I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round.

But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:

I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

You might want to look at the equations in their integral forms. They
seem to be a bit easier to interpret and you can usually picture what
is actually happening much better. For instance, Faraday's law
becomes simply emf = -dflux/dt.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But we don't usually solve maxwell's differential equations for E and
B. We mostly solve the differential equations in the potentials under
the appriopriate boundary conditions. Even more easily, we can
sometimes solve the integral forms of the equations, providing the
system possesses sufficient symmetry.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round.

I think you've got it a bit backwards. Faraday's law says that a
changing magnetic field induces an electric field. This is,
fortunately, a lot more easily pictured by using the integral form
above.

But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

This doesn't really matter. All Faraday's law is concerned with is a
changing B field, no matter what is causing it. And then E is a
consequence of the changing B.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This is Ampere's law in the absence of ordinary currents. And it is
just the opposite of Faraday's. A changing electric field generates a
magnetic field. Again, this one is much more easily pictured in the
integral form, where it becomes Int (B.dr) = - ep0 mu0 dflux/dt, where
the flux here is electric and not magnetic.

On 16 Maj, 18:46, Igor <thoov...@excite.com> wrote:
On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:

I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

Hmm, a typo. I meant of course that I consider _curl E_ as a measure
of the "discrepancy" of E, which causes _B_ to change,

I think you've got it a bit backwards. Faraday's law says that a
changing magnetic field induces an electric field. This is,
fortunately, a lot more easily pictured by using the integral form
above.

But why can't it equally well be interpreted as saying that curl E
causes B to change? To me, this seems more natural, mathematically.

"Igor" <thoov...@excite.com> wrote in messagenews:1179334006.157965.81870@n59g2000hsh.googlegroups.com...
On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

He might have made a few typos there.
I think he meant to say something like
| But, from a mathematical standpoint, this seems a little
| odd. Isn't it more natural to view the equation this way:
| The "discrepancy" of E causes B to change? Here, curl E is
| considered as a measure of the "discrepancy" of E.
| Zero curl of E means no [spatial] discrepancy in E and
| therfore no [temporal] change of B. I'm imagining that the
| fields try to "flatten out", getting rid of the discrepancies ...
| ... [etc]

An original viewpoint

On 16 Maj, 19:02, "Dirk Van de moortel" <dirkvandemoor...@ThankS-NO-
SperM.hotmail.com> wrote:
"Igor" <thoov...@excite.com> wrote in messagenews:1179334006.157965.81870@n59g2000hsh.googlegroups.com...
On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

He might have made a few typos there.
I think he meant to say something like
| But, from a mathematical standpoint, this seems a little
| odd. Isn't it more natural to view the equation this way:
| The "discrepancy" of E causes B to change? Here, curl E is
| considered as a measure of the "discrepancy" of E.
| Zero curl of E means no [spatial] discrepancy in E and
| therfore no [temporal] change of B. I'm imagining that the
| fields try to "flatten out", getting rid of the discrepancies ...
| ... [etc]

An original viewpoint :-)

Yes, that's precisely what I mean. Thank's Dik. Not sure how original
is, though, I wonder if not Maxwell had similar thoughts, although he
imagined fluctuations in an ether that we know doesn't exist.

Anyway, this view seems to me as a natural one, mathematically, giving
rise to a system of PDEs with a set of initial values at time t=0. But
when I try to understand it physically, it makes no sense...

I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.
I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round. But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This seems to go in circles, I can't get it to make sense. Can you?

Regards,

Erland Gadde

"Erland Gadde" <erland@bredband.net> wrote in message news:1179341376.360608.39170@o5g2000hsb.googlegroups.com...
On 16 Maj, 18:46, Igor <thoov...@excite.com> wrote:
On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:

by the law of induction, Maxwell's third equation (that
seldom is mentioned in high school, though): curl E = -dB/dt.

But why can't it equally well be interpreted as saying that curl E
causes B to change? To me, this seems more natural, mathematically.

The [TEST mass m] equation || The 'TEST mass m1' equation
F = m a || Fg = m1*g
expresses the fact that || expresses the fact that
a force F causes an object || a weight Fg causes an object
to move with acceleration || to move with acceleration
a = F/m, || g = Fg/m1,
or that an object in order || or that an object in order
to get an acceleration a, || to get an acceleration g,
needs a force || needs a weight (i.e. force)
F = m a || Fg = m1*g
to be applied to it. || to be applied to it.

Mathematically it could || Mathematically, it could
just as well tell you that || just as well tell you that
an object with acceleration || an object with acceleration
a causes a force || g causes a weight (i.e. force)
F = m a. || Fg = m1*g
[This can be a REAL force.] || = G*M*m1 / (n - 1)*rA^2.
$$ See 'magneto-hydrodynamics'.|| Apply the SAME "reasoning" here?.
||
$$ Re: F_a varies, with mass m,|| Re: F_g is *independent* ..of the

Does the mathematics tell you that? [See GUESS equation-of-state].
Nature doesn't listen to mathematics. [We have to get math RiGHT].
We find mathematical laws that describes how we experience nature.
And when we write down the mathematical equations, we make sure to
use words to explain what they mean. Right? Dirk Vdm [End POST].

On May 16, 11:34 am, Erland Gadde <erl...@bredband.net>:

by the law of induction, Maxwell's third equation
(that seldom is mentioned in high school, though):
curl E = -dB/dt.

But why can't it equally well be interpreted as saying that
curl E causes B to change? To me, this seems more natural,
mathematically.

||
The [TEST mass m] equation || The 'TEST mass m1' equation
F = m a || Fg = m1*g
expresses the fact that || expresses the fact that
a force F causes an object || a weight Fg causes an object
to move with acceleration || to move with acceleration
a = F/m, || g = Fg/m1,
or that an object in order || or that an object in order
to get an acceleration a, || to get an acceleration g,
needs a force || needs a weight (i.e. force)
F = m a || Fg = m1*g
to be applied to it. || to be applied to it.

Mathematically it could || Mathematically, it could
just as well tell you that || just as well tell you that
an object with acceleration || an object with acceleration
a causes a force || g causes a weight (i.e. force)
F = m a. || Fg = m1*g
[This can be a REAL force.] || = G*M*m1 / (n - 1)*rA^2.
$$ See 'magneto-hydrodynamics'.|| Apply the SAME "reasoning", HERE.
||
$$> Assume LATERAL F force is equal to GRAViTATiONAL F_g ..at, rA & M:
||
$$ CONCLUSiON a: || CONCLUSiON g:
$$ ACCELERATiON a varies with || ACCELERATiON g ..is *independent*
$$ mass m (FORCE F_a constant).|| ..of *MAGNiTUDE*, of TEST mass m1.
$$ ||
$$ Acceleration isN'T CONSTANT.|| Acceleration g CONSTANT at rA & M.
$$ The acceleration a ..ad-hoc.|| The acceleration g "rationalized".

$$ See, NATURE got a *REALLY STRONG* grip, on *REAL* number physics.

$$ Nature doesn't listen to mathematics. [NATURE-hears-a-BARYCENTRE].
$$ We find mathematical laws that describes how we experience nature.
Re: How to view induction [ACCELERATiON ..for TWO forces] End-of-POST.

On 16 Maj, 18:46, Igor <thoov...@excite.com> wrote:





On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:

I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

Hmm, a typo. I meant of course that I consider _curl E_ as a measure
of the "discrepancy" of E, which causes _B_ to change,





I'm imagining that the fields try to "flatten out", getting rid of the
discrepancies, viewing the Maxwell's fourth equation, curl H - j = dD/
dt in the same way.

You might want to look at the equations in their integral forms. They
seem to be a bit easier to interpret and you can usually picture what
is actually happening much better. For instance, Faraday's law
becomes simply emf = -dflux/dt.

This view seems natural, because if we know E and B (and hence D and
H) at a time, t=0, say, then we can solve Maxwell's equations with
these initial values, and then calculate E and B for all future and
past times.

But we don't usually solve maxwell's differential equations for E and
B. We mostly solve the differential equations in the potentials under
the appriopriate boundary conditions. Even more easily, we can
sometimes solve the integral forms of the equations, providing the
system possesses sufficient symmetry.

OK, but still there is nothing that stops us from solving for E and B,
or..?

But if we try to apply this viewpoint to the simple magnet/conductor
experiment above, it doesn't make sense physically. Because then, we
must say that the change in B is caused by E (more precisely, curl E),
and not the other way round.

I think you've got it a bit backwards. Faraday's law says that a
changing magnetic field induces an electric field. This is,
fortunately, a lot more easily pictured by using the integral form
above.

But why can't it equally well be interpreted as saying that curl E
causes B to change? To me, this seems more natural, mathematically.

But there wouldn't be any E if we didn't
move the magnet. And B isn't caused by E but by internal processes in
the magnet. These internal processes are unknown (at least by me), but
to get a better understanding, substitute the bar magnet for another,
thin but long, coil inductor with a constant current flowing through
it, thus giving rise to a magnetic field similar to the bar magnet's
field.

This doesn't really matter. All Faraday's law is concerned with is a
changing B field, no matter what is causing it. And then E is a
consequence of the changing B.

By our view, the only that can cause a change in E (or D) is Maxwell's
fourth equation. But in the outer inductor, there is initially no
current, thus dD/dt = curl H there, and H must be caused by the inner
inductor. But then D would change even if the inner inductor (or
original bar magnet) is at rest, unless curl H = 0, but then D
wouldn't change, and there would be no induced current in the (outer)
inductor...

This is Ampere's law in the absence of ordinary currents. And it is
just the opposite of Faraday's. A changing electric field generates a
magnetic field. Again, this one is much more easily pictured in the
integral form, where it becomes Int (B.dr) = - ep0 mu0 dflux/dt, where
the flux here is electric and not magnetic.

Yes, but, again, why is it necessarily wrong to consider the change in
E as a consequence of j and the "discrepancy", measured by curl, of B?

I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

Erland Gadde wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

Actually Maxwell's equations do NOT solve or "explain" the above
experiment!
First off, B is not changing. There is no dB/dt as the B is fixed to
the magnet and constant.

The "true" situation is that you are moving a magnetic field past a
wire coil creating relative motion in exactly the same way as a moving
wire in a magnetic field (generator) creates an emf. The operative
equation is qV x B. That equation is NOT part of Maxwell's set.

Now here is where things get interesting. How does one "explain"
induction when things are NOT moving? The classic experiment is two
coils of wire. One to a galvanometer and one to a battery. When you
close the circuit to the battery, the meter jumps. But NOTHING is now
moving relative to each other?

It is known that the first coil creates a magnetic field at the second
coil when the current flows, but that is NOT the answer to the
mystery. One can easily show (toroid or outside a long solenoid) that
induction occurs not only where there is no motion, but ALSO happens
when there is NO magnetic field present at the wire in which the
voltage is induced!!!

So what in hell is going on? The secret is that induction is the
result NOT of a changing B field but rather a changing Vector Magnetic
Potential field! As Feynman has suggested, A may actually be MORE
fundamental than B! B is of course obtainable as the curl of A, but
induction requires a non-zero A and yet occurs in regions of zero B.

Adding to the confusion is the fact that if one calculates the
magnetic flux (B integerated over the area of the wire loop) OFTEN
(but not always!) one finds that such an operation gives the induced
potential even if the B field inside the loop does not extend to the
loop itself. This is very odd in that one has to ask just HOW the wire
loop "knows" that flux is pouring through it's center? Clearly an
"explanation" requires some kind of bogus "action at a distance"
theory. Nay. Things stay much more clear if you stick with A and
forget about the Flux thing which just happens to work sometimes.

Benj

On May 17, 2:13 pm, Benj <bjac...@iwaynet.net> wrote:





Erland Gadde wrote:
I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

Actually Maxwell's equations do NOT solve or "explain" the above
experiment!
First off, B is not changing. There is no dB/dt as the B is fixed to
the magnet and constant.

The "true" situation is that you are moving a magnetic field past a
wire coil creating relative motion in exactly the same way as a moving
wire in a magnetic field (generator) creates an emf. The operative
equation is qV x B. That equation is NOT part of Maxwell's set.

Now here is where things get interesting. How does one "explain"
induction when things are NOT moving? The classic experiment is two
coils of wire. One to a galvanometer and one to a battery. When you
close the circuit to the battery, the meter jumps. But NOTHING is now
moving relative to each other?

It is known that the first coil creates a magnetic field at the second
coil when the current flows, but that is NOT the answer to the
mystery. One can easily show (toroid or outside a long solenoid) that
induction occurs not only where there is no motion, but ALSO happens
when there is NO magnetic field present at the wire in which the
voltage is induced!!!

So what in hell is going on? The secret is that induction is the
result NOT of a changing B field but rather a changing Vector Magnetic
Potential field! As Feynman has suggested, A may actually be MORE
fundamental than B! B is of course obtainable as the curl of A, but
induction requires a non-zero A and yet occurs in regions of zero B.

Adding to the confusion is the fact that if one calculates the
magnetic flux (B integerated over the area of the wire loop) OFTEN
(but not always!) one finds that such an operation gives the induced
potential even if the B field inside the loop does not extend to the
loop itself. This is very odd in that one has to ask just HOW the wire
loop "knows" that flux is pouring through it's center? Clearly an
"explanation" requires some kind of bogus "action at a distance"
theory. Nay. Things stay much more clear if you stick with A and
forget about the Flux thing which just happens to work sometimes.

Benj

That's one way of putting it that I can somewhat agree with :)

But getting back to the relativistic approach, the B field is composed
of two crossed E fields. When a conductor moves toward a stationary
current carrying conductor, for instance, the B field of the
stationary conductor doesn't change, but wrt the electrons in the
moving conductor the two E fields are changing. What is really
happening is that the balance of the two E fields is disrupted via the
relative motion, i.e. in the frame of the moving wire, leaving a net E
field acting on the electrons within it.

The reason given by Purcell for the relative change in the crossed E
fields is contraction of lines of charge and/or contraction of the
fields of the indidual electrons and protons within the current
carrying conductor. So in essence, B can be completely omitted from a
complete electromagnetic theory with no particular consequence.

The equal sign that separates two sides of an equation generally means
"x is the same as y", i.e. the two sides are simply different
expressions of precisely the same thing.- Hide quoted text -

- Show quoted text -

On May 16, 2:57 pm, "Dirk Van de moortel" <dirkvandemoor...@ThankS-NO-
SperM.hotmail.com> wrote:
"Erland Gadde" <erl...@bredband.net> wrote in messagenews:1179341376.360608.39170@o5g2000hsb.googlegroups.com...
On 16 Maj, 18:46, Igor <thoov...@excite.com> wrote:
On May 16, 11:34 am, Erland Gadde <erl...@bredband.net> wrote:

I think all of us made this experiment in high school:

Push a bar magnet forward and back into a coil inductor. Then, current
will flow in the inductor. The explanation is that the changing of the
magnetic field caused by moving the magnet induces an electric field,
an EMC, in the inductor, that produces the current. This is described
by the law of induction, Maxwell's third equation (that seldom is
mentioned in high school, though): curl E = -dB/dt. Thus: The _change_
in B _causes_ E.

But, from a mathematical standpoint, this seems a little odd. Isn't it
more natural to view the equation this way: The "discrepancy" of E
causes B to change? Here, curl B is considered as a measure of the
"discrepancy" of B. Zero curl means no discrepancy and no change of B.

Not quite true. Curl has a particular meaning that is not connected
to general changes in B.

Hmm, a typo. I meant of course that I consider _curl E_ as a measure
of the "discrepancy" of E, which causes _B_ to change,

yes, that's what I thought.

[snip]

I think you've got it a bit backwards. Faraday's law says that a
changing magnetic field induces an electric field. This is,
fortunately, a lot more easily pictured by using the integral form
above.

But why can't it equally well be interpreted as saying that curl E
causes B to change? To me, this seems more natural, mathematically.

The equation
F = m a
expresses the fact that a force F causes an object to
move with acceleration
a = F/m,
or that an object in order to get an acceleration a, needs
a force
F = m a
to be applied to it.
Mathematically it could just as well tell you that an
object with acceleration a causes a force
F = m a.

Does the mathematics tell you that?
Nature doesn't listen to mathematics.
We find mathematical laws that describes how we
experience nature. And when we write down the
mathematical equations, we make sure to use words
to explain what they mean.
Right?

Dirk Vdm

You're correct. An equation alone cannot depict causal
relationships. For example, in the case of Faraday's law, certainly a
changing magnetic flux can induce an emf. But an arbitrary emf will
not necessarily induce a changing magnetic flux. So while I thought
that the OP might have had a new way of interpreting Maxwell's
equations, I'm not so sure in general.