what does a moving charge experience when it is near a magnetic field This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you Why do moving charges produce magnetic fields?. Following along are instructions in the video below:
Everyone here we are with some physics fundamentals so magnetic field is created only by by moving charges. But why well but at first it started with a mail from he said every book i can apple says one thing that only moving charges can produce magnetic field and not the static charges. But no one is answering why well so thats really a big problem here is the answer.
But at first it would be better if you take a pen and paper and sit in front of this video and in the every calculation with us well so lets start it here. We have two frames s and s prime. We will do some special theory of relativity in this video.
If you know special theory of relativity. Thats great. But if you dont then also its not a big problem you will understand the concept okay.
So there are two frames s and s prime how are they connected s. Prime is moving with velocity v. Along x direction.
And they have a common x axis. Now what is the relation between these two frames. The relation is governed by a factor gamma where gamma equals to 1 by root under 1 minus v.
Square by c square where c is the velocity of light now how does gamma govern the relation between these two frames. Well see. But before that we have two charges q.
1. And q. 2 in s.
Prime frame now keep it in mind. If you are in s. Prime frame.
The charges are actually in rest with respect to you. But if you are in s. Prime.
The charges are moving with respect to you ok so if the distance between q. 1. And q.
2. Is our then in s. Prime frame.
The forces are simple if x prime equals to 0. Because there is no charge in x. Prime direction.
If y prime equals to the simple. Electrostatic force 1. By 4 pie epsilon not into q 1 q.
2 r square. If jet prime equals to again zero now in astrium every force will be defined by multiplying. 1.
By gamma into the force in s. Prime. Frame.
Like if x. Plus. 2.
1. By gamma into fx. Prime equals to zero.
If y. Equal to 1.
By gamma into f. Y. Prime.
Equals to 1. By gamma into the electrostatic force. 1.
By 4 pie epsilon. Not into p 1 q. 2.
By r square. If jet equals to 1 by gamma into fz prime equals to 0. Is that fine after now well lets move forward for simplicity.
Lets take q. 1. Equal.
To q. 2. Equal to q.
Which means if y equal to 1. By gamma into a phi prime that was before equals to gamma into 1. By gamma square into 1.
By 4 pie epsilon not into q square by r square. Well. That means equals to gamma into 1 by gamma square means 1 minus p square by c square right so equals to gamma into 1 minus v.
Square by c square into 1 by 4 pie epsilon not into q square by r square. Now. What we will do is well multiply this one with this factor and then again v square.
By c square with this factor. So then this becomes gamma into 1. By 4 pie epsilon.
Not into q square by r squared minus. 1. By 4 pi epsilon naught c square into p.
Squared q. Square. By r square.
So please close this v square. By c square. Is multiplied.
Here. Here is bri square and here is c square right. Hope.
There is no confusion then now practically. 3 equals. 2.
Electron moves with a velocity field well. 2. Is the order of 10 to the power minus 4.
And c. The order of 10 to the power. 8.
Now p square by c square. Is again order of say 10 to the power minus 24.
So that means gamma is practically 1. Another thing is that 1 by c square equal to mu naught epsilon naught. Where mu naught is the magnetic permeability in backcomb okay so then putting these values.
So well put gamma equals to 1 and 1. By c square equals to mu naught epsilon naught. So if we put gamma equals to 1.
Only this remains right and 1 by c square equal to mu naught epsilon naught. Then epsilon naught will cancel only mu naught will remain in the above okay. So if white wells 2 1.
By 4 pi epsilon naught q square by r square minus mu chart mu 0. By 4 pi into d square q. Square by r square well so now.
See. The this term is the field dependent term right the simple intercept attic pores. You will see if you are in spm.
But there is an extra part also which is like mu. 0. By 4 pi into p.
Squared q. Square. By r square.
So this part also already looks like something magnetic right so well go for that and actually we found by osowiec law. Each here ok. So this is the velocity dependent term with vector notation fy.
12. To 1. By 4 pi epsilon naught into q square by r square minus.
Mu naught by 4 pi into v square q. Square by r square into j. Camp right so the force will we are seeing is in the y direction.
Only but so we can write so j comes here so if i create to 1 by 4 pi epsilon naught q. Square by r squared j. Cap.
There is no confusion this has become plus because j equal to k cross. I but we are writing i trust k. So j equal to minus.
I cross k. So this minus and this minus gives you a plus right so mu naught by 4 pi into v square by q square. I cross k.
Now if we write only the best independent term then because the other term is simple electrostatic force. There is no point in writing this again and again. We will see only this part okay so if i feel the peapod velocity dependent equal to mu naught by 4 pi b square q.
Square by a square into. I cross k. Equals to q.
Into p. Vector. Because if we write if we take 1 qb outside then qp.
I cap now velocity is along x direction. So we can write p. I cap.
Equals to v. Vector.
So q into v. Vector. Cross nu naught by 4 pie into qb by r square k.
Cap again till. It works to i cross j. Okay.
So equals to q. V. Vector.
In 2. Mu. Naught by 4 pi qb by r square.
I cross j. Now we can write q. Pik f.
Equal to ai. Tilta l. Where i is the current and delta l.
Is the length element in the where of the current. Okay and check app. Equal to r cap.
Because the charges are separated in y direction. So the unit vector. Along their separation.
Is equals to the unit. Vector in y direction. Right.
So. Then. If yt equals to q into v.
Vector. Cross mu naught. By 4 pi.
I delta l. Cross r. Cap by r square.
Now. See you already get the bio sauvarts law. Here.
And the total force is given by f. Yp. Plus.
2. Q. P.
Cross p. Because. This is this total is the magnetic field.
So. Qv cross b. Is the total lorentz force right okay.
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