aspect of the Lorentz force which I never understood. What is the fundamental reason for the cross product to be added and not subtracted or why to use the right hand rule to determine the direction instead of the left hand?
Lorentz force tells you the NET force acting on a charge, that is, the sum of all forces. Either force (due to E or B) can be positive or negative depending on the reference frame you choose (so in one particular situation you could have F=qE-qv×B). Which I think is your doubt.
On the other hand , the right hand rule is just a convention used to define the cross product (which by definition is perpendicular to the plane formed by the two vectors) and to determine its direction we tend to use the right hand. You could have well used the left hand, it would not change anything but the definition of your right-handed coordinate system
Parth which microphone you are using?
Brother ( X) represents A current or magnetic field going into the plane but you said OUTWARD THE SCREEN at 6:58 correct 🤔
The magnetic field view should be represented as a screw. When you see it from behind, you see the X (the spot where the screwdriver enters), when it comes to you you see the ( . ), which is its tip
Thanku
Why magnetic force is always perpendicular to magnetic field, I can't imagine i
,also why Cross product of two vectors is always perpendicular to both the vectors?
4:56 Why doesn't the stationary particle "feel" a force. What can I do to demonstrate this idea? If I pin that charge to that point, what do I use to show that it will not "feel" a force? Gauss's Law? Every answer I have found just skips over how we know this is the case, but I want to know how we know it doesn't "feel" a force. What was the initial experiment that showed this?
If v = 0 then Magnetic force =0 only a moving charge experience the Magnetic force means stationary particle can not feel Magnetic force because its velocity become zero (0)
@@reamtech9309 That's not an answer but a description. I found the real answer. A point charge has an electric monopole and therefore has an electric field and therefore can interact with an electric field whether moving or not. A charged particle doesn't have a magnetic field and therefore cannot interact with a magnetic field. Only a moving charge has a magnetic field, and therefore motion generates its ability to interact with a magnetic field. It's all about the fields and field interactions.
Here is some interesting history. It was Benjamin Franklin who used positive and negative for electric charge. He thought of electricity as some type of fluid that flows from an area where there is an excess of charge (positive) to a place lacking charge (negative). Positive charge is like a hill of built-up charge while negative charge is like a hole, so naturally electric charge (at least positive charge does) flows downhill from positive to negative.
Sir please describe the eqn of electromagnetic wave in easy way
If you think of the x as an arrow, then you are seeing it go into the screen, no? Doesnt change anything, just curious.
Thank u, thank u, thank u.
Make video on black body radiation and ultra violet catastrophe parth
The term north pole is a shortened version of the original name which was "north seeking pole", in other words the pole of the magnet that points toward what we call the north pole of the Earth. The etymology of north and south is somewhat confused, but that is not important here.
Hey Parth ... i have a doubt.
Why charged particle not experiencing any force on it when it is in rest at magnetic field. i.e. v=0
When it's moving, it sees itself as stationary & the rest of the world as moving therefore the world is Lorentz contracted. This causes electric charges to appear contracted & packed into a small space & therefore they exert a strong electric force on the charged particle, either attracting it or pushing it away. When it stops moving this forcce stops existing. There are some YT videos explaining how special relativity creates magnetism.
Wash away the anger
HERE I STAND BENEATH THE WARM AND SOOTHING RAIN
@@Yamamba THE DROPPLETS GENTLY FALL DAWN IN TERRAIN
@@yoshisuperficial8546 WASH AWAY THE SORROW ALL THE STAINS OF TIME
BUT THERE'S NO MEMORY IT'S ONLY DRY INSIDEEE
Suppose you could create a very large magnetic field in the direction UP. Incoming particles from the cosmos will spiral away or spiral toward this large field. Instead of a cylinder field, suppose you could create a cone-shaped magnetic field with the apex near the ground and the base toward the sky. Particles would spiral down into the apex where they could be made to impact onto a plate to charge it electrically. Suppose you could use that electric field as a potential to increase your magnetism in the cone-shaped magnetic field. This is an open circuit because the electric energy is arriving from the outside into your system. We know that energy can be transmitted wirelessly. It therefore should be possible to make machines that can harvest incoming, highly energetic particles. We just need magnetism that is strong enough to pull them toward a collector. Are any of you good at building machines like this?
The big mystery is WHY does the moving electric charge experience a force perpendicular to both the magnetic field and velocity.
First of all, magnetic fields are generated by moving electric charges. A moving POSITIVE charge generates a circular magnetic field that is perpendicular to the direction of the velocity. It is simple to represent by pointing the thumb of your RIGHT hand in the direction the POSITVE charge is moving and curling your fingers, the direction they point is the direction of the circular magnetic field surrounding the moving charge. The interaction of that field with the existing magnetic field gives rise to the Lorents Force.
Exactly how this works is not well understood. The most popular mechanism as explained by Maxwell and reproduced in the textbook by S.G. Starling, "Electricity and Magnetism for Degree Students" (7th Ed., 1941) p. 240, goes like this.
Imagine a magnetic field pointing from left to right across your screen (arrows point to the right). A positive charge travels away from you into the screen perpendicular to the magnetic field. The moving charge will generate a clockwise magnetic field around itself. At the top the magnetic lines around the charge point in the same direction as the surrounding magnetic field, at the bottom they point in opposite directions. The magnetic field warps around the moving charge so that more field lines are on top resulting in a greater concentration (they are pushed closer together) causing a downward force much like greater air pressure. At the bottom there are fewer filed lines similar to a low-pressure area in the air. The net result is a downward force acting on the charged particle.
This is a simplistic explanation and not universally accepted as true, but it is one plausible explanation and the easiest to understand. I leave it to you the reader to decide. I have included the link below if you want to read it for yourself.
www.conspiracyoflight.com/Lorentz/Lorentzforce.html
For those with more advanced degrees able to understand more complex mathematics here is a link to Saha's translation: The Principle of Relativity (1920), Calcutta: University Press, pp. 70-88, of the original German: Raum und Zeit (1909), Jahresberichte der Deutschen Mathematiker-Vereinigung, 1-14, B.G. Teubner
A Lecture delivered before the Naturforscher Versammlung (Congress of Natural Philosophers) at Cologne - (21st September, 1908).
Scroll down to section 12 which is actually an explanation of the force exerted by one moving charge on another, which can be used to understand the force acting on a charge moving through a magnetic field since the magnetic field around one of the charges can be used as the background magnetic field through which the second charge is moving.
en.wikisource.org/wiki/Translation:Space_and_Time
Amazing video. The only thing I don't like (and sadly this is a very bad one) is that you contradict the convention for representing the magnetic field. Crosses are the feathers of the arrow: if you see them, the arrow is pointing into the screen. If you see a dot, you are seeing the tip towards you from the screen. Fixing that would make for a perfect video.
So if there is no initial velocity of the charged particle placed in magnetic field will it be not affected in any way??
that's right
video on reimann hypothesis please Dr. Kumar Eswaran solved it 161 years later