Page 1
A homogeneous electric field of two flat parallel oppositely charged plates is obtained by superimposing the fields of the positive and negative plates. Between plates electrical lines both plates are directed in the same way. Outside the plates, the lines are directed oppositely and at the same charge density the field strength is zero. The electric field is observed only between the plates. These two plates form a flat capacitor.
A uniform electric field of intensity il 0 - 104 u / m is formed by two electrified plates located at a distance of 2 0 cm from each other in air.
A uniform electric field, the intensity of which is 1 0 - W V / m, is formed by two charged plates located at a distance of 2 0 cm from each other in air.
Uniform electric field with a strength of 100 V / cm perpendicular to the uniform magnetic field with induction 0 020 T. At what initial speed the electron will move in these fields in a straight line. At what speed the protons will move in a straight line.
A uniform electric field with a strength of 1 0 - 10 - t / M is formed by two electrified plates located at a distance of 2 0 cm from each other in air.
A uniform electric field with a strength of 1 0 - 104 V / m is formed by two electrified plates located at a distance of 2 0 cm from each other in air.
A uniform electric field with a strength of 10,000 V / cm accelerates these electrons and directs them onto a silicon substrate covered with an electron resist. The electrons are focused by an axial magnetic field of about 1000 V / cm generated by the focusing coils. The device forces electrons leaving a given point of the photocathode at any angle to focus on the corresponding point of the anode. As a result, the entire pattern is transferred on a 1: 1 scale from the cathode to the silicon substrate - the anode.
A uniform electric field is characterized by a linear potential distribution. Vector Е in magnitude and direction corresponds to the force, expressed in newtons, with which the field acts on a positive charge equal to one coulomb.
A uniform electric field with a strength of 1 0 - 10 V / m is formed by two electrified plates located at a distance of 20 cm from each other in air.
Homogeneous electric field with a strength of 100 V / cm perpendicular to a homogeneous magnetic field with an induction of 0 020 T. The electron flies into these fields perpendicular to the vectors E and B. At what speed the electron will move in a straight line. At what speed the protons will move in a straight line.
A homogeneous electric field with a strength of 1 0 10 V / m is formed by two electrified plates located at a distance of 2 0 cm from each other in air.
Homogeneous electric field with a strength of 100 V / cm perpendicular to a homogeneous magnetic field with an induction of 0 020 T. The electron flies into these fields perpendicular to the vectors E and B. At what speed the electron will move in a straight line. At what speed the protons will move in a straight line.
The gas breakdown phenomenon depends on the degree of homogeneity of the electric field in which the breakdown occurs. Electric fields are usually divided into uniform and non-uniform.
Homogeneous electric field is called a field, at different points of which the strength has the same values. For example, the field in the middle part of a flat capacitor is uniform (Fig. 5.4, a).
Figure: 5.4. Distribution of field strength in the middle part of air gaps with electrodes of various shapes
In such a field, breakdown occurs almost instantly when a strictly defined voltage is reached, which depends on the temperature and pressure of the gas. Homogeneous fields corresponds to the highest dielectric strength of gases.
IN heterogeneous the field strength at different points has different values. In electrical installations, most fields are highly heterogeneous... In such fields, the tension between the electrodes at different points differs by more than three times. An example of highly inhomogeneous fields can be the fields between the point-point and point-plane electrodes (Fig. 5.4, b, c), which are analogs of real wire-wire and wire-ground electrode systems on overhead power lines.
In inhomogeneous fields, the electric strength of gases is always lower than in homogeneous ones. This is due to the fact that in inhomogeneous fields there are places with increased strength, where impact ionization begins at relatively low voltages at the electrodes. The smaller the dimensions of the electrode, the greater the electric field strength around it (Fig. 5.4, c).
With asymmetrical electrodes and constant voltage, the breakdown voltage also depends on the polarity of the electrodes. Since the field strength is highest near the tip, the process of impact ionization begins there, resulting in the formation of charged particles - electrons and ions. Electrons are more mobile particles, therefore they quickly leave the ionization zone and give their charge to the positive anode. As a result, an excess of positive ions (positive space charge) is formed in the ionization zone, which is limited to a small area at the tip. In the case of a positive tip, the positive space charge is, as it were, a continuation of the tip and increases the tension in the section " x"(Fig. 5.5, a), which contributes to the development of ionization in this section. With a negative tip, the positive space charge screens the tip and thereby reduces the tension in the section." x"(Fig. 5.5, b), which complicates the ionization processes to the right of the space charge.
Figure: 5.5. Explanation of the difference between the breakdown voltages for positive polarization of the tip (a) and with negative polarization of the tip (b)
So, a positive space charge promotes the development of a discharge with a positive tip and complicates it with a negative one. As a result, the discharge voltage at the negative tip is approximately 2 times higher than at the positive one. This difference in discharge voltages is called the "polarity effect".
If the dipole is placed in a uniform electric field, the charges forming the dipole + q and –Q will be under the influence of forces equal in magnitude but opposite in direction and.
These forces form a pair, the shoulder of which is lSin a, i.e. depends on the orientation of the dipole relative to the field. The module of each of the forces is q × E. Multiplying it by the shoulder, we get the value of the moment of the pair of forces acting on the dipole:
where r Is the electric moment of the dipole.
Formula (14.1) can be written in vector form:
The torque tends to rotate the dipole so that its dipole moment is established in the direction of the field.
To increase the angle between vectors and by 2 a,must be done against the work of the forces acting on the dipole in electric field:
This work is going to increase potential energy W, which a dipole possesses in an electric field:
. (14.3)
Integrating (14.3), we obtain an expression for the energy of the dipole in the electric field:
Finally, assuming const equal to zero, we obtain
Choice Сonst \u003d0 corresponds to the position of the dipole perpendicular to the field. The smallest energy value equal to –PE,is obtained when the dipole is oriented in the direction of the field, the largest, equal to pE, - when oriented against the field.
In an inhomogeneous field, the forces acting on the charges of the dipole are not the same in magnitude. For small sizes of the dipole, the forces and can be considered collinear. Suppose that the field changes most rapidly in the direction xthat coincides with the direction at the place where the dipole is located. Positive charge the dipole is shifted relative to the negative in the direction x by the amount.
Therefore, the field strength at the points where the charges are placed differs by 
.
Consequently, the resulting + forces acting on the dipole will be nonzero. The projection of this resultant onto the axis xis obviously equal to:
Thus, in an inhomogeneous field, in addition to the rotational moment (14.2), the force (14.5) acts on the dipole, under the action of which the dipole is either drawn into the region of a stronger field (angle a is acute) or pushed out of it (angle a is obtuse).
Polarization of dielectrics
In the absence of an external electric field, the dipole moments of dielectric molecules are either equal to zero (non-polar molecules), or distributed along directions in space in a chaotic manner (polar molecules). In both cases, the total electric moment of the dielectric is zero. The dielectric is polarized under the action of an external field. The resulting electric moment per unit volume characterizes the degree of polarization of the dielectric. If the field or dielectric is inhomogeneous, the degree of polarization at different points of the dielectric will be different. To characterize the polarization at a given point, it is necessary to select the physically infinitesimal volume that contains this point, find the sum of the moments contained in this volume of molecules, and take the ratio
R Is the polarization vector of the dielectric.
In dielectrics of any type (except for ferroelectrics), the polarization vector is related to the field strength at the same point by a simple relationship:
where c - dielectric susceptibility.
For dielectrics built from non-polar molecules, formula (13.7) follows from the following simple considerations. The volume contains the number of molecules equal to, where n - the number of molecules per unit volume.
.
Dividing this expression by, we obtain the polarization vector.
Hence it follows that.
The field strength in a dielectric is understood to mean the value obtained by averaging the true field over a physically infinitely small volume.
The field is obtained as a result of the superposition of two fields: the field created by free charges, i.e. such charges that can be transferred from one body to another when they touch, and the field of bound charges. Due to the principle of superposition of fields:
Bound charges differ from free charges only in that they cannot leave the limits of the molecule (or atom), which they are part of. Otherwise, their properties are the same as for all other charges. In particular, on bound charges vector lines start or end. Therefore, the Gauss theorem for the vector defined by expression (1) should be written in the form:
Substituting the expression for into formula (14.12), we get:
Dimensionless quantity (14.15)
called the relative dielectric constant.
Therefore, relation (14.14) can be written in the form. Electrical displacement fields point charge in vacuum is equal to:
.
Page 1
An inhomogeneous electric field in infinitely small volumes can be considered as uniform.
An inhomogeneous electric field is formed in the gap between electrodes with different surface curvatures, to which a voltage of several kilovolts is applied.
The simplest inhomogeneous electric field can be obtained using a system of electrodes in the form of two infinitely long concentric cylinders with radii r, and r In such a system, in the absence of a space charge, the field at any point is inversely proportional to the distance from the axis.
The gradient of the inhomogeneous electric field created on the nucleus by the surrounding charges is also a symmetric tensor, the trace of which is Uxx Uyy Uzz0, and in the system of principal axes the tensor of the diagonals.
In an inhomogeneous electric field, the electric quadrupole moment of nuclei with J1I2 causes broadening of the nuclear resonance line.
In an inhomogeneous electric field, the polarization of the dielectric is also inhomogeneous: its polarization P depends on the coordinates. In this case, in addition to surface polarization charges, volume polarization charges can also arise.
In heterogeneous electric fieldswhen the dielectric properties of the particles and environment are different, forces appear that lead, in addition to orientation, to the appearance of particle motion in a certain direction.
In an inhomogeneous electric field, a noticeable dependence of the breakdown voltage on the polarity of the electrodes is observed.
In inhomogeneous electric fields, as well as in gases, there may be an incomplete breakdown - a corona. The corona in liquid dielectrics is unacceptable for any length of time, since it causes the liquid to decompose. Repeatedly repeated spark discharges in a relatively small volume of liquid can cause both a drop in dielectric strength and an increase. The first is possible in the case when repeated discharges lead to the draining of the liquid, which, under the influence of the discharges, is not prone to a large release of carbonaceous formations - soot; this is observed in petroleum oil. The second is observed in liquids that form a large amount of soot under the influence of electrical discharges, for example, in a sovol.
In inhomogeneous electric fields, as well as in gases, there may be an incomplete breakdown - a corona. Long-term corona in liquid dielectrics is unacceptable, as it causes liquid decomposition. Repeatedly repeated spark discharges in a relatively small volume of liquid can cause both a drop in the dielectric strength and an increase in it. An increase is possible in the case when repeated discharges lead to the draining of the liquid, which, under the influence of the discharges, is not inclined to a large release of carbonaceous formations - soot; this is observed in petroleum oil. A decrease is observed in liquids that form a large amount of soot under the influence of electrical discharges, for example, in a sovol. With sufficient power, the breakdown of a liquid dielectric can be arc. In this case, intensive decomposition of the liquid occurs.
It is difficult to obtain a solid corona in the form of a luminous shell in an inhomogeneous electric field. Corona discharge in oil is a series of restless, alternating between emerging and disappearing incomplete sparks, the length of which depends on the applied voltage. This phenomenon is similar to incomplete discharges in air that occur between electrodes with a relatively large radius of curvature. During the discharge, the resulting small amount of gas dissolves in the oil, rapid deionization occurs and the dielectric properties are restored again. In this case, for a repeated breakdown, a further increase in voltage may be required, but much less than in a homogeneous floor.
In an inhomogeneous electric field, the intensity of movement of water microdroplets along the trajectories of the field lines increases with an increase in the gradient of its intensity. The required gradient requires a fairly high voltage across the electrodes (more than 3 kV), which depends on the distance between the electrodes. It should be borne in mind that with a decrease in the interelectrode distance, the voltage gradient increases, but the risk of breakdown increases.
