8 Logical justification of the Hall effect
Ed 01.12.31 
Abstract

Exerting a magnetic field normal to a currentcarrying strip we cause a
deviation in the path of moving electrons as if our conducting path is
a wire along an edge of the strip which at a point is deflected normal
to the edge and reaches the other edge and afterwards is continued
along
this other edge in the same direction as before. It is clear that
connecting
the two end points of the transverse part of such a wire by a minor
wire
we expect a part of the main current to pass through this minor wire.
The direction of such a current flowing in the minor wire is such that
as if the currentcarrying charges in the main currentcarrying strip
are positive charges. This is the basis of this article. A quite
practical
experiment is proposed for testing the presented theory.
I. Introduction

In the Hall effect it is observed that when we exert a magnetic field
normal to the surface of a currentcarrying conducting strip, if two
opposite points of the two edges of the strip is connected together
by a minor wire, an electric current will flow in this wire. Provided
that the direction of current in the strip remains unchanged, it is
seen that the direction of current in the minor wire depends on the
kind of the strip.
What is noticeable in this effect is that existence of two different
directions in the wire, which depends on the kind of the
currentcarrying
strip, in the first instance indicates that the kind of the carriers
of current in the strip depends on the kind of the strip, ie in some
cases, as usual, electrons are the carriers of current, and in other
cases positive charges must be carriers of current.
There is no dispute over the mechanism of carrying current by the
electrons. Difficulty in explaining the mechanism of carrying current
will appear if positive charges are to be carriers of current assuming
that positive charges in solids are stationary. To obviate this
difficulty, it is claimed that it is not in fact the positive ions
that flowing in a wire cause an electric current, but it is the
holes or in fact empty places of electrons that with an apparent
motion carry current as if positive ions are doing so.
It is clear that when the empty places of electrons (or holes) are to
be displaced, indeed the electrons move in the same their usual
direction, and in fact nothing new occurs. Furthermore, while it is
quite reasonable that a moving electron in a magnetic field endures
a force (normal to both the electron path and the magnetic field),
it is quite irrational that an empty place (of an electron or a hole),
which is seemingly being displaced in a magnetic field, feels any
force causing its motion towards one of the two edges of the strip,
because, force can be exerted only on substance not on "nothing" (ie
on empty place or hole)!
As an attempt to justify carrying of current by the displacement of
holes, maybe it can be said that although it is in fact the moving
electrons that in the currentcarrying strip in the magnetic field
are drawn towards one of the two edges of the strip, but crystalline
structure of the strip and of the minor wire are such that when for
continuation of the current an electron, in order to flow in the strip,
leaves its atom just at the edge of the strip in the point of
connection
of the minor wire, its empty place has such electron affinity that
before the next moving electron in the strip reaches this empty place
abundant valence electrons of the minor wire are attracted by this
hole. Therefore, we shall have an electron current in the transverse
wire in the direction opposite to one expected. But such a
justification
is also very weak, because it is quite clear that the next electrons
in the strip which due to the existence of current in the strip are
moving towards this empty place are much closer to this empty place
than the valence electrons of the minor wire. And in principle
certainly the next electrons in the strip, which are themselves moving
towards the empty place, will be involved in the intense electron
affinity of the empty place much more than the stationary valence
electrons of the minor wire. Consequently it is quite obvious that
eg there will be no reason that such an unexpected current will
appear in the transverse wire if this wire is of the same kind of
strip; while this is not the case in practice.
This article has been intended to solve this difficulty of
justification of the Hall effect in a logical simple manner.
II. The justification

Consider a currentcarrying wire which ideally has no resistance.
Connect two points of this wire by a similar wire. How is the electric
current divided between these two wires? For answering this question
notice Fig. 1.
2
_____ R
__(_____)__/\/\/\/\__
 a 1 b 
  
___________ _____
 

Fig. 1
The two above mentioned points are points a and b in this figure.
Suppose that the two wires connecting these two points have the same
electrical resistivity, <rho>, and their cross section areas are
the same, A, and the length of the wire 1 is L1 and the length of
the wire 2 is L2. In a simple elrctrical analysis (that can be done
by the reader) in which equivalent resistances are used, it can be
shown easily that always we have I2/I1=L1/L2 for the ratio of the
current passed through the wire 2, I2, to the current passed through
the wire 1, I1, provided that the electrical resistivity of all the
wires is considered equal to zero. Therefore, if the point b is a loop
of the wire 2 sliding on the length of the wire 1, bringing the point
b close to the point a the current in the wire 2 (with the costant
length L2) will approach zero, and taking the point b away from the
point a the current in the wire 2 will increase (approaching half
of the constant current passing through the circuit).
Now suppose that instead of the wire 1 and its continuation we have a
strip of the same kind of the wire 2. Furthermore, suppose that the
point a is on an edge of this strip and the point b is on the other
edge of the strip; see Fig. 2.
It is natural that in this state too, a similar mechanism for dividing
the current is expected, ie assuming that the arrow shown in the figure
indicates the direction of the current of electrons, we expect, by
bringing the point b, on the edge which it is located on it, close to
a point just opposite to the point a, the current in the (transverse)
wire to decrease approaching zero, and taking it away, this current
to increase.
That the current passing through the wire increases by taking the
point b away from the point opposite to the point a on the same edge
on which b is located, will be certainly true even if a magnetic field
is exerted normal to the surface of the strip, because although in this
state the current of electrons is drawn eg towards the edge related
to the point a, but since as before the electrons are moving in the
same previous direction, in any case we must expect increasing
of the contribution of current flowing in the (transverse) wire
when taking the point b away. Therefore, if the kind of the strip
is such that when the point b is just opposite to the point a we
have an electron current from b to a instead of one from a to b when
exerting the above mentioned magnetic field, this will be certainly
the case that by displacing the point b in the direction of the
current of electrons in the strip on the same edge related to b we
shall observe that gradually the current of electrons from b to a
(existent in the wire) will decrease and at a point will vanish and
afterwards current of electrons from a to b will appear which will
increase gradually by taking the point b away more and more.
But, while there is not any current in the wire when b is opposite
to a and there exists no magnetic field, why does in principle there
exist current in the transverse wire when b is opposite to a and a
magnetic field normal to the strip is being exerted? And why can the
direction of this current be changed depending on the kind of the
strip while keeping the direction of current in the strip constant?
The reason can be simply that by exerting a magnetic field normal to
the surface of current we cause the (currentcarrying) moving electrons
to be drawn towards an edge of the strip and in fact with this act we
create a local deviation in the path of the current, ie exerting the
magnetic field, path of the moving electrons will be one shown Fig.
3(b)
not one shown in Fig. 3(a).
Now let's assume ideally that by exerting the field the
currentcarrying
conductor will be no longer straight as shown in Fig. 4(a) (which is
equivalent to the same strip), but wil be the deviated (major) wire
shown in Fig. 4(b).
In this manner the points a and b in Fig. 4(b) will be the same points
a and b in Fig. 2 if the point b is located just opposite to the point
a in this figure and the magnetic field normal to the strip is being
exerted in this figure. By connecting the two points a and b in Fig.
4(b)
by another (minor) wire we expect according to the reasoning related
to Fig. 1 that the electrons flow from b to a in this minor wire. This
means that we similarly should expect that when b is located opposite
to a in Fig. 2 and the normal magnetic field is being exerted the
electrons flow from b to a not from a to b in the minor wire in
Fig. 2 (ie just the same phenomenon which seems unusual to us and for
some substances such as Fe and Al occurs).
But why in many cases do we have flowing of electrons from a to b
instead of b to a in the minor wire in Fig. 4(b)? Because when the
elerctrons rushing from b to a in the major wire in Fig. 4(b) reach
the point a, they meet a right angle which force them to turn and
continue their motion upwards; consequently because of their direct
collision with the point a they in fact strike an impact on this
point. When these points of a and b are connected to each other by
another minor wire, these impacts or in fact these exertions of
electronic forces can cause current of electrons from a to b in the
minor wire if they are sufficiently strong, although as we said,
in the usual state this current shoud be from b to a in the minor
wire. (Obtaining of such a situation depends directly upon the electric
resistances of the materials of the currentcarrying strip and minor
wire and also upon the configuration of the minor wire.) But if these
impacts are not sufficiently effective, such a situation will not
occur and direction of the current of electrons in the minor wire
will be, as before, from b to a.
The above mechanism of striking of impacts and exertion of electronic
forces may seem rudimentary but is not at all invalid and has been
presented in this form only for simplicity at present. Indeed such a
mechanism is almost the same one presented for current justification
of the Hall effect which states that the electronic current is drawn
towards an edge and because of the assembling of electrons at this
edge a potential difference is produced which causes flowing of current
in the minor wire connecting the two wdges of the strip to each other.
The mechanism presented in this article can be tested by a proposed
experimental way: If really electrons rushing from b to a in the minor
wire in Fig. 4(b) can exert force on the electrons of the point a and
cause partial flowing of electrons from a to b in the minor wire in
some cases, we can expect that they do similar work in similar cases.
Suppose that we have made a right angle loop as shown in Fig. 5 from
a conducting wire such that in the vertex point of the right angle the
two crossing parts of the wire are welded together.
It is clear that assuming that the arrows show the direction of the
current of electrons, we expect that we have also an anticlockwise
electron current in the loop from b to a, because in the path of the
main current, b has been located before a and according to the
reasoning related to Fig. 1 we expect that a part of the current to
flow from b to a in the loop. But when the main current is sufficiently
intense and the related conditions including resistances related to
the materials of the circuit are provided properly, it is possible
that impacts from the electrons of the right branch moving towards the
vertex point, directly exerted on the electron of the crosssection
of the circuit (or in fact of the loop) in the point a, are such strong
that cause a clockwise electron current in the loop from a to b which
predominates the usual anticlockwise current from b to a, and
consequently we observe a clockwise current in the loop from a to b.
Performing such an exact experiment can test the validity of the
theory presented in this article.
Hamid V. Ansari
The contents of the book "Great Mistakes of the Physicists":
0 Physics without Modern Physics
1 Geomagnetic field reason
2 Compton effect is a Doppler effect
3 Deviation of light by Sun is optical
4 Stellar aberration with ether drag
5 SternGerlach experiment is not quantized
6 Electrostatics mistakes; Capacitance independence from dielectric
7 Surface tension theory; Glaring mistakes
8 Logical justification of the Hall effect
9 Actuality of the electric current
10 Photoelectric effect is not quantized
11 Wrong construing of the Boltzmann factor; E=h<nu> is wrong
12 Wavy behavior of electron beams is classical
13 Electromagnetic theory without relativity
14 Cylindrical wave, wave equation, and mistakes
15 Definitions of mass and force; A critique
16 FranckHertz experiment is not quantized
17 A wavebased polishing theory
18 What the electric conductor is
19 Why torque on stationary bodies is zero
A1 Solution to fourcolor problem
A2 A proof for Goldbach's conjecture
My email addresses: hamidvansari<at>yahoo<dot>com or
hvansari<at>gmail<dot>com
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