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On the magnetic field of bound charges current.
Alexander I. Korolev, Saint-Petersburg, Russian Federation
Measurements of magnetic induction near an ice rod in the strong electric field were carried out.
Theoretical estimation of the magnetic induction was made. It was found that in the average the
experimental values of magnetic induction were an order less than theoretical value. A conclusion about
the non- equivalence of magnetic fields of bound charges current and conduction current was made.
Therefore, the magnetic field near an energized conductor is caused not directly by moving charges but
by their influence on the propagation medium. The similar effect could occur at diffusion of other
particles through the medium.
The bound charges current is a component of total current in the system of Maxwell’s
equations. Its dimension is the same as for the free charges current, namely, Ampere. As it is
stated in classical electrodynamics, magnetic action of this current is similar to the action of
conduction current . The pioneer investigators of magnetic action of bound charges current
were Roentgen  and Eichenwald [3,4]. The conducted experiments consisted in study of the
magnetic field near the rotating disks of polarized dielectric. The discs were placed in electric
field of flat conductive plates that caused induction of the surface bound charges. Sensitive
magnetic needles were used to measure the magnetic field. Density of bound charges current
at disc rotation was calculated:
is the surface density of bound charges, is the angular velocity, b is a numerical
coefficient. Roentgen discovered and qualitatively investigated the magnetic field of bound
charges. Eichenwald carried out quantitative research, improving the setup and measurement
technique. According to the obtained results, it was concluded that magnetic field of the bound
charges current was identical to this one of the conduction current. However, the procedure of
the magnetic field measurement using magnetized needles is not correct. It was the degree of
influence of the charges on the existing magnetic field of the needle that was measured but not
the magnetic field of moving charges directly. Sensors, operating on the Hall effect, could be
used to measure the magnetic field correctly. The magnetic field of electron current in them is
Measurement of magnetic field of bound charges current in ice
The current of bound charges appears when they move linearly and simultaneously as well as
when electrical dipoles rotate around the center of mass. Essential difference between these
types of currents is that in the former case, the current can be maintained continuously, and in
the second case - only in the form of short pulses during the polarization establishing. The
advantage of the second method is the essential current density, due to contribution of
rotation of every electric dipole into the total current. This allows the use of Hall's sensors with
average sensitivity to measure the magnetic field. Reasoning from their response time, ice with
temperature of 0 ° C is chosen as a dielectric to be investigated. The ice is made by freezing
Scheme of the experimental setup is presented in Fig. 1. High-voltage pulses are formed in a
pulse generator ("Laska- super" shocker) and are fed onto a thin copper plate 100 x 100 mm in
size. An isolated ceramic plate 8 mm in thickness is fixed on the copper plate. A plastic cylinder
with walls 0.5 mm thick, 10 mm in diameter and 20 mm in length is placed in the centre of the
isolated plate. The cylinder is filled up with thawing ice at 0 °С. The magnetic field of current
pulses from molecules H
O is measured by two Hall's probes Honeywell SS495A1. The sensors
are located closely with wide faces to each other, at that their orientation is opposite with
respect to the field. Sensitivity of the sensors under normal conditions is 3.1 mV / G, and the
response time is 3 μs. The sensors are fixed normally to the imaginary magnetic field lines
around the cylinder with ice (a piece of the conductor). Distance from the center of the sensor
to the center of the cylinder is about 10 mm. To shield the sensors against the strong electric
field from the copper plate, a grounded shield of aluminum foil on a plastic frame is used. A
signal from the sensor is fed to the digital oscilloscope Hantek DSO-2090 and analyzed by PC.
Ground connections of the oscilloscope and the screen are electrically isolated.
Fig. 1. Scheme of experimental setup for measurement of ice rod magnetic field. Notes: 1 - copper plate, 2 - ceramic
plate, 3 - plastic cylinder with ice, 4 - two Hall's sensors, 5 - electrostatic screen.
Fig. 2 shows the voltage pulses U(t), incoming onto the copper plate from the pulse generator
(PG). The pulse size is limited by a discharge gap at the output of the PG. The pulses are
obtained by processing the electric signal from the piece of the conductor located near the
plate. Normalization of the received signal is made to the nameplate output voltage of the PG.
The electric field intensity above the center of the ceramic plate is:
Here L is the distance from the center of the copper plate to the points of ice molecules
location, . The value of intensity in the area of the cylinder with ice during the
voltage pulse is:
. These values are significantly smaller than the
value of intensity of water molecules decomposition. Thus, it is possible to carry out multiple
repolarization with no destruction of the ice structure.
Fig. 2. Shape of pulses incoming onto the copper plate from pulse generator.
Two series of measurements are carried out, during which the signals from the magnetic
sensors are recorded when applying voltage pulses. In the first series the cylinder with ice is
present, in the second it is removed. Each series consists of two parts. One part includes 25
measurements. The series of measurements were divided into two parts in order to avoid
significant melting of outer layers of the ice rod, placed under normal conditions (no more than
0.5 mm). In data processing the signals from magnetic sensors are subtracted to reduce noise
and double the signal of interest. The differential signals received in this way are processed
with a digital low-pass filter, the cutoff frequency is 1 MHz. Then we sum up the 50 signals in
the series with the ice rod, as well as the 50 noise signals in the series without ice. After that,
the total signals are subtracted. It enables to remove the systematic measurement error
occurred due to the stray fields. The accuracy of the measurements of the magnetic induction is
limited by ADC resolution of the oscilloscope, which makes up 0.2 mV (0.064 G for one
magnetic sensor). The resulting voltage is converted to the value of magnetic induction
corresponding to a measurement of one sensor by dividing by the number of measurements
made by both sensors (100). Such method is applicable due to synchronization of the signals
recording against the voltage pulses in course of the measurements. The result of signals
processing from the Hall sensors is shown in Fig. 3.
Fig. 3. Dependence of magnetic induction on time near ice rod with the imposed electric field calculated from
In the obtained dependence there is no periodic signal with a frequency corresponding to the
electric pulse-repetition interval. The dependence is like a noise, the mean deviation of the
values of magnetic induction is 0,063 G.
Theoretical estimation of magnetic field of bound charges current in ice
The bound charges current in process of ice polarization represents rotation of charges around
the center of mass of their electric dipoles. At that the positive hydrogen ions shift in one
direction and the negative oxygen ions - in the opposite. The shift occurs along the axis of the
plastic cylinder. Let us investigate the shift process of the charges on micro-level to calculate
the current flowing through the ice rod during the pulse propagation. The explanatory
illustration to the calculation is given in Fig. 4.
Fig. 4. Illustration to estimation of the bound charges current in ice. is the average interparticle
distance , s is the cross- section of ice.
In the absence of the external field the electric dipoles of water molecules are directed in
different directions. When the electric field is imposed, the dipoles tend to turn along the
direction of the field. Polarization relaxation time of ice at 0 ° C, when the dipoles rotate, is 20
µs [5-7]. Average distance between the water molecules in ice makes up 2,76 Å. Ice has a high
viscosity that stabilizes the rotation process of the dipoles under the influence of the external
electric force. Thus, we can assume that the dipoles rotation is uniform when an electric field is
imposed. During the propagation of the electric field pulse (t ≈ 1,5 µs) each dipole turns on
average by 1.5 / 20 = 0.075 fraction of the full turn. At that, an average charge passing through
a cross section of the rod, along the axis in both directions, makes up
Here N is the number of water molecules in the cross section,
is the part of the charge of
two hydrogen ions passing through the cross section at the point of time t, averaged over the
is the part of the charge of one oxygen ion passing through the cross section
at the point of time t , averaged over the cross section. Estimation of the number of molecules
in the ice rod cross section gives:
Let us simplify the task to estimate the charge that passes through the cross section of the ice
rod in the polarization relaxation time. Let us consider the case of an "ideal" section passing
through the centers of mass of N dipoles. In this case, when the dipoles are oriented towards
the external field initially, the maximum transferred charge is the charge of all three ions and
makes up 3e. When the dipole is oriented initially along the field, the charge is equal to zero.
The average transferred charge is equal to 3/2e. Let us consider now the case of an "ideal"
boundary section, separating the layers of N dipoles. Flow of the charge through it is absent.
Ideally, when the molecules of ice are placed in the planes oriented perpendicular to the axis;
those two types of sections are extreme. We can estimate the average charge that flows
through the middle section between these extreme sections. It is approximately . In a real
crystal of ice the water molecules form a complex spatial ensemble, this gives an amendment
to the estimation of the charge transferred across the section.
Now we can estimate
over the time t. It makes up
current of bound charges through the ice rod over the pulse time and according to the
Let us calculate the hypothetical intensity of magnetic field created by this current in the area
of the magnetic sensor location. The calculation scheme is presented in Fig. 5.
Fig. 5. Calculation scheme for magnetic field generated by bound charges current in ice rod.
To estimate the intensity we assume that all the current flows near the axis of the rod. Using
the Biot-Savart law, we obtain an expression for the required magnetic induction of bound
charges current in the segment of conductor (the ice rod):
Substituting the known parameters into (5), we get an estimate of the magnetic induction
magnitude at the point of location of the magnetic sensor over the pulse time: B ~ 0,6 G.
Thus, the magnitudes of the magnetic induction/noise (see Fig. 3) calculated from the
experimental data in the average are an order less than the theoretical estimate.
Results and discussion
The lack of magnetic field of the bound charges current in the ice is ascertained with accuracy
of an order of magnitude of the magnetic induction. This leads to a conclusion about the
nonequivalence of magnetic fields of bound charges current and conduction current. Thus, the
magnetic field is not caused by moving electric charges only , but it is due to their influence
on the propagation medium. Symmetry breakdown of electron shells that explains the
magnetic properties of magnetoactive atoms may also cause magnetism in the magnetically
inactive medium. Symmetry breakdown of the electron outer shells occurs at the directed flow
of electrons through a substance.
Magnetic field of moving electrons was found in investigation of glow and arc discharges. The
experiments were carried out under the supervision of A. F. Ioffe in the early 20th century .
However, magnetized needles were used to measure the magnetic field. Their deviations could
be caused by the force that is opposite to the Lorentz force. The backward force should appear,
according to Newton's third law, from the moving electrons and ions of the discharge. It also
explained deviation of the needles in [2-4]. The further experience of scientists and engineers
worked with electrovacuum equipment did not reveal the magnetic properties of charged
beams in the absence of external magnetic field.
From the results of investigation the hypothesis occurs that the magnetic properties of a
substance can be caused by diffusion both of charged and neutral particles through it. The key
condition is the directional impact on the electron shell structure in the atoms of the substance.
Demonstration of the inverse Faraday effect  shows the possibility of magnetization under
the influence of diffusion of polarized photons (laser beam). The next possible candidate for
magnetization is the beam of polarized neutrons.
The author thanks a radio engineer under the pseudonym of Varjag, whose keenness of
observation gave impetus to the present work and Mr. E. Ryabchikov for helpful comments.
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