The schematic diagram of the motion law of the charged spring oscillator in the uniform electric field is known from the external uniform electric field E_. Is E_. =E.sinAi_-E.cosAk_The electric field force F_ is F_=qE_. =qE.sinAi_-qE.cosAk_elastic force is f_=kli_ Since the charged spring oscillator only moves on the x-axis, the new law of motion of Newton is d2ldt2+X2l=A(1) where: l(t) is spring-shaped The variable, X2=km, A=qE.sinA, (1) is a second-order constant coefficient linear non-homogeneous differential equation whose general solution is l(t)=Ccos(Xt+U)+AX2(2) where C and U is a pending constant and the value is determined by the initial conditions. The initial condition of the charged spring oscillator is: lt=0=l., it=0=dldt=0, which can be obtained: C=l.-AX2, U=0.
The motion law of the charged spring oscillator from (2) and initial conditions is l(t)=(l.-AX2)cosXt+AX2(3) The velocity of the vibrator is v_(t)=-(l.-AX2) XsinXti_ where the negative sign indicates the direction of the velocity is opposite to the x-axis direction.
The electromagnetic field strength of the space point is set on the vibrator to observe the electromagnetic field at the space point. Then the space electric field E_cp generated by the charged spring oscillator is obtained by the literature <2>: E_cp=q4PE.r2. R_^=q(xl)4PE.(r2.-2xl+l2)3/2i_-qy4PE.(r2.-2xl+l2)3/2j_+qz4PE.(r2.-2xl+l2)3/2k_=E_cpxi_ -E_cpyj_+E_cpzk_29 where E_cpx=q(xl)4PE.(r2.-2xl+l2)3/2E_cpy=-qy4PE.(r2.-2xl+l2)3/2E_cpz=qz4PE.(r2.-2xl+l2) 3/2r.=(x2+y2+z2)1/2Set p(x,y,z) points farther away from point N, the amplitude of the vibrator is relatively small, |r.|m|l|, omitting l2 The value of Ecp has little effect. In the denominator, the l2 term is omitted and E_cpUq(xl)4PE.(r2.-2xl)3/2i_-qy4PE.(r2.-2xl)3/2j_+qz4PE.(r2.-2xl) ) 3/2k_=q4PE.r3. (1-2xlr2.) 3/2(4) by Taylor series: (1+x)m=1+mx+m(m-1)2x2+,+m(m-1),(mn-1)nxn+ , m is a real number, |x|<1, (4) is developed according to the Taylor series and takes the first two terms to get E_cp=q4PE.r3.
Since the moving velocity of the charged spring oscillator is small for the speed of light, the change of its velocity can be considered as a slow change. The gravitational field is considered to be a quasi-static field, and it is observed on the transverse system E, and the Lorentz transformation of the time is obtained. The electromagnetic field at point p is E_p=E_cp, B_p=vc2E_p, where (vnc). Where: Epx == (a + bcosXt) + E.sinA > Epy = = y (h + RcosXt) Epz = = (h + RcosXt) - E.sinA, -2xlr2.
Discussion of the problem First, we can see that the charged spring oscillator is in the uniform electric field E_ by (1). Under the action, it is still a simple harmonic vibration, the frequency of vibration is kX, the amplitude is l.-AX2, and the equilibrium position is AX2.
Secondly, it can be seen from (6) that when (|r.|m|l|) is at a spatial point far from the vibrator, the combined electric field E is composed of three parts, and the first part is determined by the position of the spatial point. The second part is due to the movement of the vibrator. It is a periodic function that changes with time t. The third part is the external electric field E...
Third, it can be seen from equation (7) that the magnetic induction intensity B_ of the p(x, y, z) point is a function of time t, which changes periodically as time t changes. Fourth, when Xt=0 or 2nP, as obtained by (6), as long as |r.|m|l|, the combined electric field strength E_ of point p can be approximated as E_combination=x(a+b+ E.sinA)i_-y(h+R)j_+
Here you can find the related products in Dissolved Oxygen Meter, we are professional manufacturer of Dissolved Oxygen Meter,Dissolved Oxygen Tester,Portable Dissolved Oxygen Meter,Dissolved O2 Meter. We focused on international export product development, production and sales. We have improved quality control processes of Dissolved Oxygen Meter to ensure each export qualified product.
If you want to know more about the products in Dissolved Oxygen Meter, please click the product details to view parameters, models, pictures, prices and other information about Dissolved Oxygen Meter,Dissolved Oxygen Tester,Portable Dissolved Oxygen Meter,Dissolved O2 Meter.
Whatever you are a group or individual, we will do our best to provide you with accurate and comprehensive message about Dissolved Oxygen Meter!
Dissolved Oxygen Meter,Dissolved Oxygen Tester,Portable Dissolved Oxygen Meter,Dissolved O2 Meter
Xi'an Gavin Electronic Technology Co., Ltd , https://www.gaimcmea.com