i think my comment didn't post : the magnetic field outside of a solenoid is not 0, it just drops quickly because it isn't contained. As such, if you flip the current or the solenoid, the crt image will tilt in the opposite direction.
For an ideal infinitely long solenoid, the magnetic field is absolutely zero. It must not vary, otherwise Ampere's law is violated. But absolute zero does not exist. For my solenoid, the magnetic field is 0.7% of the central field.
can you explain why this would be the case? I imagine the 2 dimensional case per ring: -out of the page current at the top dot, into the page current at the bottom dot -results in magnetic field leftwards straight above + slightly weaker (cause farther away) magnetic field rightwards. -sum is field pointing to the left above each each ring. -all adjacent rings will create a field left+down or left+up at this same point and as the rings extend to infinity, the field they create will just be down+up and will cancel.
replace each coil with 2 vertically seperated points with current coming out of the page at the top point, and into the page at the bottom. Point above some coil = P
at P, coil(x) produced leftwards net B field , coil(x-w) produce left+up net B field , coil(x+w) produce left+down net B field , coil(x-infinity) produces an infinitely small upwards B field , coil(x+infinity) produces an infinitely small downward B field
the sum of these at point P results in a leftward field. P is above the coil which means P is outside of the solenoid.
So how is there no magnetic field outside of an infinitely long solenoid?
just read a bunch and it looks like it is 0 outside, but i'm not sure where the above argument fails. That being said, your solenoid definitely has a field outside which is pushing the electrons. You can verify this by making the solenoid even longer and seeing a drop in shift. What does your theory predict about a toroidal solenoid's effect on the ray tube?
Here is a figure that shows how to compute the magnetic field in and out of a solenoid. http://phy214uhart.wikispaces.com/file/view/solenoid3.bmp/82803565/solenoid3.bmp
The closed loop "abcd" is the path along which the line integral of magnetic field is done. Then, the closed line integral is: Amp = integral on (ab) + integral on (bc) +integral on (cd) + integral on (da)
The solenoid is infinitely long, so the magnetic field is parallel to it. As the field vector is perpendicular to the path "bc" and "ad" the value of the line integral along them are zero: integral on (bc)=0 integral on (da)=0
Then: Amp = integral on (ab) + integral on (cd)
Now put the "ab" outside the solenoid as shown by the figure http://upload.wikimedia.org/wikipedia/commons/7/79/Solenoid_with_3_loops_%281%29.png in which the closed line integral along the path a is zero, because there is no current inside.
Then: Amp = integral on (ab) + integral on (cd) = 0
So for all rectangle outside, integral on (ab) = - integral on (cd)
The magnetic field is zero at infinitely far, so fo "cd" infinitely far: integral on (cd) =0
We have for all points outside the solenoid: integral on (ab) = 0
So, the field is zero for all points outside the solenoid.
the issue I have with that argument is that you can apply it to a finite lengths solenoid, and i the path is centered, all of the above would still be correct. But we know for a fact that a solenoid, and a bar magnet, have a magnetic field all around them - more concentrated near the poles.
I have drawn a figure to explain how the vectors cancel. https://lh3.googleusercontent.com/-Q8HspNgAEhc/VVUao4JV66I/AAAAAAAAAcI/e3Sfc3xuInc/w1320-h821-no/Solenoid%2Bfield%2Bvector.JPG
The central winding creates the black vector. The left one creates the blue and the right one the red. When we add the blue and the red, they sum up to a horizontal vector contrary to the black one. When all the windings are added up, the black one is canceled by the blues and reds.
This is a classical theoretical result. For an infinitely long solenoid, the poles are far away so that their field is zero in the center. But this result is contradicted by my experiment.
Ok, I just forgot to switch my hand direction for the opposite side of the ring. Makes sense now.
That being said, while the magnetic field outside of your not-super-long solenoid isn't very strong, it seems to be strong enough to move the electrons considerably.
One of three things must be happening:
-your under estimate the magnetic field outside of the coil. You can try to build a much longer coil to perhaps get closer to 0 field outside...or you can make a torus, which should be 0 outside if it's closed.
or
-the coil itself along with whatever circuit is in is affecting the inductance of the coils in the tube, which affect how they perform. Flipping the current shouldn't then flip the affect, but from your text it seems that it did.
-something else is happening that doesn't follow theory
I think it's most likely the first one - but let's say its the last one, you mentioned some transverse magnetic field. Can you draw out what this field would be outside of a single coil of wire.
It cannot be the first, underestimation. For showing this, I have placed the end of the solenoid next to the screen and shown how much the deflection is. Sequence 15. Then I placed the solenoid above the screen to show how much the deflection is in the center field, sequence 16. We see that the deflection is of the same order. For classical theory, the field in the center is 0.6% of that at the end. This is not the case in the experiment.
In fact, the field outside is of tensor nature. Classical theory uses vector for magnetic field but it cannot describe tensor field. Tensor field is what the classical theory does not handle and creates this inconsistency. The vector field in the center is zero but not the tensor one. Below are the articles in which I explain tensor field.
However, I will do an experiment which will compare the strength of force in the center and near the end. This way, one will understand that the force is really out of proportion in the center.
OK; good demonstration, Peng. I had a similar conversation with a "professor" that worked with Aharonov in some AB set-ups...and tried to point out from the exper. set-up that the phase change was actually a result of (and could equally be explained by) a "bending" in the electron beam...a suggestion he resisted. You set=up seems to suggest that also.... Your conclusion (that there is a "magnetic field" outside that is responsible) is not necessarily true however. IMHO; it merely points to the fact that the Vector potentials are providing far more physical effect than is classically allowed and cannot be completely attributed to the "fields" .... a supposition I have held for a long time. IOWs; it is entirely possible that the B "FIELDS" outside the coil are zero and yet it is the Vector Potential that is providing the phase shift, AND alters the electron course. However, I have not fully reviewed your other theoretics, etc. in this blog... I will try to read when I get time. I pulled your original discussion off Physorg forums where I am ... Lunar landing
In fact, My experiment shows that the electron beam is deflected by the current in the solenoid. But it does not decide what of the field or potential was really responsible. In my next experiment, there will possible be an clearer answer. In fact, I have found that the direction of the B field is opposite to what is predicted, that is, the B outside and inside have the same direction.
I have put the same coil near the top of the solenoid, see this blog A 1.95 m long solenoid exerting Aharonov–Bohm force on a coil http://pengkuanem.blogspot.com/2015/10/a-195-m-long-solenoid-exerting.html .
When moving toward the center, I notice that the rotation of the coil changed direction, signaling a change of direction of the B field.
I have posted my response to your apparent problem with rotating coil near a magnet in the BlogSpot above.... the solution is simply by realizing that the B field around the magnet is NOT uniform... All that is required for an induced current to appear in the coil (according to Faraday Law) is that the coil "experience" a change in B field with time. The rotating coil in your example outside the edges of a magnet experiences a changing flux as it intersects a NON-Uniform magnetic field.... IOW, it intersects a B field gradient. Thus no problem with Faradays law. Lunar
I have explained here http://pengkuanem.blogspot.fr/2014/12/tangential-emf-experiment.html that whatever the field shape is, the field lines cancel and no flux variation exists.
i think my comment didn't post
ReplyDelete: the magnetic field outside of a solenoid is not 0, it just drops quickly because it isn't contained. As such, if you flip the current or the solenoid, the crt image will tilt in the opposite direction.
For an ideal infinitely long solenoid, the magnetic field is absolutely zero. It must not vary, otherwise Ampere's law is violated. But absolute zero does not exist. For my solenoid, the magnetic field is 0.7% of the central field.
Deletecan you explain why this would be the case?
DeleteI imagine the 2 dimensional case per ring:
-out of the page current at the top dot, into the page current at the bottom dot
-results in magnetic field leftwards straight above + slightly weaker (cause farther away) magnetic field rightwards.
-sum is field pointing to the left above each each ring.
-all adjacent rings will create a field left+down or left+up at this same point and as the rings extend to infinity, the field they create will just be down+up and will cancel.
So why would it be 0?
You ask "So why would it be 0?"
DeleteAnd your "the field they create will just be down+up and will cancel" is the explanation. I do not understand your mind. Please explain.
replace each coil with 2 vertically seperated points with current coming out of the page at the top point, and into the page at the bottom.
DeletePoint above some coil = P
at P, coil(x) produced leftwards net B field
, coil(x-w) produce left+up net B field
, coil(x+w) produce left+down net B field
, coil(x-infinity) produces an infinitely small upwards B field
, coil(x+infinity) produces an infinitely small downward B field
the sum of these at point P results in a leftward field. P is above the coil which means P is outside of the solenoid.
So how is there no magnetic field outside of an infinitely long solenoid?
just read a bunch and it looks like it is 0 outside, but i'm not sure where the above argument fails. That being said, your solenoid definitely has a field outside which is pushing the electrons. You can verify this by making the solenoid even longer and seeing a drop in shift.
DeleteWhat does your theory predict about a toroidal solenoid's effect on the ray tube?
Can I explain with Ampere's law?
DeleteHere is a figure that shows how to compute the magnetic field in and out of a solenoid.
http://phy214uhart.wikispaces.com/file/view/solenoid3.bmp/82803565/solenoid3.bmp
The closed loop "abcd" is the path along which the line integral of magnetic field is done. Then, the closed line integral is:
Amp = integral on (ab) + integral on (bc) +integral on (cd) + integral on (da)
The solenoid is infinitely long, so the magnetic field is parallel to it. As the field vector is perpendicular to the path "bc" and "ad" the value of the line integral along them are zero:
integral on (bc)=0
integral on (da)=0
Then:
Amp = integral on (ab) + integral on (cd)
Now put the "ab" outside the solenoid as shown by the figure
http://upload.wikimedia.org/wikipedia/commons/7/79/Solenoid_with_3_loops_%281%29.png
in which the closed line integral along the path a is zero, because there is no current inside.
Then:
Amp = integral on (ab) + integral on (cd) = 0
So for all rectangle outside,
integral on (ab) = - integral on (cd)
The magnetic field is zero at infinitely far, so fo "cd" infinitely far:
integral on (cd) =0
We have for all points outside the solenoid:
integral on (ab) = 0
So, the field is zero for all points outside the solenoid.
the issue I have with that argument is that you can apply it to a finite lengths solenoid, and i the path is centered, all of the above would still be correct. But we know for a fact that a solenoid, and a bar magnet, have a magnetic field all around them - more concentrated near the poles.
DeleteI have drawn a figure to explain how the vectors cancel.
Deletehttps://lh3.googleusercontent.com/-Q8HspNgAEhc/VVUao4JV66I/AAAAAAAAAcI/e3Sfc3xuInc/w1320-h821-no/Solenoid%2Bfield%2Bvector.JPG
The central winding creates the black vector. The left one creates the blue and the right one the red. When we add the blue and the red, they sum up to a horizontal vector contrary to the black one. When all the windings are added up, the black one is canceled by the blues and reds.
This is a classical theoretical result. For an infinitely long solenoid, the poles are far away so that their field is zero in the center. But this result is contradicted by my experiment.
Ok, I just forgot to switch my hand direction for the opposite side of the ring. Makes sense now.
DeleteThat being said, while the magnetic field outside of your not-super-long solenoid isn't very strong, it seems to be strong enough to move the electrons considerably.
One of three things must be happening:
-your under estimate the magnetic field outside of the coil. You can try to build a much longer coil to perhaps get closer to 0 field outside...or you can make a torus, which should be 0 outside if it's closed.
or
-the coil itself along with whatever circuit is in is affecting the inductance of the coils in the tube, which affect how they perform. Flipping the current shouldn't then flip the affect, but from your text it seems that it did.
-something else is happening that doesn't follow theory
I think it's most likely the first one - but let's say its the last one, you mentioned some transverse magnetic field. Can you draw out what this field would be outside of a single coil of wire.
It cannot be the first, underestimation. For showing this, I have placed the end of the solenoid next to the screen and shown how much the deflection is. Sequence 15. Then I placed the solenoid above the screen to show how much the deflection is in the center field, sequence 16. We see that the deflection is of the same order. For classical theory, the field in the center is 0.6% of that at the end. This is not the case in the experiment.
DeleteIn fact, the field outside is of tensor nature. Classical theory uses vector for magnetic field but it cannot describe tensor field. Tensor field is what the classical theory does not handle and creates this inconsistency. The vector field in the center is zero but not the tensor one. Below are the articles in which I explain tensor field.
http://pengkuanem.blogspot.com/2013/09/correction-to-biot-savart-law.html
http://pengkuanem.blogspot.com/2013/06/macroscopic-aharonovbohm-effect.html
http://pengkuanem.blogspot.com/2013/09/why-magnetic-field-must-be-tensor.html
However, I will do an experiment which will compare the strength of force in the center and near the end. This way, one will understand that the force is really out of proportion in the center.
OK; good demonstration, Peng. I had a similar conversation with a "professor" that worked with Aharonov in some AB set-ups...and tried to point out from the exper. set-up that the phase change was actually a result of (and could equally be explained by) a "bending" in the electron beam...a suggestion he resisted. You set=up seems to suggest that also....
DeleteYour conclusion (that there is a "magnetic field" outside that is responsible) is not necessarily true however. IMHO; it merely points to the fact that the Vector potentials are providing far more physical effect than is classically allowed and cannot be completely attributed to the "fields" .... a supposition I have held for a long time.
IOWs; it is entirely possible that the B "FIELDS" outside the coil are zero and yet it is the Vector Potential that is providing the phase shift, AND alters the electron course.
However, I have not fully reviewed your other theoretics, etc. in this blog... I will try to read when I get time.
I pulled your original discussion off Physorg forums where I am ...
Lunar landing
Thanks.
DeleteIn fact, My experiment shows that the electron beam is deflected by the current in the solenoid. But it does not decide what of the field or potential was really responsible. In my next experiment, there will possible be an clearer answer. In fact, I have found that the direction of the B field is opposite to what is predicted, that is, the B outside and inside have the same direction.
What did you use to make you think the "direction" of the B field outside is the 'same" as the inside ?
DeleteI have put the same coil near the top of the solenoid, see this blog
DeleteA 1.95 m long solenoid exerting Aharonov–Bohm force on a coil
http://pengkuanem.blogspot.com/2015/10/a-195-m-long-solenoid-exerting.html .
When moving toward the center, I notice that the rotation of the coil changed direction, signaling a change of direction of the B field.
I have posted my response to your apparent problem with rotating coil near a magnet in the BlogSpot above.... the solution is simply by realizing that the B field around the magnet is NOT uniform... All that is required for an induced current to appear in the coil (according to Faraday Law) is that the coil "experience" a change in B field with time. The rotating coil in your example outside the edges of a magnet experiences a changing flux as it intersects a NON-Uniform magnetic field.... IOW, it intersects a B field gradient. Thus no problem with Faradays law.
DeleteLunar
I have explained here
Deletehttp://pengkuanem.blogspot.fr/2014/12/tangential-emf-experiment.html
that whatever the field shape is, the field lines cancel and no flux variation exists.