无磁场参与的时变电场

一般而言,时变场情况下电场和磁场是相互作用且同时存在的。依据电磁感应定律,容易理解无电场伴随的纯粹时变磁场是不存在。然而,本文强调,纯粹的时变电场是可以存在的。例如,在导电媒质的电荷弛豫过程中,如果传导电流与位移电流正好处处相互抵消,则此时可以不出现磁场。在这种场中,没有电磁能量的流动,空间储存的电场能量就地通过欧姆损耗转化为热能。

时变电场不能产生磁场的实例

设真空中一点电荷q位于O点,q随时间t成正弦变化,q=q_0sinωt, 它周围的电场呈球体状向周围扩散,构成一区域Ω,其中各点的电场强度E都随时间变化,从动态标量位函数φ的波动方程出发可算出该区域内磁场为零。但运用麦克斯韦第一方程式计算将得出Ω内有磁场存在的错误的结果。其原因在于麦克斯韦第一方程式的积分式中同一时刻L环路所张的曲面S可以有无穷多张,该积分式要求L环路所张的的所有曲面S_n上对δD/δ_t的积分值应相同。但是某些特殊情况下,例如本例就不满足这一点。麦克斯韦第一方程式的微分式所算出的“H”矢量在某些特殊情况下,例如本例仅仅是代表一种数学意义上的存在而非物理意义上的磁场强度H矢量存在。在真空中,如时变电场方向呈均匀球状均匀分布,则该电场所在的区域不产生磁场,麦克斯韦第一方程式在此区域内不成立。

Numerical modeling of the 2D time-domain transient electromagnetic secondary field of the line source of the current excitation

To effectively minimize the electromagnetic field response in the total field solution, we propose a numerical modeling method for the two-dimensional （2D） time- domain transient electromagnetic secondary field of the line source based on the DuFort- Frankel finite-difference method. In the proposed method, we included the treatment of the earth-air boundary conductivity, calculated the normalized partial derivative of the induced electromotive force （Emf）, and determined the forward time step. By extending upward the earth-air interface to the air grid nodes and the zero-value boundary conditions, not only we have a method that is more efficient but also simpler than the total field solution. We computed and analyzed the homogeneous half-space model and the fiat layered model with high precision--the maximum relative error is less than 0.01% between our method and the analytical method--and the solution speed is roughly three times faster than the total-field solution. Lastly, we used the model of a thin body embedded in a homogeneous half-space at different delay times to depict the downward and upward spreading characteristics of the induced eddy current, and the physical interaction processes between the electromagnetic field and the underground low-resistivity body.

Movement of dispersed droplets of W/O emulsion in a uniform DC electrostatic field: Simulation on droplet coalescence

Considering the droplet coalescence, the motion of a group of dispersed droplets in W/O emulsion in a DC electric field is simulated. The simulation demonstrates the evolutions of droplet number, size as well as its distribution,local concentration distribution and droplet size-velocity relation with the applied time of electric field. The simulated average droplet size is roughly consistent with the experimental value. The simulated variation of droplet number with time under several applied voltages shows that increasing voltage is more effective for raising the rate of droplet coalescence than extending exerting time. However, with the further raise of applied voltage, the improvement in droplet coalescence rate becomes less significant. The evolution of simulated droplet size–velocity relationship with time shows that the inter-droplet electric repulsion force is very strong due to larger electric charge on the droplet under higher applied voltage, so that the magnitude and the direction of droplet velocity become more random, which looks helpful to droplet coalescence.

Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin(FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system.An exact analytical expression is established for the evolution of the eigenstates.This result then provides a general solution to the time-dependent Schro¨dinger equation.

Magnetic fields-induced modification of DNA content in date palm （Phoenix dactylifera L.）

Plant stress caused by exposure to magnetic fields （MF） induces modifications at molecular level, particularly in DNA synthesis, structure, and function. The objective of this study was to determine the effect of various doses of non-ionizing radiation of magnetic field on date palm （Phoenix dactylifera L.） based on DNA content. Date palm seedlings （cv. Khalas） established for 2 weeks on filter paper were subjected to static magnetic field and alternating magnetic field. Static magnetic fields （SMF） were applied at 10, 50 and 100 mT for 30, 60, 120, 180, 240 and 360 min; while alternating magnetic field applied by magnetic resonance imaging （MRI） at 1500 mT for 1, 5, 10 and 15 min. The seedlings were grown in potting soil following exposure for 4 weeks after which DNA was extracted from leaves and its content was determined. Generally, the exposure to magnetic field caused reduction in the content of DNA. The lowest exposure time tested, 30 rain, was sufficient to induce reduction in DNA content. This was true even at the lowest intensity, 10 mT. This dosage caused the DNA content to decrease from 49 ~tg/g to 45 pg/g. Further, increase of the exposure duration to 60 min caused significant reduction in the DNA content, 36 μg/g. At intensities higher than 10 mT, DNA content decreased significantly even at the shortest exposure of 30 min. At 50 and 100 mT, significant decrease in DNA content was also noticed in response to 30 min exposure; whereas the level of DNA increased after 1 min of MRI exposure to 52 ~g/g, then decreased after 5 min to 46 ~g/g. However, longer durations caused no further decrease in the DNA content. These observations indicate that magnetic fields interact with DNA processes, probably by inhibiting synthesis or stimulating degradation of DNA. This response merits further exploration as a mutational agent for date palm genetic manipulation.

An Exotic Phase Change in Dynamic Electrorheological Fluids

It is well known that constant or time-varying electric fields can induce phase changes in electrorheological(ER) fluids, from a liquid to semi-solid state, provided the field strength is larger than some critical value. We describe here an experimental and theoretical study considering yet a different class of phase changes, specifically those for an ER fluid in the presence of both shear flow and a time-varying electric field. We note that as the frequency of the field is decreased, the ER fluid will go from a liquid to an intermediate transition state, and eventually to a shear banding state. Our theoretical analysis further indicates that this phase change originates from competing effects of viscous and electrical forces. Ultimately, we conclude that it is possible to achieve various states and corresponding(desired)macroscopic properties of dynamic colloidal suspensions by adjusting the frequency of the externally applied electric field.

Development characteristics of cloud-to-ground lightning with multiple grounding points

Using the optical images of a cloud-to-ground lightning flash with multiple grounding points obtained by a highspeed video system in the Qinghai Province of China along with synchronous radiated electric field information, the propagation characteristic and the electric field change features of the leaders and the grounding behavior of discharge channels are analyzed.In addition, the two-dimensional velocity of the leader was estimated and its correlation with the time interval of the corresponding subsequent return stroke, and that with the peak current of return stroke are investigated. The results show that the average distance between the three obvious grounded points of the first return stroke channel is about 512.7 m, and the average time interval between the pulses of the corresponding electric field fast changes is 3.8 μs. Further, the average time interval between electric field pulses from the stepped leader is smaller than that of normal single grounding lightning. The observed lightning in our study has two main channels, namely the left and right channels. Based on our observations, it is clear that the dart leader comes close to the ground in case of the left channel after the first return stroke, but it fails to form a return stroke.However, the right channel exhibits a relatively rare phenomenon in that the subsequent return stroke R2 occurred about 2.1 ms after the dart leader arrived at the ground, which was unusually long; this phenomenon might be attributed to the strong discharge of the first return stroke and insufficient charge accumulation near the grounded point in a timely manner. The two-dimensional velocities for the stepped leader of the two main channels are about 1.23×105 and 1.16×105 m s-1, respectively. A sub-branch of stepped leader for the left channel fails to reach the ground and develops into an attempt leader eventually; this might be attributed to the fact that the main branch connects considerably many sub-branches, which leads to the instantaneous decline of the potential difference between the sub-branch and ground. Furthermore, it might also be because the propagation direction of this sub-branch is almost perpendicular to the atmospheric electric field direction, which is not conducive to charge transfer. The two-dimensional velocities for the dart leaders of five subsequent return strokes are all in the normal range, and they positively correlate with the peak current of the subsequent return stroke.