The easy way to do this is to write down the E-field in the particle rest frame, plug it in to the Faraday tensor and Lorentz transform (remembering to transform the coordinates).aliinuur said:
Then it is clearly wrong. You have field lines intersecting where there is no charged particlealiinuur said:
it is 2D plot, black dots are the particle trace from bottom to top. Lines are the electric field linesIbix said:
Electric field lines should start on the charge; some of yours are closed loops. What are they?aliinuur said:
So it is clearly wrong for the reason I said above.aliinuur said:
i used circles to draw electric fields, no need to mind themIbix said:
I see.aliinuur said:
that figure is based on that every time the particle changes its positon information aboout it travels with the speed of light like waves on a puddle, thats how i got curved lines. It feels for me that straight lines mean infinite information travel velocityIbix said:
How would you propose to send any information via the straight lines from the E field of an inertially moving charge? They are straight. They do not send information faster than caliinuur said:
So your graph is not a graph of "electric field". It's a graph of "information about the position of the particle". Which just raises the question: what do you mean by "information about the position of the particle"? Math would help here.aliinuur said:
If E-field lines are straight it means even at infinited distance space derivative of E-field points in direction of the particle. Curved lines however point where the particle was in distance/c ago.Dale said:
So, let's say the particle is moving along the y axis at velocity v, so ##x=0##, ##y=vt##. You want to draw the field at ##t=0##, so you drew a circle of radius ##1c## centered on ##(x,y)=(0,-v)## with vectors all around it pointing at its center. Then you drew a circle of radius ##2c## centered on ##(0,-2v)##, with vectors all around it pointing at its center. And so on. And then you tried to draw the integral curves of this field?aliinuur said:
Well, you don't know that it hasn't accelerated. I wouldn't say that the field points at where the particle is now. Rather, it points at the forecast of where the charge should be now if it maintained its inertial motion in the time since our delayed image of it. The forecast happens to be correct in this case.aliinuur said:
You mean that in the frame/coordinate chart where the source charge is moving there is an Electric field and a magnetic field (due to the motion of the charge in that frame) as well. One can calculate both Electric and magnetic fields in that frame using Liénard–Wiechert potential.Ibix said:
First I draw a circle with radius c*5t and center at the origin, then a circle with radius c*4t pointing at (0,vt), then with radius c*3t pointing at (0, v*2t) and so on. The point is circle with radius c*t points where the particle was t ago.Ibix said:
Magnetic field is actually electric field stressed along one of the 3 dimensions, there are no magnetic fields in special relativity.Ibix said:
That's what I said, just with a different origin. Fine. And you have electric field vectors on those circles pointing at the center of each one?aliinuur said:
This is not correct. ##B^2-E^2## is an invariant, so if this is positive (i.e. ##|\vec B|>|\vec E|##) you can never make ##\vec B## zero by changing frames. In fact, although there is a certain amount of observer dependence in electric and magnetic fields, all six components of the two vectors (or the six independent components of the Faraday tensor, equivalently) are needed to describe an EM field. If you don't believe me, start in a frame where there is a uniform magnetic field pointing in the z direction and zero E field and try to find a frame in which this is purely an electric field.aliinuur said:
I dont get how one possibly get magnetic field with zero E-field. For me, this is like gravitaional field without a mass, or electric field without a charged particleIbix said:
The field around a straight current carrying conductor is a magnetic field with no electric field.aliinuur said:
The standard response to that is to point out that physics doesn't really care how unintuitive something seems to you. It is the way it is.aliinuur said:
there is electric field though.Ibix said:
yeah, how is magnetic field relevant to my question? you have started talking about magnetic fieldIbix said:
yeah, you got it rightrenormalize said:
I've a doubt here. In the model of straight conductor carrying current (a flow of electrons moving with constant velocity) is the net charge inside each volume/segment of the conductor supposed to be zero (due to the presence of positive metal ions) ?Ibix said:
you are right, even the hydrogen atom is a dipole, i.e. has a electric fieldcianfa72 said:
Since the 1s ground state of the hydrogen atom is spherically-symmetric, can you tell us in which direction this electric field points?aliinuur said:
its dipole moment has equal chance of pointing in any direction :)renormalize said:
