Today I repeated my experiment on the field due to a single turn of wire
carrying two amps.

It shows that the field rises towards to wire as the measurement point is
moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:
http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.

Chris wrote:
Today I repeated my experiment on the field due to a single turn of wire
carrying two amps.

It shows that the field rises towards to wire as the measurement point is
moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:
http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.



This is a nice measurement, but I fail to see why you think
it's surprising.

I'm not sure what you mean by "Gauss' prediction". I think
maybe you're either misinterpreting Gauss' Law for magnetism,
or somehow mixing it up with Ampere's Law, or both.

Or perhaps you're mixing up a single current loop with a
long solenoid??

In any event, the Biot-Savart Law is 100% consistent with
Ampere's Law and Gauss' Law.

On the other hand, if Gauss *did* make an incorrect
prediction for the field in a current loop, I'd appreciate
a reference

-Eric

Thank you.

I did think Gauss had predicted a constant magnetic field across the
diameter of a single turn.

Please point me to a recent elementary physics text where these things are
set out and explained.

If it had been explained to me when I was at school I would have spent the
last fourty years more profitably.

Brian washing is not a way to treat inquisitive school children. A good
discussion and demonstration is the way to go.

When I pointed this distribution of field out to my superiors I was met with
"don't ask that question" or "we should not ask these questions".

I though that the Gaussian construction of magnetic shells as applied to a
current loop showed that the field inside the loopp was constant. Now you
are saying it does not.

Another experiment I carried out today on a solenoid was entirely consistant
with Gauss. So what is special about a single turn? Please point me to a
text that will reveal the solution to my confusion.

..... Thank youu.
"Eric Prebys" wrote in message
...
Chris wrote:
Today I repeated my experiment on the field due to a single turn of wire
carrying two amps.

It shows that the field rises towards to wire as the measurement point
is
moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:

http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.



This is a nice measurement, but I fail to see why you think
it's surprising.

I'm not sure what you mean by "Gauss' prediction". I think
maybe you're either misinterpreting Gauss' Law for magnetism,
or somehow mixing it up with Ampere's Law, or both.

Or perhaps you're mixing up a single current loop with a
long solenoid??

In any event, the Biot-Savart Law is 100% consistent with
Ampere's Law and Gauss' Law.

On the other hand, if Gauss *did* make an incorrect
prediction for the field in a current loop, I'd appreciate
a reference

-Eric

Chris wrote:
Thank you.

I did think Gauss had predicted a constant magnetic field across the
diameter of a single turn.


Possible, but I seriously doubt it. Gauss had a tendency to get things
right.

Please point me to a recent elementary physics text where these things are
set out and explained.


The general field of a current loop is kind of ugly, so most elementary
physics books will restrict themselves to special cases, such as along
the axis or far away (i.e. the dipole field). Some might have the field
in the plane as a homework problem.

However, this is dealt with in almost all advanced E&M texts, usually
as an example of how to use the magnetic potential. Just looking
at my shelf, Jackson has it, as does Eyges "The Classical
Electromagnetic Field".

These are not "recent", but neither is E&M.

If it had been explained to me when I was at school I would have spent the
last fourty years more profitably.


I don't know what you're talking about, but before you spend
40 years on something, you might want to research it a bit more
carefully. This calculation was done well over 100 years ago.

Brian washing is not a way to treat inquisitive school children. A good
discussion and demonstration is the way to go.


I'm not sure where you went to college, but I certainly had plenty
of demonstrations and lab exercises involving magnetic fields.

When I pointed this distribution of field out to my superiors I was met with
"don't ask that question" or "we should not ask these questions".

I though that the Gaussian construction of magnetic shells as applied to a
current loop showed that the field inside the loopp was constant. Now you
are saying it does not.


I'm not sure what you mean by "Gaussian construction of magnetic
shells". When applied to magnetic fields, Gauss's law tells us
that the total magnetic flux through any *closed* surface is
exactly zero. This is just a statement that there are no
magnetic monopoles (at least none have ever been found).

You might be confusing this with Ampere's Law, which tells
us the integrated magnetic field around any closed path.
Unfortunately, this can only be used to calculate the
field *if* you can invoke some symmetry to relate the
integrated field to the value at any point along the path.
You can't in the case of a single current loop.

Another experiment I carried out today on a solenoid was entirely consistant
with Gauss. So what is special about a single turn? Please point me to a
text that will reveal the solution to my confusion.


The relationship between a single turn and a solenoid is
more or less the same as the relationship between the
electric field from a line of charge and uniform plane
of charge; that is, when you integrate the field
(correctly), you actually get a much simpler expression.

Solenoidal fields are calculated in virtually every
E&M and intro physics texts using Ampere's Law and
a bit of hand-waving. Some texts might have you show
that the Biot-Savart Law gives you the same answer
as a homework problem (not so hard along the axis,
kind of ugly elsewhere).

-Eric

.... Thank youu.
"Eric Prebys" wrote in message
...

Chris wrote:

Today I repeated my experiment on the field due to a single turn of wire
carrying two amps.

It shows that the field rises towards to wire as the measurement point

is

moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:


http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.



This is a nice measurement, but I fail to see why you think
it's surprising.

I'm not sure what you mean by "Gauss' prediction". I think
maybe you're either misinterpreting Gauss' Law for magnetism,
or somehow mixing it up with Ampere's Law, or both.

Or perhaps you're mixing up a single current loop with a
long solenoid??

In any event, the Biot-Savart Law is 100% consistent with
Ampere's Law and Gauss' Law.

On the other hand, if Gauss *did* make an incorrect
prediction for the field in a current loop, I'd appreciate
a reference

-Eric

Hi,

Thank you for your chat. From what you say about the current loop, it may
be that the lecturer who taught me the theory of magnetic shells as applied
to a current loop, learned his E&M from another book.

We did do plane charged sheets and charged wires where a little Gauss box
was put round to enclose the charge and the field calculated, one result was
that there is no resultant field inside any electostatically charged
enclosure. The Farasday cage is an example of its application.

However the geometry of a magnetic shell is that of a current loop with no
resultant field inside so that the magnetic flux on the surface of the plane
of the shell is uniform, similar to the Farady cage or the Newtonian theory
of gravitational shells.

I think now that the measurements I made yesterday on the current loop of a
single turn were subject to errors. All my measurements of both experiments
are extremely inaccurate but I did not expect the single turn to have a peak
near the wire even though it has been observed many times before.

It could be that the single turn is too thin for accurate measurements to be
made.

The off-axis field of either a solenoid or a single turn when calculated by
the Biot-Savart hypothesis is very messy and I cannot do it analytically. I
have never seen the calculation in any text book and when I attempted the
calculation it was numerical. However my maths is not brilliant and is is
obviously mistaken as my calculation predicted a rise toward the wire in
both cases. But then I took a solenoid to be a sucsession of loops and
summed. If the calculation for the loop is wrong then all of it is.

Can you give the isbn number of the best textbook (by that I mean the
clearest) where they give the calculation by Biot-Savart of the off axis
field? I only have undergraduate General degree maths so nothing too
complicated! And it was taken thirty years ago. (I got a 2.2).

I've obviously not spent forty years worrying about this but it has come up
from time to time. It would be nice to get one of those things I have
never really understood in place. But then perhaps I'm thick!

Chris.
"Eric Prebys" wrote in message
...
Chris wrote:
Thank you.

I did think Gauss had predicted a constant magnetic field across the
diameter of a single turn.


Possible, but I seriously doubt it. Gauss had a tendency to get things
right.

Please point me to a recent elementary physics text where these things
are
set out and explained.


The general field of a current loop is kind of ugly, so most elementary
physics books will restrict themselves to special cases, such as along
the axis or far away (i.e. the dipole field). Some might have the field
in the plane as a homework problem.

However, this is dealt with in almost all advanced E&M texts, usually
as an example of how to use the magnetic potential. Just looking
at my shelf, Jackson has it, as does Eyges "The Classical
Electromagnetic Field".

These are not "recent", but neither is E&M.

If it had been explained to me when I was at school I would have spent
the
last fourty years more profitably.


I don't know what you're talking about, but before you spend
40 years on something, you might want to research it a bit more
carefully. This calculation was done well over 100 years ago.

Brian washing is not a way to treat inquisitive school children. A good
discussion and demonstration is the way to go.


I'm not sure where you went to college, but I certainly had plenty
of demonstrations and lab exercises involving magnetic fields.

When I pointed this distribution of field out to my superiors I was met
with
"don't ask that question" or "we should not ask these questions".

I though that the Gaussian construction of magnetic shells as applied to
a
current loop showed that the field inside the loopp was constant. Now
you
are saying it does not.


I'm not sure what you mean by "Gaussian construction of magnetic
shells". When applied to magnetic fields, Gauss's law tells us
that the total magnetic flux through any *closed* surface is
exactly zero. This is just a statement that there are no
magnetic monopoles (at least none have ever been found).

You might be confusing this with Ampere's Law, which tells
us the integrated magnetic field around any closed path.
Unfortunately, this can only be used to calculate the
field *if* you can invoke some symmetry to relate the
integrated field to the value at any point along the path.
You can't in the case of a single current loop.

Another experiment I carried out today on a solenoid was entirely
consistant
with Gauss. So what is special about a single turn? Please point me to
a
text that will reveal the solution to my confusion.


The relationship between a single turn and a solenoid is
more or less the same as the relationship between the
electric field from a line of charge and uniform plane
of charge; that is, when you integrate the field
(correctly), you actually get a much simpler expression.

Solenoidal fields are calculated in virtually every
E&M and intro physics texts using Ampere's Law and
a bit of hand-waving. Some texts might have you show
that the Biot-Savart Law gives you the same answer
as a homework problem (not so hard along the axis,
kind of ugly elsewhere).

-Eric

.... Thank youu.
"Eric Prebys" wrote in message
...

Chris wrote:

Today I repeated my experiment on the field due to a single turn of
wire
carrying two amps.

It shows that the field rises towards to wire as the measurement point

is

moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:



http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.



This is a nice measurement, but I fail to see why you think
it's surprising.

I'm not sure what you mean by "Gauss' prediction". I think
maybe you're either misinterpreting Gauss' Law for magnetism,
or somehow mixing it up with Ampere's Law, or both.

Or perhaps you're mixing up a single current loop with a
long solenoid??

In any event, the Biot-Savart Law is 100% consistent with
Ampere's Law and Gauss' Law.

On the other hand, if Gauss *did* make an incorrect
prediction for the field in a current loop, I'd appreciate
a reference

-Eric

FYI, some formulae for current loops that you may not have seen:

http://www.netdenizen.com/emagnet/of...oopoffaxis.htm

Field is not constant in the plane of the loop!

Eric

On Thu, 18 Sep 2003 11:00:54 +0100, "Chris"
wrote:

Today I repeated my experiment on the field due to a single turn of wire
carrying two amps.

It shows that the field rises towards to wire as the measurement point is
moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:
http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.

Chris wrote:
Hi,

Thank you for your chat. From what you say about the current loop, it may
be that the lecturer who taught me the theory of magnetic shells as applied
to a current loop, learned his E&M from another book.


If any textbooks disagree about the field from a current loop, they are
wrong.

We did do plane charged sheets and charged wires where a little Gauss box
was put round to enclose the charge and the field calculated, one result was
that there is no resultant field inside any electostatically charged
enclosure. The Farasday cage is an example of its application.

However the geometry of a magnetic shell is that of a current loop with no
resultant field inside so that the magnetic flux on the surface of the plane
of the shell is uniform, similar to the Farady cage or the Newtonian theory
of gravitational shells.


I suspect you misunderstood the lecture.

I think now that the measurements I made yesterday on the current loop of a
single turn were subject to errors. All my measurements of both experiments
are extremely inaccurate but I did not expect the single turn to have a peak
near the wire even though it has been observed many times before.

It could be that the single turn is too thin for accurate measurements to be
made.

The off-axis field of either a solenoid or a single turn when calculated by
the Biot-Savart hypothesis is very messy and I cannot do it analytically. I
have never seen the calculation in any text book and when I attempted the
calculation it was numerical. However my maths is not brilliant and is is
obviously mistaken as my calculation predicted a rise toward the wire in
both cases. But then I took a solenoid to be a sucsession of loops and
summed. If the calculation for the loop is wrong then all of it is.

You have to be careful to sum the vector components correctly.

Starting from scratch to calculate the field in a solenoid from
the Biot-Savart Law is very hard.

You can cheat and calculate the field just at the center and
then integrate it for a series of loops. You'll find that it's
fairly constant once you get away from the ends. Because the
magnetic field is divergenceless, the fact that it's constant
with longitudinal position also implies it's uniform (think
about how the field lines look).


Can you give the isbn number of the best textbook (by that I mean the
clearest) where they give the calculation by Biot-Savart of the off axis
field? I only have undergraduate General degree maths so nothing too
complicated! And it was taken thirty years ago. (I got a 2.2).


It's handled in Jackson "Classical Electrodynamics" and Eyges
"The Classical Electromagnetic Field". There are probably better
texts out there. E&M hasn't changed, but teaching has.

The general expression is extremely ugly however you do it,
and in any practical case where you needed it, you would likely
do it numerically.

-Eric

I've obviously not spent forty years worrying about this but it has come up
from time to time. It would be nice to get one of those things I have
never really understood in place. But then perhaps I'm thick!

Chris.
"Eric Prebys" wrote in message
...

Chris wrote:

Thank you.

I did think Gauss had predicted a constant magnetic field across the
diameter of a single turn.


Possible, but I seriously doubt it. Gauss had a tendency to get things
right.


Please point me to a recent elementary physics text where these things

are

set out and explained.


The general field of a current loop is kind of ugly, so most elementary
physics books will restrict themselves to special cases, such as along
the axis or far away (i.e. the dipole field). Some might have the field
in the plane as a homework problem.

However, this is dealt with in almost all advanced E&M texts, usually
as an example of how to use the magnetic potential. Just looking
at my shelf, Jackson has it, as does Eyges "The Classical
Electromagnetic Field".

These are not "recent", but neither is E&M.


If it had been explained to me when I was at school I would have spent

the

last fourty years more profitably.


I don't know what you're talking about, but before you spend
40 years on something, you might want to research it a bit more
carefully. This calculation was done well over 100 years ago.


Brian washing is not a way to treat inquisitive school children. A good
discussion and demonstration is the way to go.


I'm not sure where you went to college, but I certainly had plenty
of demonstrations and lab exercises involving magnetic fields.


When I pointed this distribution of field out to my superiors I was met

with

"don't ask that question" or "we should not ask these questions".

I though that the Gaussian construction of magnetic shells as applied to

a

current loop showed that the field inside the loopp was constant. Now

you

are saying it does not.


I'm not sure what you mean by "Gaussian construction of magnetic
shells". When applied to magnetic fields, Gauss's law tells us
that the total magnetic flux through any *closed* surface is
exactly zero. This is just a statement that there are no
magnetic monopoles (at least none have ever been found).

You might be confusing this with Ampere's Law, which tells
us the integrated magnetic field around any closed path.
Unfortunately, this can only be used to calculate the
field *if* you can invoke some symmetry to relate the
integrated field to the value at any point along the path.
You can't in the case of a single current loop.


Another experiment I carried out today on a solenoid was entirely

consistant

with Gauss. So what is special about a single turn? Please point me to

a

text that will reveal the solution to my confusion.


The relationship between a single turn and a solenoid is
more or less the same as the relationship between the
electric field from a line of charge and uniform plane
of charge; that is, when you integrate the field
(correctly), you actually get a much simpler expression.

Solenoidal fields are calculated in virtually every
E&M and intro physics texts using Ampere's Law and
a bit of hand-waving. Some texts might have you show
that the Biot-Savart Law gives you the same answer
as a homework problem (not so hard along the axis,
kind of ugly elsewhere).

-Eric


.... Thank youu.
"Eric Prebys" wrote in message
...


Chris wrote:


Today I repeated my experiment on the field due to a single turn of

wire

carrying two amps.

It shows that the field rises towards to wire as the measurement point

is


moved away from the centre of the loop.
For photographs of the apparatus and the observations,
see:


http://www.chrisweb.pwp.blueyonder.c...gle%20Turn.htm

Any comments would be appreciated.

Please contact me on mailto:chris@(remove this)chrisscrazyideas.co.uk

Thanks

Chris.



This is a nice measurement, but I fail to see why you think
it's surprising.

I'm not sure what you mean by "Gauss' prediction". I think
maybe you're either misinterpreting Gauss' Law for magnetism,
or somehow mixing it up with Ampere's Law, or both.

Or perhaps you're mixing up a single current loop with a
long solenoid??

In any event, the Biot-Savart Law is 100% consistent with
Ampere's Law and Gauss' Law.

On the other hand, if Gauss *did* make an incorrect
prediction for the field in a current loop, I'd appreciate
a reference

-Eric