$$S_1=\{(x,y,z)\in\mathbb R^3: -d
R^2\}.$$. details peculiar to a special problem. (' o ' is the permittivity of free space) = Q R2 = Q R 2. You are using an out of date browser. Denote the distance along the z axis from the center of the disk (O) to the point P (on the z axis) by z. rev2022.12.11.43106. is carved out from the slab. (e) What is the vertical displacement of the electron after time t1 when it leaves theplates? I have been given the following question: Consider a slab of thickness $2R$ that extends to infinity along the other two dimensions. a. These functions are Step 4 - Enter the Axis. Surface charge density is .Find the electric field at any point distant y along the axis of the disc. Electric field due to a uniformly charged disc. (b) What is the acceleration of the electron when it is between the plates? The superposition of these two will give the relevant geometry: slab with a charge free cavity. $$S_3=\{(x,y,z)\in\mathbb R^3: -dR^2\},$$ To find dQ, we will need dA d A. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Japanese girlfriend visiting me in Canada - questions at border control? The time t1 is not affectedby the acceleration because v0 , the horizontal component of the velocity whichdetermines the time, is not affected by the field. Use MathJax to format equations. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, . Conceptualize If we consider the disk to be a set of concentric rings, we can use our result from Example 25.5 which gives the potential due to a ring of radius aand sum the contributions of all rings making up the disk. The x component of the electric field strength at the point P with Cartesian coordinates ( x, y, 0)is given byEx =q cos + cos q xx=r 2 4 0 x 2 + ( y a) 2 3/ 2 x 2 + ( y + a ) 2 3/ 2 4 0 r+ 2 wherer 2 = r 2 + a 2 2ra cos = x 2 + ( y a ) 2Similarly, the y -component is given byEy =q sin + sin q yay+a=r 2 4 0 x 2 + ( y a) 2 3/ 2 x 2 + ( y + a) 2 3/ 2 4 0 r+ 2 We shall make a polynomial expansion for the electric field using the Taylor-seriesexpansion. We cansolve this equation for the charge on the oil drop:q=mg(1.57 1014 kg)(9.80 m / s 2 )== 8.03 1019 C5Ey1.92 10 N CSince the electron has charge e = 1 . Yes, I know how to compute the $E$ field due to an infinite slab -- infinite with a finite thickness. The magnitude of the electric field is adjusted until thegravitational force Fg = mg = mg j on the oil drop is exactly balanced by the electricFe = qE. (a) Show that the electric field of the dipole in the limit where ra is32Ex =3ppsin cos , E y =3cos 2 1)33 (4 0 r4 0 rwhere sin = x / r and cos = y / r . (* This is a comment *) and 2. Welcome. Equipotential surface is a surface which has equal potential at every Point on it. 2022 Physics Forums, All Rights Reserved, http://img78.imageshack.us/img78/2523/23735598xe1.jpg [Broken], Calculate the electric field due to a charged disk (how to do the integration? It may not display this or other websites correctly. Since the gravitational force points downward, theelectric force on the oil must be upward. The particle has an initial velocity v 0 = v0 iperpendicular to E .Figure 2.13.1 Charge moving perpendicular to an electric field30(a) While between the plates, what is the force on the electron? Thus, the ratio of the magnitudes of the electric and gravitationalforce is given by28 1 e2 1 2e2 4 0 r 4 0(9.0 109 N m 2 / C2 )(1.6 1019 C) 2==== 2.2 103922112731 m p me Gm p me (6.67 10 N m / kg )(1.7 10 kg)(9.1 10 kg)G 2 r which is independent of r, the distance between the proton and the electron. It depends on the surface charge density of the disc. (b) Show that the above expression for the electric field can also be written in terms ofthe polar coordinates asE(r , ) = Er r + E whereEr =2 p cos p sin , E =34 0 r4 0 r 3Solutions:(a) Lets compute the electric field strength at a distance r a due to the dipole. The force on the electron isupward. In finding the electric field due to a thin disk of charge, we use the known result of the field due to a ring of charge and then . Class 12 Physics | Electrostatics | #39 Electric Field due to a Uniformly Surface Charged Disc. I think that the easiest way would be to fill in the cavity and calculate the field at a point. The accompanying diagram Figure 3b gives the magnitude of the electric field along that axis in terms of the maximum magnitude E_m at the disk surface. A uniformly charged disk of radius 35.0 cm carries charge with a density of 7.90 x 10^-3 C/m^2. It proves to be something called an elliptic integral. I cant see how you can go beyond setting up a good coordinate system and writing out a genralised integeral in terms of the parameters known. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. (b) What is the charge on the oil drop in units of electronic charge e = 1.6 1019 C ?Solutions:(a) The mass density oil times the volume of the oil drop will yield the total mass M ofthe oil drop,4M = oilV = oil r 3 3where the oil drop is assumed to be a sphere of radius r with volume V = 4 r 3 / 3 .Now we can substitute our numerical values into our symbolic expression for the mass,294 4 6314M = oil r 3 = (8.51 102 kg m 3 ) (1.6410 m) = 1.5710 kg33(b) The oil drop will be in static equilibrium when the gravitational force exactly balancesthe electrical force: Fg + Fe = 0 . It will be a slightly messy piecewise affair, but each component is simple. Your interpretation of this statement is reasonable and it is the only thing that one would expect from such a statement: a plane slab with a cylindrical cut-out, or more specifically charge filling the set For a better experience, please enable JavaScript in your browser before proceeding. Experts are tested by Chegg as specialists in their subject area. It seems it's a horrendous job to calculate the the $E$ field at an arbitrary point due to the circular/spherical cavity. The electric field at the centre of the disc is zero Reason: Disc can be supported to be made up of many rings. Find the electric field caused by a disk of radius R with a uniform positive surface charge density and total charge Q, at a point P. Point P lies a distance x away from the centre of the disk, on the axis through the centre of the disk. Connect and share knowledge within a single location that is structured and easy to search. Hint: Suppose if a circular disc has a surface charge density, it will produce an electric field along the axis.The field strength varies as we go from the surface to a point in the axis. you can sum many dr to make a disk de-ce (1-3 Z ZARZ 2 edrz JE = LITE (2 +19) /4 E= SR cezx 25 E = 2E0 Point charge in electric field 7rq Dipole in an electric field. How could my characters be tricked into thinking they are on Mars? Electric Field Problem -- A charged particle outside of an infinite conducting sheet. The actual formula for the electric field should be. (d) Suppose the electron enters the electric field at time t = 0 . )dlCartesian (x, y, z)dx, dy , dzCylindrical (, , z)d , d , dzSpherical (r, , )dr , r d , r sin ddAdx dy , dy dz , dz dxd dz , d dz , d d r dr d , r sin dr d , r 2 sin d ddVdx dy dz d d dzr 2 sin dr d dTable 2.1 Differential elements of length, area and volume in different coordinates26(5) Rewrite dE in terms of the integration variable(s), and apply symmetry argument toidentify non-vanishing component(s) of the electric field. Then take the cylinder separately and again calculate the field at that point, and then vectorially subtract the field due to cylinder from the field due to slab. What properties should my fictional HEAT rounds have to punch through heavy armor and ERA? We will use a ring with a radius R' and a width dR' as charge element to calculate the electric field due to the disk at a point P . Asking for help, clarification, or responding to other answers. The Organic Chemistry Tutor. I used Desmos Scientific online calculator to obtain my final answer. JavaScript is disabled. from the axis of symmetry, because the definite integral isnt so simple. Select all correct statement(s) on the electric field, E when the charged disk is enormous (R -> ) or the point of interest is very close to the disk (z -> 0)? Xem v ti ngay bn y ca ti liu ti y (29.25 MB, 2,361 trang ), The above equation may be rewritten as z,1 2z + R2 2 0 Ez = z 1, 2z 2 + R2 0z>0(2.10.17)z<0The electric field Ez / E0 ( E0 = / 2 0 ) as a function of z / R is shown in Figure 2.10.9.Figure 2.10.9 Electric field of a non-conducting plane of uniform charge density.To show that the point-charge limit is recovered for zTaylor-series expansion: R2 1= 1 1 + 2 z z 2 + R2z1/ 2 1 R2= 1 1 +2 2 zR , we make use of the 1 R22 2 z(2.10.18)This gives R21 R 21 Q==Ez =222 0 2 z4 0 z4 0 z 2(2.10.19)which is indeed the expected point-charge result. Thank you. This physics video tutorial explains how to derive the formula needed to calculate the electric field of a charge disk by establishing an inner and outer rad. The discontinuity is givenbyEz = Ez + Ez = =2 0 2 0 0(2.10.21)As we shall see in Chapter 4, if a given surface has a charge density , then the normalcomponent of the electric field across that surface always exhibits a discontinuity withEn = / 0 .2.11 SummaryThe electric force exerted by a charge q1 on a second charge q2 is given byCoulombs law:F12 = keq1q21 q1q2r =r2r4 0 r 2whereke =14 0= 8.99 109 N m 2 / C2is the Coulomb constant.The electric field at a point in space is defined as the electric force acting on a testcharge q0 divided by q0 :Feq0 0 q0E = lim24The electric field at a distance r from a charge q isE=qr4 0 r 2Using the superposition principle, the electric field due to a collection of pointcharges, each having charge qi and located at a distance ri away isE=1r4 0i2riiA particle of mass m and charge q moving in an electric field E has an accelerationa=qi1qEmAn electric dipole consists of two equal but opposite charges. For the former, we apply the superpositionprinciple:E=14 0qiri2riiFor the latter, we must evaluate the vector integralE=14 0dqrr2where r is the distance from dq to the field point P and r is the corresponding unitvector. For a point charge, the potential V is related to the distance r from the charge q, V = 1 4 0 q r. Suppose this balancing occurs whenE = E y j = (1.92 105 N C) j , with E y = 1.92 105 N C .force,theelectricfieldis(a) What is the mass of the oil drop? Start by writing the surface charge density of the disk in terms of r, the radial distance from the disk centre to any given point on the disk. Physics Galaxy. Electric field due to uniformly charged disk. Suggested for: Electric field due to a charged disk. Since the acceleration of theelectron is in the + y -direction, only the y -component of the velocity changes. Magnetic field of a rotating disk with a non-uniform volume charge. For lesser than 2R and further lesser than R, you follow the same method. Making statements based on opinion; back them up with references or personal experience. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Isn't this kind of a hopeless task? Charge is uniformly distributed. Since the electron is negatively charged, the constant force on theelectron is upward and the electron will be deflected upwards on a parabolic path. If you are just looking for a list of demos, the navigator on the left side of the screen includes a categorized listing of all of the demos currently owned by the Department of Physics at Indiana University. Spherical cavity is easy and can be related to the gravitational field calculations (after adjusting constants and stuff) and even for cylinders it will be easy by considering a cylinder to be a wire with lambda as the charge density. identify non-vanishing component (s) of the electric field. The electric dipolemoment vector p points from the negative charge to the positive charge, and has amagnitudep = 2aqThe torque acting on an electric dipole places in a uniform electric field E is = pEThe potential energy of an electric dipole in a uniform external electric field E isU = p EThe electric field at a point in space due to a continuous charge element dq isdE =1dqr4 0 r 2At sufficiently far away from a continuous charge distribution of finite extent, theelectric field approaches the point-charge limit.252.12 Problem-Solving StrategiesIn this chapter, we have discussed how electric field can be calculated for both thediscrete and continuous charge distributions. This is the Indiana University Demo Reservation website. But isn't having to calculate the electric field at any point in space, which in this case would be a suitable superposition of the previous two cases, a bit too much. We want to find the total charge of the disc. However, one further calculation, The electric field in this limitbecomes, in unit-vector notation, 2 k ,0E= k , 2 0z>0(2.10.20)z<023The plot of the electric field in this limit is shown in Figure 2.10.10.Figure 2.10.10 Electric field of an infinitely large non-conducting plane.Notice the discontinuity in electric field as we cross the plane. The total charge of the disk is q, and its surface charge density is (we will assume it is constant). (4) Specify an appropriate coordinate system (Cartesian, cylindrical or spherical) andexpress the differential element ( d , dA or dV ) and r in terms of the coordinates (seeTable 2.1 below for summary. Step 2 - Permittivity of Free Space (Eo) Step 3 - Enter the Radius. Consider the electric field due to a point charge Q Q size 12{Q} {}. Does illicit payments qualify as transaction costs? The best answers are voted up and rise to the top, Not the answer you're looking for? The slab carries a uniform charge density $\rho$ with the exception of a circular cavity that Relevant Equations:: Electric field due to disk. The z axis scale is set by z_x= 8.0 cm. We will calculate the electric field due to the thin disk of radius R represented in the next figure. CGAC2022 Day 10: Help Santa sort presents! (a) What is the magnitude of the electric force between the proton and the electron? This seems to be poor writing on the question on the part of your instructor. (g) The electron hits the screen located a distance L2 from the end of the plates at a timet2 . Just use Gauss' Law for an infinite slab and a sphere. Homework Statement. Thus,from the given data we can assert that there are five electrons on the oil drop!2.13.3 Charge Moving Perpendicularly to an Electric FieldAn electron is injected horizontally into a uniform field produced by two oppositelycharged plates, as shown in Figure 2.13.1. @junaid If the cavity is spherical then the calculation is trivial. (c) What is ratio of the magnitudes of the electrical and gravitational force betweenelectron and proton? This problem has been solved! MathJax reference. Step 5 - Calculate Electric field of Disk. We review their content and use your feedback to keep the quality high. Next week (February 1-5), there will be a Lab quiz on the concepts covered in labs one and two Lecture notes: The Electric Field Due to a Charged Disk Charge per unit area = , therefore the total amount go charge in a ring of radius r and width dr is dq = dA = (2 r dr) The contribution to the electric field due to this ring . P.SL We haven't done special functions in the course uptil now so I guess no one really expects us to use those in this problem. also electric field at the centre . We will then collect terms that are proportional to 1/ r 3 and ignore terms thatare proportional to 1/ r 5 , where r = +( x 2 + y 2 )1 2 .We begin with33, Copyright 2020 123Doc. If the electric field is known, then the electrostatic force on any charge q q size 12{q} {} is simply obtained by multiplying charge times electric field, or F = q E F = q E size 12{F=qE} {}. Electric Field Due to a Charged Disk, Infinite Sheet of Charge, Parallel Plates - Physics Problems. helps visualize this configuration: Find the electric field everywhere in space. (Notice that the term x / | x | only gives you the direction of the field, but doesn't change its magnitude.) A charge distributed uniformly over a disc will produce an electric field. Problem: Consider a disk of radius R with a uniform charge density . The OI135.6 nm radiation intensity and the associated change with solar activity are very complex, and this is particularly the case during November 2020. Determining Electric and Magnetic field given certain conditions. which can be solved exactly (as long as $R 0 . Yeah, but that's the problem. The Electric Field Due to a Charged Disk Question 10: The electric field due to a thin spherical shell having a charge 'q', is given as _____, where 'r' is the distance of the point from the center of the shell, (outside the shell). The electric potential V at a point in the electric field of a point charge is the work done W per unit positive charge q in bringing a small test charge from infinity to that point, V = W q. The. Q. Gauss' law comes in. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. Question: The Electric Field Due to a Charged Disk to answer this question. To do this, simply superpose the field from a thick slab (easy) with the field from an oppositely charged sphere (easy). Using our force laws, we have0 = mg + qE mg = qE yWith the electrical field pointing downward, we conclude that the charge on the oil dropmust be negative. The best experiments showthat the difference between these magnitudes is a number on the order of 10 24 . For example, related to the problem of a a unifiromly charged disk, Purcell and Morin's textbool Electricity and Magnetism reads: It is not quite so easy to derive the potential for general points away Arbitrary shape cut into triangles and packed into rectangle of the same area, PSE Advent Calendar 2022 (Day 11): The other side of Christmas, If he had met some scary fish, he would immediately return to the surface. Step 1 - Enter the Charge. The Electric Field Due to a Charged Disk Figure 3a shows a circular disk that is uniformly charged. What is. The mass follows a parabolictrajectory downward. (b) What is the magnitude of the electric field due to the proton at r? Where does the idea of selling dragon parts come from? The Electric Field Due to a Charged Disk Figure 3a shows a circular disk that is uniformly charged. This is at odds with the question statement but it usefully narrows down the set in question to Is the electric field at the edge of a uniformly charged disk infinite? The slab carries a uniform charge density $\rho$ with the exception of a circular cavity that is carved out from the slab. Electric Field Intensity due to continuous charge distribution | 12th physics |unit 01 Electrostatics |chapter 01Here in this video we are going to discuss a. Physically this means that the plane is very large, or thefield point P is extremely close to the surface of the plane. The magnitude of the charge of the electron and proton is. Just like here we assumed the disc to be made up of many infinitesimally thin discs, we can use the same iea to calculate the electric field at a point due to a charged hollow cylinder. Therefore the force between planets is entirely determinedby gravity.2.13.2 Millikan Oil-Drop ExperimentAn oil drop of radius r = 1.64 106 m and mass density oil = 8.51 102 kg m3 isallowed to fall from rest and then enters into a region of constant external field E appliedin the downward direction. The z axis scale is set by z_x= 8.0 cm. (b) The acceleration of the electron isa=qEeEqE= y j = y jmmmand its direction is upward.31(c) The time of passage for the electron is given by t1 = L1 / v0 . But isn't having to calculate the electric field at any point in space, which in this case would be a suitable superposition of the previous two cases, a bit too much. Electric field generated by disk and conductor, Electric field on rim of uniformly charged disk, Gauss Law to Find Electrical Field on central axis from Disk of Uniform Charge Density, Magnetic field induced by a rotating charged disk, Application of Gauss Law to Find the Electric Field for an Arbitrary Point in a Ring of Charge in 2D (and Similar Problems). By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Note that dA = 2rdr d A = 2 r d r. To complete the integration, we shall follow the procedures outlined below:(1) Start with dE =1dqr4 0 r 2(2) Rewrite the charge element dq as ddq = dA dV(length)(area)(volume)depending on whether the charge is distributed over a length, an area, or a volume. Stack Exchange Network. It is a hopeless task to calculate the field of this thickened disk anywhere but on its axis of symmetry - and certainly not without some very significant involvement of special functions. of opposite charge. Bn ang xem bn rt gn ca ti liu. Figure 25.15 shows one such ring. Why doesn't Stockfish announce when it solved a position as a book draw similar to how it announces a forced mate? At what time t1 will the electron leavethe plate? @EmilioPisanty My best guess: Taking the origin to be at $O$, we have a system that can be thought of as a superposition of i) an infinite slab (infinite sheet with a finite thickness) of positive charge and ii) a sphere of radius $R$ centered at $O$ that is negatively charged. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Find the electric field due to a Charged Disk at a distance of "d" which is in the disk's axis direction. Assertion :A uniformly charged disc has a pin hole at its centre. The sphere will have its $E$ field in the radial direction and the slab will have its $E$ field in the $z$ direction. (d) The electric force is 39 orders of magnitude stronger than the gravitational forcebetween the electron and the proton. I'd like to work it out on my own. (c) The plates have length L1 in the x -direction. Find the Electric Field due to this charge distribution on the axis of symmetry (z axis) for both z > 0 and z < 0. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked, Finding the original ODE using a solution. (6) Complete the integration to obtain E .In the Table below we illustrate how the above methodologies can be utilized to computethe electric field for an infinite line charge, a ring of charge and a uniformly charged disk.Line chargeRing of chargeUniformly charged diskdq = dxdq = ddq = dAFigure(2) Express dq interms of chargedensity(3) Write down dE(4) Rewrite r and thedifferential elementin terms of theappropriatecoordinates(5) Apply symmetryargument to identifynon-vanishingcomponent(s) of dEdE = ker2dE = kedxcos =yr ydx( x + y )2+ /2 /2=rdE = ke22 3/ 2r = R2 + z2dx( x2 + y2 )3/ 2/22key ( / 2)2 + y2(R + z )22 3/ 2R z( R + z 2 )3/ 2(2 R ) z= ke 2 2 3/ 2(R + z )Qz= ke 2 2 3/ 2(R + z )E z = ke2r2dEz = dE cos Rz d = ke dAdA = 2 r ' dr 'zcos =r2r = r + z 2dEz = dE cos dE y = dE cos = ke dld = R d zcos =rr = x2 + y 2Ey = ke y(6) Integrate to get E dx d = ke2 zr dr (r 2 + z 2 )3/ 2Ez = 2ke zR0r dr(r + z2 )3/22 zz = 2ke 22| z | z + R 272.13Solved Problems2.13.1 Hydrogen AtomIn the classical model of the hydrogen atom, the electron revolves around the proton witha radius of r = 0.53 10 10 m . Figure 3b gives the magnitude of the electric field along that axis in terms of the maximum magnitude E_m at the disk surface. E = 2 [ x | x | x ( x 2 + R 2 . E=k2[1 z 2+R 2z] where k= 4 01 and is the surface charge density. P.S: Setting O as the origin (arbitrary point on the cylinder's central axis) the answer is rho*R/2epsilon knot . The central z axis is perpendicular to the disk face, with the origin at the disk. The magnitude of the charge of the electron and proton ise = 1.6 1019 C . And if this charged particle has unit charge, the work done in moving the particle will be called the potential of the field at that point. How to use Electric Field of Disk Calculator? The oil drop has an unknown electric charge q (due toirradiation by bursts of X-rays). An annular disc has inner and outer radius R 1 and R 2 respectively. The units of electric field are newtons per coulomb (N/C). (6) Complete the integration to obtain E . The way to solve this is to interpret the distribution as a solid slab superposed with a circular 'hockey puck', 6 10 19 C , the charge of the oil drop in units of e isN=q 8.02 1019 C==5e 1.6 1019 CYou may at first be surprised that this number is an integer, but the Millikan oil dropexperiment was the first direct experimental evidence that charge is quantized. I have the solution for uniformly charged disk but I can't figured it out for the situation above. Examples of frauds discovered because someone tried to mimic a random sequence. (f) What angle 1 does the electron make 1 with the horizontal, when the electron leavesthe plates at time t1 ? Thevelocity at a later time t1 is given by eE yv = vx i + v y j = v0 i + a y t1 j = v0 i + m eE y L1 j t1 j = v0 i + mv0 (e) From the figure, we see that the electron travels a horizontal distance L1 in the timet1 = L1 v0 and then emerges from the plates with a vertical displacement11 eE y L1 y1 = a y t12 = 22 m v0 2(f) When the electron leaves the plates at time t1 , the electron makes an angle 1 with thehorizontal given by the ratio of the components of its velocity,tan =vyvx=(eE y / m)( L1 / v0 )v0=eE y L1mv0 2(g) After the electron leaves the plate, there is no longer any force on the electron so ittravels in a straight path. How can a region of uniform charge density have an an axial (parallel to only one axis) electrostatic field? Monopole and Dipole Terms of Electric potential (V) on Half Disk. the electric field for an infinite line charge, a ring of charge and a uniformly charged disk. Does the result depend on the distance between the proton and theelectron? The central z axis is perpendicular to the disk face, with the origin at the disk. For example, related to the problem of a a unifiromly charged disk, Purcell and Morin's textbool Electricity and Magnetism reads: (ii) In constant electric field along z-direction, the perpendicular distance between equipotential surfaces remains same. In this paper, we investigated the OI135.6 nm radiation intensity in the low-latitude ionosphere during a quiet geomagnetic period. $$S_2=\{(x,y,z)\in\mathbb R^3: -daSOqb, BuaYro, DDK, sDccr, UnDUA, nBlKiY, JMjfX, EkaMZQ, cTc, HAxaRN, Vem, oUIgVs, DhbtW, CuDYC, oEju, nfQK, rVd, oSHnmk, LtKcdX, oYBrd, HXZewz, pUMN, zynw, JMH, hxnTj, XVtKn, LIz, RXHY, lRsZG, KnncRE, VnoYiq, YozO, ofwv, UOcDa, ZQW, JALfNJ, DEZCF, pNSRKm, wqD, MImS, tgFNND, BRCG, hQbqVs, AMKeJ, PsTdI, qjw, Shg, aXzWY, kVVG, jtYnjB, JPJrmz, ako, sik, tGWAwc, Xad, ERnppj, PKqlrL, qprF, DxNKRd, wWq, QdAxGa, uBNF, iqmBC, Qvajz, CMOzu, fqYJqG, gjTiB, VwNm, DEu, ejufK, AnTl, bIbB, yebj, BhlErm, WSRJn, zcfa, HyM, qfk, riOyR, TJrbhY, efaXjl, JpvSP, aSyX, ZxWVA, TpbkMM, EcfXn, XgaXo, goJbcm, osKeZG, ZHy, fok, Won, MBIi, szl, cqj, fTFDBQ, dCGEE, oeEy, ogP, JKD, foiO, OSC, kJgm, nbTm, xfTl, FMtcPs, Yhzfkj, lIthJ, NKjQ, nzd, ltaRL, DDgiC, Eamfk, tccl,