Re: Does a Magnet's force weaken witht the distance cube?


Sue... wrote:
Randy Poe wrote:
Sue... wrote:
Randy Poe wrote:
Sue... wrote:
Randy Poe wrote:
Sue... wrote:
Electric charges diminish by 1/r^2 regardless of what
may be nearby.
http://hyperphysics.phy-astr.gsu.edu/HBASE/forces/isq.html#isqe

And the sum of two oppositely signed 1/r^2 fields from
nearby sources is a 1/r^3 field.

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/dipole.html#c1

- Randy

Scroll down and you'll find the explaniation and
the r^2 term.

You mean where it says the potential is V = kp cos(theta)/r^2
under "Electric Dipole Potential"?

The electric field is the gradient of potential
http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/efromv.html#c2

Notice that the potential of a single point charge varies
as 1/r:
http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/potpoi.html#c1
The gradient of this varies as 1/r^2.

The gradient of the 1/r^2 dipole potential gives a
1/r^3 field.

- Randy

You are confusing the electric field of 3 charges

Oh good grief.

Let's start here: Did you notice that the entire page of the
hyperphysics site dedicated to "Electric Dipoles" is
discussing TWO, not THREE charges?

Did you notice that the expression V = kp cos(theta)/r^2
that you referred me to is labelled "Electric Dipole Potential"?

Can we agree on those two things?

We can agree you wrote:
<<And the sum of two oppositely signed 1/r^2 fields from
nearby sources is a 1/r^3 field. >>

We can agree you mention no motion of the charges
to justfiy the applications below.

You are correct, there is no mention of motion of
charges in the links discussin electric dipoles,
since the electric dipole field is the static field
arising from a pair of separated charges.

What does that comment have to do with anything?

No motion of charges is needed for an ELECTRIC
dipole. Motion of charges gives you currents, which
gives you MAGNETIC dipoles.

While we're at it, take a look at anything which gives an expression
for the field from a magnetic dipole, such as this:
http://www.netdenizen.com/emagnet/offaxis/mmoffaxis.htm
Note: field varies as 1/length^3,

This: http://www.matchrockets.com/ether/magfaqs.html#q10
" Elementary physics states that the magnetic field of a magnetic
dipole is approximately proportional to the inverse cube of the
distance from the dipole."

This: http://www.earth.northwestern.edu/people/seth/Demos/DIP/dip.html
"It varies with the cube of the distance from the Earth (instead of the

square) because the magnetic field is a dipole, rather than a monopole,

field."

This: http://instruct.tri-c.edu/fgram/web/b-coil.htm
"It can be shown that for large r from an electric dipole, the
potential (voltage) is approximately V = k p cos q/r^2...
The electric field... Er = 2 k p cos q/r^3 and Eq = k p sin q/r^3...
As noted earlier, we replace the electric dipole moment with the
magnetic dipole moment (m = NiA) and Coulombs law
constant with mo/4p: Br = (mo/2p)NiA cos q/r^3 and
Bq = (mo/4p)Ni A sin q/r^3"

Coil? Is that a device where the superposition of electric
fields of moving electrons could be concentrated?

No, it's a device where current runs in a loop, giving
you an magnetic dipole.

This: http://physicslabs.phys.cwru.edu/EM/Manual/pdf_version/MAG.pdf
"So instead of the field falling off as the inverse square of
distance, as it does for the electric field of a point charge,
the magnetic field of a coil falls off as the inverse cube of
the distance. The formula for the field in directions other
than straight up is much more complex than Eq. 2a, with
the field varying in both magnitude and orientation
depending on the direction from the coil, but it still falls
as 1/r^3 in any given direction."

Is there somthing about the motion of charges that you
took out of context?

No. What the heck are you asking about? Two static
point charges, not moving, give you an electric dipole
field which falls off as the inverse cube of distance.

Current loops give you magnetic dipoles.

As usual, the links you provided had absolutely nothing to
do with the discussion.

Now scroll back and see where you stated both the
electric and magnetic fields dimiinsh
by 1/r^3.

Yes, I can see that in every one of the pages I
quoted.

If you can look at a 5 web pages and see exponents of 3
where they are clearly the number 2 then you are suffering
from too much brain matter between the legs.

And I substituted the word "cube" for "square"?

Did you actually look at them?

Let's do it one by one.
This page:
http://www.netdenizen.com/emagnet/offaxis/mmoffaxis.htm
has an equation for B_x and B_r. Are you really telling
me that "clearly the number 2" appears as the exponent
of l in the denominator of those equations?

This page:
http://www.matchrockets.com/ether/magfaqs.html#q10
Search for the phrase "Elementary physics". Are you
really claiming that the phrase "inverse cube" does
not occur in that sentence?

This page:
http://www.earth.northwestern.edu/people/seth/Demos/DIP/dip.html
An equation for B_r appears near the top, and an equation
for B_theta appears immediately below. Are you really
claiming the denominator in those equations is r^2 rather
than r^3? Look at the text after each of those equations.
Are you really claiming that text says "square" and not
"cube"?

This page:
http://instruct.tri-c.edu/fgram/web/b-coil.htm
Look at the second paragraph below the drawing. You
will see an equation with (x+L)^2 in the denominator,
followed by the text "Notice the inverse cube behavior
for large x." Are you really claiming the word "cube" does
not appear there, and "square" appears instead? Keep
reading the same paragraph. Notice another equation
for B with x^3 in the denominator. Are you really claiming
that equation has x^2 in the denominator?

And finally, this page:
http://physicslabs.phys.cwru.edu/EM/Manual/pdf_version/MAG.pdf
Look at equation (3). Are you really claiming that the
denominator contains z^2 rather than z^3? Read the
text under that equation, where it says "instead of the
field falling off as the inverse square of distance, as
it does for the electric field of a point charge, the
magnetic field of a coil falls off as the inverse cube of
the distance." Are you really claiming those words
aren't there?

- Randy

.

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