1.11) combines the concepts of classical h Planck constant 6:626 10 34 J s mechanics with the idea of wave-like properties by showing that a particle with momentum mv (m mass and n 1; 2; 3 . As d E is given by, Here, d q and r is already given, 2 is similar to that of a stationary one. A novel method for the quantitative verification of Faradays, The quantum-mechanical phase of the wavefunction of an electron can be changed by electromagnetic potentials, as was predicted by Aharonov and Bohm in 1959. The electrostatic potential resulting from a metallic probe tip near a semiconductor is examined. ESICM LIVES 2016: part two. Variations in the magnetic field or the electric charges cause electric fields. dy tfe Zytfabnrea` Xfenrek. describing a given orbit v velocity of the particle) possesses an associated wave . STRATEGY Follow the problem-solving strategy, finding the electric field at point P due to each individual charge in terms of x- and y-components, then adding the components of each type to get the x- and y-components of the resultant electric field at P. The magnitude of the. Q 2- Determine the potential of a charge of 10pC at a distance of 0.5 m due to the charge. The difference here is that the charge is distributed on a circle. V=9 109 x 2 x 10-12. -; P>S)jgPhhua5g OidPGz[ta5qg `5q; Ah. In fact, electric field lines always point from higher potential to lower. Abdul Wahab Raza Follow Student of computer science Advertisement Recommended Physics about-electric-field The field for a ring must be a power series of the form: You could generate this series from your integral. Solution Before we jump into it, what do we expect the field to "look like" from far away? 3Bdwp3%X B}1 b1(d 4j"Cj(cgF,r [Sb(>b(#db51[j`5h-h7VC6dtoh :u / Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. The following diagram depicts this scenario. For 3D applications use charge per unit volume: = Q/V . Find the electric field at P. (Note: Symmetry in the problem) Electric Field Due to a Ring of Charge Rishi Dadlani January 2022 1 f1 Introduction In this derivation, we will find the electric field on a point particle in space as a result of a ring of uniform charge. Electric Field due to Ring The electric field of a ring of charge on the axis of the ring can be found by superposing the point charge fields of infinitesimal charge elements. ~s)go|Fc-Ah=lhPh S-y[C%{P )Ah>Z9 Electric Field of Charged Ring Total charge on ring: Q Charge per unit length: l = Q/2pa Charge on arc: dq dE = kdq r 2 kdq x +a dEx = dEcosq = dE x p x 2+a kxdq (x 2+a )3/2 Ex = kx Proof for Electric Field Formula from a Ring of Charge, Electric_Field_Due_to_a_Ring_of_Charge (1), 0% found this document useful, Mark this document as useful, 0% found this document not useful, Mark this document as not useful, Save Electric_Field_Due_to_a_Ring_of_Charge (1) For Later, C` tfcs hercvatcn`, we wcii `h tfe eiemtrcm eih n` a pnc`t partcmie c` spame as a, Ct cs iadeieh wctf varcadies, aii n wfcmf wcii de he`eh hurc`b tfe hercvatcn` nr, Nur nrcbc`ai equatcn` hesmrcdes tfe eiemtrcm eih n` a pnc`t partcmie as equai tn, Mnuinkds Iaw teiis us tfat tfe nrme exerteh dy partcmies as a resuit n, tfecr mfarbe cs prnpnrtcn`ai tn tfe kuitcpie n tfe twn mfarbes nver tfe hcsta`me, C` nur mase, we hn`t fave twn partcmies, sn we equcvaie`tiy rehe`e, -pia`e, ct hnes`t katter) tn tfe partcmie cs. The theorem states that the total external potential for all the chemical species, \ D (r ) V (r ) PD , is uniquely determined by the spatial distribution of the fluid species given by the equilibrium fluid . to(F:C`V The electric fields of the charged, A new method to calculate the electric field inside a spherical shell with surface charge = o cos in terms of solid angle is presented. Electric field due to a ring, a disk and an infinite sheet In this page, we are going to calculate the electric field due to a thin disk of charge. Find the electric potential at a point on the axis passing through the center of the ring. Each segment of the loop is located at the same distance from P (see Figure 2.3). In vector form if the unit vector towards x-direction is ^i i ^, the above equation is. Problems are suggested for an arbitrarily charged ring. The outside field is often written in terms of charge per unit length of the cylindrical charge. We will assume that the charge is homogeneously distributed, and therefore that the surface charge density is constant. Problems are suggested for an arbitrarily charged ring. Point P is a distance r x P x from dx. Coulomb's law gives the electric field at P due to the charge dq . Other, The purpose of this paper is to show the influence of the edge-effect on the electric field distribution, and hence on the inner capacitance and outer capacitance of a cylindrical capacitor. Let's do this. You know the electric field magnitude E E from the above equation and therefore, the total electric field is. 3. Enter the email address you signed up with and we'll email you a reset link. To the electric field generated by charges outside the sphere one must add the electric field generated at the center of the sphere by <> A point P lies a distance x on an axis through the centre of the ring-shaped conductor. B jV1u$?jr$y/cQ&\ We will notice that the equation of electric potential at the centre of the ring is the same as the electric potential due to a point charge.. To understand the reason behind is, you can imagine that circular ring is nothing but will behave like a charge if we compare it to heavy bodies such as moon or earth. Understanding the fundamental reactivity of polymetallic complexes is challenging due to the complexity of their structures with many possible bond breaking and forming processes. Answer: The potential of a charge of 2pC at a distance of 1m due to the given charge is 18103. 6 0 obj Electric field due to a ring of charge at any point in the plane containing the charge (my handout) (worth up to 2 lab grades). xZ[ovb4K~Iqc*q$MF:]i4>g!g-h Jgsi(a l.ng7 ??Wl5Lm$9'g@ip@rr6{y>_kyRa =)$_3\Xcfd\[%dn32{>>\t/Z\qE;8;Tf-qS(S*RBaK]KwH1WHl3g"{_{zok`"VdX-gkR J=!w/dDj#k>vp#Ns-J|}tT 37u?ly1 '9g )SAFzHm. This electrostatic problem was solved long ago, and its gravitational analogue was solved, Off-axis electric field due to cylindrical distribution of charge is studied in various geometries, including solid cylinder, cylindrical shell, disk, and ring. Solution: The formula for evaluating potential due to point charge is as follows: V=140.Qr. ^&BOpuX2\ i/UCF iT*t'.V `2 %:Huf4+$ N<33/weYT?=zFjgErEUVPc{qndb_YB_0tQ'~+D-%Y02o3 Fcdi~c}=%LZ]a,59Hd(/5Jyx:%ke(njb,=5+^m xDTVApxRCP }[b/J"op[9;ze"VR)kp>5)ErHZu9"$nsw186X,_O8 e=z]% :6We&s|i4gX+>O2:F==Z*"b,jf>$z0lBUp9n%ZZ!!/ouZ|CJLAFh0>_g@S![B*B"Q^M@$,oVMYyQ4_n_;+g+.Z@&[UE/OKB/ Ut2|.CsV-lYa-PtUTT:fbJcjB})jofciQd,3?jzgoNqA#f;55)WkgG?4lvG9NVKdK70dtiZ,}UAfn1^+q*\+AeX))@?2VbUM; Science Advisor. Electric field intensity can be determined by the amount of electric force experienced by a test charge q in the presence of the electric field. Mar 2, 2022. Francesca Rubulotta. electric field, an electric property associated with each point in space when charge is present in any form. Experiments on propagating electron waves, Three different methods for generating numerical solutions of Laplaces equation are derived using a differential operator formalism for a Taylor series expansion of the electric potential about a, The Penning trap mass spectrometer at the University of Washington is described along with the relevant detection mechanisms and the systematic shifts associated with the finite energies in the, The lifetimes of the metastable 1 s2s2p 4 P5/2 level of He 2 , as well as the lifetime of the average of the 4 P 3/2 and 4 P 1/2 levels, have been measured using a new type of ion trap that stores. It means that the scattered field of the moving electron in Fig. Field of a Continuous Ring of Charge Let's find the field along the z-axis only. We divide the ring into infinitesimal segments of length dl. F is the force on the charge "Q.". 9!{HC[+j(sM3X :Zjrhm&Pl 2 VS,t8Yb5u91P.by[Cx+Pg3#X @FY7VC}fiX B}L Electric field due to. Furthermore, in order to calculate the electric field of a charged disc, the ring field can be used as an element. The electric field, then, is the mechanism by which the electric properties of the source charge are transmitted to and through the rest of the universe. wish to find the electric field produced by this line charge at some field point P on the x axis at x x P, where x P L. In the figure, we have chosen the element of charge dq to be the charge on a small element of length dx at position x. <> The field is simply the force per unit charge. The integral can be readily carried out without invoking, We present a comprehensive numerical analysis of the peculiarities of the electric field, equipotential surfaces, capacitance, and surface charge density at different thickness of a charged, It is shown that the Lorentz transformation cannot in general be formally applied to potentials and fields of particles locked in a certain region. The magnitude and direction of the electric field are expressed by the value of E, called electric field strength or electric field intensity or simply the electric field. If the charge is characterized by an area density and the ring by an incremental width dR', then: . h4{Pay: zd-`P{D4=o11hlmNA9I,BGTA2Gzb(a#HAC H:yk(#AO}1T#re-9G,"=vX*WCvH{Cv t5M(bto(aj2hWCv[{H@t{Cv2yk(:tgdd3%X B]qX :%9A. Appendix of my handout on motion of a charged particle in a constant magnetic field. Introduction In addition to systemic hemodynamics, the management of neurocritically ill patients is often informed by neuromonitoring. (Again, the range of the electric force is infinite.) It is conceivable that different parts of the field could provide different types of samples in terms of nitrogen content. My handout on muonium. E = k2qcos r2 (1) (1) E = k 2 q cos r 2. We consider the electric field produced by a charged ring and develop analytical expressions for the electric field based on intuition developed from numerical experiments. The field image is as follows: the accelerated motion of charge q1 generates electromagnetic waves, which propagate at c, reach q2, and exert a force on q2. | Find, read and cite all the research you . Then, field outside the cylinder will be. We denote this by . . The farmer wants to know whether he needs to apply a nitrogen-containing fertilizer to his field. 2. The following example addresses a charge distribution for which Equation is more appropriate. Our solution involves the approximation of elliptic integrals. This external potential could arise from the presence of a surface, or from some other kind of field such as an applied electric field. Divide the charge distribution into innitesimal blocks. The de Broglie rela- 8:854 10 12 F m 1 tionship (eq. Get a quick overview of Electric Field Due to Ring from Electric Field Due to Ring in just 2 minutes. . For 1D applications use charge per unit length: = Q/L. Such samples are called selective samples. Electric field can be considered as an electric property associated with each point in the space where a charge is present in any form. Notice that both shell theorems are obviously satisfied. 4. E=mc2 : Poincare's derivation of it for light from electrodynamics. Our solution involves the approximation of elliptic integrals. We are interested in finding the electric field at point P that lies on the axis of the ring at a distance x from its centre. The final design uses planar rather than hyperbolic, A very simple numerical method for solving boundary problems in electrostatics is presented. Knowledge of the value of the electric field at a point, without any specific knowledge of what produced the field . Ring has radius R, charge per unit length . That is, when viewed far away, the field is just that due to a point charge. We will see in subsequent chapters that the speed at which electrical phenomena travel is the same as the speed of light. In the absence of high-level evidence clinicians are often guided by . The change in potential energy is UU==BAUqE0d. The formula of electric field is given as; E = F / Q Where, E is the electric field. Formula for finding electric field intensity for line charge is given by E=pl/2op p Where pl =line charge density p=x^2+y^2 Or u can write as E=2*kpl/p p Where K=910^9 Consider a Numerical problem Consider that there is infinite line charge on z-axis whose line charge density is 1000nC/m. Calculate the value of E at p=100, 0<<2. where R is the radius of the ring, iand jare unit vectors and a is the parametric angle. Hold on to your pants. Biot-Savart operator on . The concept of electric field (strictly, electromagnetic field) is intuitive and extremely useful in this context. Electric field due to ring of charge Derivation Nov. 19, 2019 11 likes 11,912 views Download Now Download to read offline Education This is derivation of physics about electric field due to a charged ring.This is complete expression. Get Most Demanded Physics Notes, Chemistry notes and Biology notesfor 11th, 12th, NEET \u0026 IIT Subscribe E-Books (on Our App https://dhxel.courses.store/ ) Hardcopy of Notes is Available ( on Amazon \u0026 Flipkart visit https://www.sccsikar.com/blog/ ) Learn Physics in Easiest way Join 12th Physics Online course(Videos+Notes+Mind Maps+Test Papers+Doubt Solutions etc. Problem 2.5. Substituting the numerical values, we will have E=\frac {240} {2.4}=100\,\rm V/m E = 2.4240 = 100V/m Note that the volt per . Multiplying 0 0 by R2 R 2 will give charge per unit length of the cylinder. If is large, the first term dominates, hence the field is approximately that of a point charge. By symmetry, only Ez is non-zero (the x-y components cancel) dq dq' dE dE R r z 0 2 2 K yy E == D. Acosta Page 6 9/1/2005 where Q is the total charge and R is the radius of the disk. Suppose I have an electrically charged ring. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. ESICM LIVES 2016: part two. Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. We consider the electric field produced by a charged ring and develop analytical expressions for the electric field based on intuition developed from numerical experiments. The radius of this ring is R and the total charge is Q. An electric field is a region of space around an electrically charged particle or object in which an electric charge would feel force. x}M,Gr]+oM{{fw-20"x]*? By clicking accept or continuing to use the site, you agree to the terms outlined in our. UY1: Electric Field Of Ring Of Charge June 1, 2015 by Mini Physics A ring-shaped conductor with radius a carries a total charge Q uniformly distributed around it. . A ring of thickness da centered on the disk as shown has differential area given by . The electric field due to a given electric charge Q is defined as the space around the charge in which electrostatic force of attraction or repulsion due to the charge Q can be experienced by another charge q. An electric charge is a property of matter that causes two objects to attract or repel depending on their charges (positive or negative). PDF | Magnetic flux ropes (MFRs), playing a crucial role in particle energization and energy transport in the solar-terrestrial space, are helical. dq = Q L dx d q = Q L d x. This is a suitable element for the calculation of the electric field of a charged disc. where Q=2R. It is given as: E = F / Q. The particle is free to move along the z-axis, but is fixed within the xy-plane. Electric field intensity due to a single charged particle is given as, We can find an electric field at any point, due to a charged object, by identifying the type of charge distribution. Q is the charge. Electric field due to the uniformly charged large surface is given as: E = / 2 o ----- (1) From equation (1) it is clear that the electric field due to a uniformly charged surface is independent of distance from the surface. The electric field at point P can be found by applying the superposition principle to symmetrically placed charge elements and integrating. By principle of superposition, the Electric field at a point will be the sum of electric field due to the two charges +8q and -2q "NfTViwO8|Nz=C)~zK=v-y[[O_?RSq2 :}j9^tn\s/8eK# J7? V=9 109 x 2 x 10-12/1. Since q>0,we haveU<0, which implies that the potential energy of a positive charge decreases as it moves along the direction of the electric field. A tiny electric field is generated by the tiny charge dQ, and the equation for the magnitude (strength) of this electric field is given in Equation 4: dE is the tiny electric field in newtons-per . Electric field due to a charged ring along the axis. Solution Before we jump into it, what do we expect the field to "look like" from far away? However, it is much easier to analyze that particular distribution using Gauss' Law, as shown in Section 5.6. In particular, this property relates to nucleons in, A common method for solving Poisson's equation in electrostatics is to patch together two or more solutions of Laplace's equation using boundary conditions on the potential and its gradient. Find the electric field a distance z above the center of a circular loop of radius r which carries a uniform line charge l. r z P dEr dEl 2dEz Figure 2.3. The electric field at a point is defined as the force experienced by a unit positive point charge placed at that point without disturbing the position of the source charge. An electric field is defined as the electric force per unit charge. 2016, Intensive Care Medicine Experimental. The electric field can be denoted using units Volts per . Do not sell or share my personal information. We provide examples of how a computer algebra system can be used to investigate the motion of an electric charge in an electric or magnetic dipole field. 1 DERIVATIONS OF ELECTRIC FIELD INTENSITY DUE TO A UNIFORMLY CHARGED RING 1.1 SPECIAL CASES 1.2 MAXIMUM ELECTRIC FIELD INTENSITY DERIVATIONS OF ELECTRIC FIELD INTENSITY DUE TO A UNIFORMLY CHARGED RING Let's consider a uniformly charged thin ring of radius a. Solution: Prove true also for electric field Use our knowledge of electric field lines to draw the field due to a spherical shell of charge: There is no other way to draw lines which satisfy all 3 properties of electric field lines, and are also spherically symmetric. As the ring is symmetric we can place the point on the XZ plane and describe it through radial distance r from the axis of the ring and axial distance a along the axis of the ring. #8. Strategy. On the microscopic scale, the electron is bound near the center of cyclotron motion. The electric field at the observer due to charges outside the sphere of radius R0 can be carried out without problems created by a vanishing denominator in Equation (2.1.5). %PDF-1.3 % The electrostatic potential, , at a distance r from a charge q is (r ) = q/r and the corresponding electric field is E = (r ). We all see several types of incredible activity in our surrounding. We know, Electric field due to a point charge is given as : E = 1 4 o q r 2, where q is the charge and r is distance from the charge to the point at which electric field is to be determined. The electric fields in the xy plane cancel by symmetry, and the z-components from charge elements can be simply added. The field produced by this ring of charge is along the x-axis and is given by the previous result: The total field is given by simply integrating over a from 0 to R Electric Field Due to Ring. x is the distance from the centre of the ring along the axis. The approximation scheme is based on the substitution of a series expansion of the electrostatic potential, A bar magnet, attached to an oscillating system, passes through a coil periodically, generating a series of electromotive force pulses. and thus a charge given by . ;)i-T@()EegW,y35B5LBe\j!s`Gg_z3i._jym\>])w)1]{|ObLbD3E= 9D|O3^TDMnOF!b.jhbs`j,AWyN c~]G x\W+qc Electric Field refers to the surrounding region produced by an electric charge whose influence is observed when another charge is brought into the electric field region. The time delay is elegantly explained by the concept of field. {b9ABmj~^ ik 3%X :)c>Pa52PB`5@{3#X EnMn3%X B}X z_y)8Y~53B=9A,>{P'Sj' Let is the linear charged density of the ring. The electric field at point P can be found by applying the superposition principle to symmetrically placed charge elements and integrating. In the case of a uniformly charged ring, the electric field on the axis of a ring, which is uniformly charged, can be found by superimposing the electric fields of an infinitesimal number of charged points. NAa9'Z cQ{(s~ v6+DOY{QL8KA|F}CeN;k2FO4/a9uyMwS}C(B#?#'jMf! For example the field (E) and field gradient (E 0 ) arising from a charge qb at b are E = qb T = qb T E0 = qb T = qb T . Q is the charge. % With the . An electric field is also described as the electric force per unit charge. In this . An electric field around any charge distribution can be found by creating an element out of infinitesimal point charges. A solution is formulated assuming circular symmetry and using prolate spheroidal coordinates in the, Proceedings of International Conference on Particle Accelerators, Electrostatic quadrupole focusing is to be used in the high precision measurement of the anomalous magnetic moment of the muon, AGS Experiment 821. Electric Field Due to a Charged Ring A conducting ring of radius R has a total charge q uniformly distributed over its circumference. Electric Field due to a Ring of Charge. Hence in both cases, the Electric field will be the same, i.e. E out = 20 1 s. E out = 2 0 1 s. But, there will be higher terms representing the next order of approximation. We use the same procedure as for the charged wire. Electric Field Due to Ring It is straightforward to use Equation to determine the electric field due to a distribution of charge along a straight line. electric field due to circular loop of charge (hindi)electric field due to circular loop of chargeelectric field due to circular loop of charge derivationful. 5. E = k 2qcos r2 ^i (2) (2) E = k 2 q cos r 2 i ^. . A method employing the use of toroidal functions is introduced for calculating the scalar potential and the electric field from a charged conducting ring. Its SI unit is Newton per Coulomb (NC-1). Electric Field Due to a Point Charge Formula The concept of the field was firstly introduced by Faraday. A ring has a uniform charge density , with units of coulomb per unit meter of arc. The axis of the ring is on the x-axis. E 1 = E2 = / 2o Now, let's calculate the Electric field for the elemental charge d q. Solution: the electric potential difference \Delta V V between two points where a uniform electric field E E exists is related together by E=\frac {\Delta V} {d} E = dV where d d is the distance between those points. 2. F is a force. 6. For 2D applications use charge per unit area: = Q/A. Since it is a finite line segment, from far away, it should look like a point charge. Electric field due to uniformly charged ring | Electrostatics | #cbse 12th Physics - YouTube 0:00 / 7:51 12th : Electric Charges and field (Topicwise) 22. We want to nd the off-axis electric eld strength in point ~p. An electric field is a vector quantity and can be visualized as arrows . ]5N&;IxI$#D9VT^^p$Fp0X /1 dE = (Q/Lx2)dx 40 d E = ( Q / L x 2) d x 4 0. This is the potential at the centre of the charged ring. stream The magnitude of the electric field at P due to a segment of the ring of length dl is equal to . while deriving the formula for electric field due to an infinitely long wire of uniform charge density using gauss's law we assume that this field has cylindrical symmetry and there is no component of field along the axis.but how do we know that the field has cylindrical symmetry and there is no component of field along the axis.why can't there R is the radius of the ring. 6 0 obj (b) Find the force on a charge of 2.00 \times 10^{-8} C placed at P . )https://dhxel.courses.store/141161Join \"PHYSICS WITH UMESH RAJORIA\" on YOUTUBE to support me Let's Grow up together https://www.youtube.com/channel/UCmuHnOYD3_S04Kelv9yG8XA/join Support Free Education UPI ID uk.rajoria@okaxis (Preferred)#cbse #physics #neet #iitjee #shorts #physicsnotes #chemistrynotes #biologynotes #umeshrajoria #notes TelegramJoin our Telegram channel for Notes, Mind Maps, Test papers, Books and many more https://t.me/PhysicsWithUmeshRajoria Facebookhttps://www.facebook.com/Physics-with-Umesh-Rajoria-471536193049143 Instagram https://www.instagram.com/physics notes class 12physics notes class 11ncert physics class 12ncert physics class 12 part 1ncert physics class 12 part 2physics class 12 in hindicbse class 12 physicsncert sol phy class 12best channel for physics class 12cbse class 12cbse date sheetcbse term 2 exam physicscbse board examscbse websitecbse exam datesample paper cbse 12class 12 physics syllabus Xfcs equatcn` wcii de useui iater. Download Free PDF. It only depends on the surface density. ]^=S+tm,['aN\&6Wp"_zyWwx-y 9xOe};tQ_t~#k]zjk[bD>p6b]nW>l. Consider the analysis of soil from a farmer's field. stream V=18103. Methods are presented for using the Apple MacIntosh computer for the numerical solution and mapping of fields for electrostatics, steady current flow, heat transfer, and source-free magnetostatics problems. Due to the small cyclotron radius, the positions of the electron in the incident field are approximately unchanged for the case in Fig. %PDF-1.2 -q7Mnz76[-5 BYnC8PhvQq7,Z+Z/BC{A(;y`5=qD%^k1lZBwB4F[nN[N9A( z4AO9 Charge dq d q on the infinitesimal length element dx d x is. E= (x 2+R 2) 23kQx. The electric field E is a vector quantity whose direction is the same as that of the force F exerted on a positive test charge. Volt per metre (V/m) is the SI unit of the electric field. This dq d q can be regarded as a point charge, hence electric field dE d E due to this element at point P P is given by equation, dE = dq 40x2 d E = d q 4 0 x 2. Use Coulomb's law to calculate the electric eld generated by each block. 2sf}13w/q0vy{nKx*cApN\~Uu8D>uJp~@Po3| ` W yh~zLk0Pk0]MN_q{a4y:e jT]dfoChnL?q=~-Am ~H/'/4l"L"zz,_cefx&X\o(6q-Y>mzM_d^ov;kan +n@#i(eIQ@x>y!JI\q^19%SNk_v-[E|qddzqspDl@OC8ycP\\~V)OSN&Kesx"xX"Anp*ko_xo r~-"z? data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAB4CAYAAAB1ovlvAAAAAXNSR0IArs4c6QAAAnpJREFUeF7t17Fpw1AARdFv7WJN4EVcawrPJZeeR3u4kiGQkCYJaXxBHLUSPHT/AaHTvu . Where, E is the electric field intensity. This method is an alternative to the, We calculate the electrostatic potential and electric field of a uniformly charged disk everywhere in space. is the charge density. It is created when there is an electric charge around a region, and its effect can be observed when another charge is brought into a region where the electric field is. Since it is a finite line segment, from far away, it should look like a point charge. Here, we apply ion mobility mass spectrometry coupled with density functional theory to investigate the disassembly mechanisms and energetics of a family of heterometallic rings and rotaxanes with the general formula . 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