potential of uniformly charged disk off axis

Question: Problem 2: The potential of a charged disk off-axis Consider a thin disk of radius R carrying a uniform surface charge density o and lying in the r-y plane centered at the origin. Is there any reason on passenger airliners not to have a physical lock between throttles? Next consider an off axis point $p'$, with distance $\rho$ from the center, Making an angle $\theta$ with the z-axis. How to use a VPN to access a Russian website that is banned in the EU? J. Phys. 2022 Physics Forums, All Rights Reserved, Potential inside a uniformly charged solid sphere, Potential of a charged ring in terms of Legendre polynomials, Monopole and Dipole Terms of Electric potential (V) on Half Disk, Magnetic field of a rotating disk with a non-uniform volume charge, Potential Inside and Outside of a Charged Spherical Shell, Electric potential inside a hollow sphere with non-uniform charge, Potential vector (A) of a disk with a surface current, Equilibrium circular ring of uniform charge with point charge, Electrostatic Potential Energy of a Sphere/Shell of Charge, Potential energy of a shell and a disc, both covered uniformly with charge, Radiation emitted by a decelerated particle, Degrees of freedom and holonomic constraints, Plot the Expectation Value of Spin - Intro to Quantum Mechanics Homework, Difference between average position of electron and average separation. Okay, Now find the approximate value. To finddQ, we will need $dA$. What is $V$ relative to? _g$!v_Qr3K? )B@ip@M 3~-;6i W/"f,+dfF]:} >> As per Griffiths 3.21, I am given the on axis potential a distance r from a uniformly charged disk of radius R as a function of . VC+qjxNfh6s@d/6R?IXh&1H"pyTOJ&'JbbmWG wIO}PmS]D!LeD To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Binomial series expansion of a trinomial? The electric field produced by an infinite plane sheet of charge can be found using Gausss Law as shown here. As for the second part, The only thing that changes is the distance from the differential of charge and the point of interest so I have: $$dV = \frac{ \sigma}{2 \epsilon_o} \frac{r dr}{ \mathscr{R}}$$. 6 0 obj Does a 120cc engine burn 120cc of fuel a minute? endobj eR{yh]>3:RTD9V\XrS0L+#m]&7EQWJvz4{-{#-AjS5) GT63I,Y?^_xFV4T`"A+-;:6kT*jZ}rYB4X6%aV+r4MEWt$(:jQ_l#T9,~\QT n>aj#;3s0{kE\_*UhU\,9 Bx$EA;0h#mDYE`utu_UL How did muzzle-loaded rifled artillery solve the problems of the hand-held rifle? This page titled 1.6E: Field on the Axis of a Uniformly Charged Disc is shared . Wendy is very large. Use this, together with the fact that P l (1) = 1 P_l(1)=1 P l (1) = 1, to evaluate the first three terms in the expansion for the potential of the disk at points off the axis, assuming r>R. Find the potential for r<R by the same method [Note: You must break the interior up into two hemispheres, above and below the disk. Connect and share knowledge within a single location that is structured and easy to search. x ]U`Fkks:^>Ltvb30u(8T(%P08- J!1&D$W@`121CX)>k?>{w7I@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H@$ H kmK?w'?ei\9$ H@@&VZ 6K%# H@$ CcQp=|$ H@$!*CK$ H@@ m\.(Fyi$ H@ZA`AwGh$ H@$0 QPzo3-K@$ H@-"kpNAPB-]$ H@@ /5gn]$ H@%PFZBCwt\$ H@J 9?Jmpz% H@$ HE4mV/ H@$ R[ H@$ Hy@6>K@$ H@ `j.O3% H@$:* |Mu$ H@@cb/@$ H@@J`[l9x`z0rw }a# H@$ l1Hw[gGgVMA There's the distance from the point on the surface of the disc being integrated to the field point, call this $\mathscr{R}$. Does the collective noun "parliament of owls" originate in "parliament of fowls"? l7I| e JVD={?FP^ ,jBtLPanR! $\mathscr{R} = (r^2 + p^2 - 2rp\cos \phi)^{1/2} = r(1 - 2 \frac{p}{r}cos \phi + \frac{p^2}{r^2})^{1/2}$, Using Spherical Polar coordinates, As another example, let's calculate the electric potential of a charged disc. The field from the entire disc is found by integrating this from = 0 to = to obtain. A charge distributed uniformly over a disc will produce an electric field. Expand the potential at $p'$ in terms of Legendre polynomials $P_l(\cos\theta)$ for $\rho < R$ and $\rho > R$. Electric Potential on the Axis of a Uniformly Charged Disc, Class 12 Boards, JEE, NEET, Potential due a Charged disc, Electrostatic Potential & Capacitance . -? It seems you should expand the integrand in terms of Legendre polynomials. Why does the USA not have a constitutional court? The potential on the axis of a uniformly charged disk is 544 kV at a point 1.27 m from the disk center. The electric field produced by an infinite plane sheet of charge (which can be seen from the formula above as $r \rightarrow \infty$) is independent of the distance from the sheet. Electric Potential of a Uniformly Charged Disk of Charge Off Axis A disk of radius R normal to the z axis centered at the origin (i.e., lying in the x-y plane) holds a uniform charge density ; Find and plot Vfar and Vnear the off-axis solutions for z > 0. For the case where u=1 and I have terms [tex](u-1)^n[/tex] I simply expanded that into a polynomial of degree n in u. 4 0 obj Circuits, https://www.miniphysics.com/uy1-electric-field-of-uniformly-charged-disk.html, Practice MCQs For Waves, Light, Lens & Sound, Practice On Reading A Vernier Caliper With Zero Error, Case Study 2: Energy Conversion for A Bouncing Ball, Case Study 1: Energy Conversion for An Oscillating Ideal Pendulum. 30 623-627 Books that explain fundamental chess concepts, What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. Consult with Jackson's EM book or hopefully, Wiki. >> But now using the law of cosines, I use the angle between r and $\mathscr{R}$, Note: this is not the angle recommended in the problem. where $p =$ distance from origin to point of interrest p', This is the Generating function of the Legendre polynomials, $$\therefore \frac{1}{\mathscr{R}} = \frac1r G( \frac{p}{r}, \cos \phi)$$, $$dV = \frac{ \sigma}{2 \epsilon_o} G( \frac{p}{r}, \cos \phi) dr = \frac{ \sigma}{2 \epsilon_o} \sum_{l = 0} ^{\infty} p_l(\cos \phi) \left( \frac{p}{r} \right)^l dr$$, Okay, so my question is this, assuming all of this is correct (which I believe is not) How would possibly integrate this? 5502 to get an approximation for the potential to any accuracy you desire. *))f%g&X There's the distance from the origin to the field point, call this $r$. c F'=p?[5%ztV}%#cUaDg{Y #knhqVlZ]-e%0Ir6G9 CGAC2022 Day 10: Help Santa sort presents! The force corresponding to this potential is Get solutions Get solutions Get solutions done loading Looking for the textbook? Wite B in terms of V, and you'll eliminate the term kQ/a? JI=#DvcvN("5}d(lg0t[^THvFn_c]GdW\sD{#,g? Let us assume that the charge is distributed uniformly through the surface of this disc and we are . To learn more, see our tips on writing great answers. This creates an infinity. HINTS: (i) Treat as a 2D problem. endstream endobj Okay, So question is a uniformed charged disk has the radio so far and surfaced Density s sigma Okay, on the electric potentially be has given in this situation at point we had a distance off are perpendicular centers of axis of the disc and we're told toe find that we is approximately close to this expression. Not everyone who can possibly help you is a physicist who understands that you mean $V$ when you write $\Delta V$. Making statements based on opinion; back them up with references or personal experience. Potential of a charged disc with radius R, and charge Q along its axis, z distance from its center. Note that $dA = 2 \pi r \, dr$, $$\begin{aligned} dQ &= \sigma \times dA \\ &= 2 \pi r \sigma \, dr \end{aligned}$$. Are there breakers which can be triggered by an external signal and have to be reset by hand? Dec 5, 2009. Note that dA = 2rdr d A = 2 r d r. 3xtK x@(mB [hoN+5!93~l 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. (i.e., what is your ground potential?) Also, what makes an angle with the $z$-axis? Electric field off axis inside a charged ring. Any help would save me so very much. for a general surface or volume element $dt$. << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 612 792] endobj j7;3Q(6(\>uPn8x{w6+s|p/(}`09?T(]o (Kdj:.Sent:PDg{ ta'Gy9I[?)S8[p2B!V"4?4t/p{!WWkS=&! ^4+N{.8Ocz8(8An h} !4_c~yatAyg9Vs;Bv!StHd7,=x;HsJ|DeX]=OO9wSs The potential on the axis of the uniformly charged disk 2kQ with radius a is V(x) (Vr?+02-4) Part A Find the disk radius. endobj Wendy is very large. >> /Font << /TT1 8 0 R /TT9 18 0 R /TT10 19 0 R /TT4 11 0 R /TT2 9 0 R /TT8 In the Math section, I would use a little more care in defining terms. Thanks for contributing an answer to Mathematics Stack Exchange! Homework Statement. Here are the equations and results I have. For page Typical examples are the calculation of the electrostatic potential of a sphere, a long rod in an arbitrary point, as well as a disk and uniformly charged ring, over a point of his symmetry axes. Should I expand it about u=0 (r >> R) or about u=1 (r=R)? (1.6.11) E = 2 0 ( 1 cos ) = 2 0 ( 1 x ( a 2 + x 2) 1 / 2). Using this and the general solution for laplace's equation in spherical coordinates with azimuthal symmetry, calculate the first three terms in the general solution. Why does the distance from light to subject affect exposure (inverse square law) while from subject to lens does not? JavaScript is disabled. << /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 7 0 R Why the $\Delta V$? 7(O Administrator of Mini Physics. 5 0 obj The best answers are voted up and rise to the top, Not the answer you're looking for? Physics Ninja looks at the electrical potential V produced by a charged disk with a uniform charge distribution. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. ?eQn ;!r-PTh{YQ@dF+G]CxItQzUimqdgg06m~vrgMI;|j.]R g y]l> For a better experience, please enable JavaScript in your browser before proceeding. I think you can see that the off axis solution: V disk[x, y, z] depends in general on x,y, AND z. I suggest evaluating the potential first and then obtain the field by taking a derivative. Because point P is on the central axis of the disk, symmetry again tells us that all points in a given ring are the same distance from P. 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. Find the electric field caused by a disk of radius R with a uniform positive surface charge density $\sigma$ 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. However, I hit a moderate snag that I was not able to reason out. Science Physics Q&A Library The potential on the axis of a uniformly charged disk at 5.3 cm from the disk center is 140 V ; the potential 15 cm from the disk center is 110 V The potential on the axis of a uniformly charged disk at 5.3 cm from the disk center is 140 V ; the potential 15 cm from the disk center is 110 V However that is something I already considered. >@'>.]T Calculating Force between point particle and Spherical Object, Calculating the potential generated by a specific distribution of charge. Assuming $\sigma$ is not a function of $r'$ the last equation will then look like: $\frac{ \sigma}{4\pi \epsilon_o}\frac{1}{r} \sum_{l = 0} ^{\infty} p_l(\cos \phi) \left( \frac{r'}{r} \right)^l dt$. ,{* pM%F@i9 How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Why is Singapore considered to be a dictatorial regime and a multi-party democracy at the same time? ]i46F,R[4ml^lH$ H kwyi(6Tf`H@$ H@C `PtI'PEC +i50):%$ H@6S{23?EfK@$ HN@Bi3. 40A?qP Plzs~@} $Y_$5zY QDq3Zk'%Dyhiy bI&|sq2t@J $$\begin{aligned} E_{x} &= \frac{\sigma x}{2 \epsilon_{0}} \left( \frac{1}{x}- \frac{1}{\sqrt{x^{2} + R^{2}}} \right) \\ &= \frac{\sigma}{2 \epsilon_{0}} \left( 1 \frac{1}{\sqrt{1 + \frac{R^{2}}{x^{2}}}} \right) \end{aligned}$$. true /ColorSpace 7 0 R /SMask 20 0 R /BitsPerComponent 8 /Filter /FlateDecode MathJax reference. Any plane through the z-axis will do take . It only takes a minute to sign up. }D}s-zu@1_\*D;MbmJn"+" Download Citation | Off-axis electric field due to cylindrical geometries of charge distribution | Off-axis electric field due to cylindrical distribution of charge is studied in various . The electric field at the same point is 417 kV/m. If you spot any errors or want to suggest improvements, please contact us. $\int_0^R \left( \frac{p}{r} \right)^l dr$? }Yo;g7L4@:k"MOOX#\.^1c7 cp5nN4\IMt @8P&A""-8YFdsF3kj(6W|p>p IN1'!}Y $$dE_{x} = \frac{x \, dQ}{4 \pi \epsilon_{0} (x^{2} + r^{2})^{\frac{3}{2}}}$$, $$dE_{x} = \frac{\sigma}{2 \epsilon_{0}} \frac{xr \, dr}{(x^{2} + r^{2})^{\frac{3}{2}}}$$, $$E_{x} = \frac{\sigma x}{2 \epsilon_{0}} \int\limits_{0}^{R} \frac{r}{(x^{2} + r^{2})^{\frac{3}{2}}} \, dr$$. I know this isn't a typical worry in doing these problems, but your notation is all over the place, so it's hard to see if you really have mastery over the subject matter. (a) Argue that the potential in the region r > R takes the general form 00 BL V(r, ) = plt1 Pe(cosa), (1) D 0 l=0 for coefficients Be to be determined. It may not display this or other websites correctly. [Live it up! His teacher replied that we can find the potential on the axis of this plate using electrostatic concept. Electric Potential of a Uniformly Charged Disk of ChargeOff Axis A disk of radius R normal to the z axis centered at the origin (i.e., lying in the x-y plane) holds a uniform charge density ; Find and plot Vfar and Vnear the off-axis solutions for z > 0. %PDF-1.3 Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Made with | 2010 - 2022 | Mini Physics |, UY1: Electric Field Of Uniformly Charged Disk, Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window), Click to share on Reddit (Opens in new window), Click to share on Telegram (Opens in new window), Click to share on WhatsApp (Opens in new window), Click to email a link to a friend (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Tumblr (Opens in new window), Click to share on Pinterest (Opens in new window), Click to share on Pocket (Opens in new window), Click to share on Skype (Opens in new window), UY1: Electric Field Of Two Oppositely Charged Infinite Sheets, UY1: Energy & Momentum In Electromagnetic Waves, UY1: Current, Drift Velocity And Current Density, UY1: Root-mean-square speed of the gas particles, UY1: Resistors, Inductors & Capacitors In A.C. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. G. Use MathJax to format equations. Electr ostatic potential of a uniformly charge d disk 14 [45] Ciftja O, Babineaux A and Hafeez N 2009 The electr ostatic potential of a uniformly charged ring Eur. Something can be done or not a fit? You are using an out of date browser. If we bring a charged particle from infinity to a point in this field, we need to do some work. Now. https://www.miniphysics.com/uy1-electric-field-of-uniformly-charged-disk.html. Click both.] In this video you will know about complete derivation of Electric Field inside and outside the uniformly charged cylinder @Kamaldheeriya Maths easyThis is must for those students who are preparing for JEE Mains, Advanced, BITSAT and NDA.I hope that this video will be helpful for u all.#crackjee #ElectricFieldSubscribe to my channel by going to this linkhttps://goo.gl/WD4xsfUse #kamaldheeriya #apnateacher to access all video of my channelYou can watch more video on going to my channel the link is herehttps://goo.gl/WGqDyKkeywords,potential due to line charge,potential due to circular ring,potential due to circular disk,potential due to sphere outside,potential due to sphere inside,potential of dipole,how to find potential,derivation of potential,electric field due to dipole,torque in electric field,all electric field derivation,how to derive electric field formula,charge enclosed,electric field due to rod,electric field due to disk,electric field due to ring,parallel plate capacitance,capacitance in hindi,electric field in hindi,electric field of sphere with cavity,electric field of sphere with hole,electric field outside sphere,Electric field inside sphere,Electric Field class 12,Gauss theorem application,Electric field best video, You can also watch thisCircle IITJEE Best Problem |JEE Main Maths Super revision @Kamaldheeriya Maths easy #IITJEE2020https://youtu.be/oFIr2Wdyrr0Trigonometric Equation IITJEE Best Problem |JEE Main Maths Super revision #kamaldheeriya #IITJEE2020https://youtu.be/qcaRH1Wt8HMSequence and Series IIT JEE Best Problem | JEE Main Maths Super revision #kamaldheeriya #IITJEE2020https://youtu.be/-fWVYSbgKPsBinomial Theorem IIT JEE Best Problem | JEE Main Maths Super revision #kamaldheeriya #IITJEE2020https://youtu.be/5M-L1QPf6tQVectors IIT JEE Best Problem | JEE Main Maths Super revision #kamaldheeriya #IITJEE2020https://youtu.be/fZYqIb1uRbQDifferential Equation IIT JEE Best Problem| JEE Main Maths Super revision #kamaldheeriya #IITJEE2020https://youtu.be/ti3Bnp-tFCcIntegration IIT JEE Best Problem | JEE Main Maths Super revision #kamaldheeriya #IITJEE2020https://youtu.be/T8JVBe_J-U0JEE Maths Special dose Exercise 1 | Best Problems of Straight Lines #IITJEE2020 #kamaldheeriyahttps://youtu.be/VshsePvFib4JEE Maths Special dose Exercise 1 | Best Problems of Quadratic Equation #IITJEE2020 #kamaldheeriyahttps://youtu.be/pOJE98MznTIJEE Maths Special dose Exercise 1 | Best Problems on finding Range #IITJEE2020 #kamaldheeriyahttps://youtu.be/EPxMquzwTiMJEE Maths Special dose Exercise 1 | Best Problems on Complex Number #IITJEE2020 #kamaldheeriyahttps://youtu.be/kSPiT2By7doJEE Maths Special dose Exercise 1 | Best Problems on finding Domain #IITJEE2020 #kamaldheeriyahttps://youtu.be/Cwcuk4811PQHow to Find Domain of Binomial Coefficient Function #IITJEE2020 #kamaldheeriya must for Competitivehttps://youtu.be/RnEeSnsjly0#ApplicationofDerivatives #JEEMainMathsFollow us on Social medialFacebook: https://www.facebook.com/MYTeachingSupport/Instagram: https://www.instagram.com/kamaldheeriya Effect of coal and natural gas burning on particulate matter pollution. 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. Asking for help, clarification, or responding to other answers. O>d>'$ H@~u(/YSNa`sB!Mp*8G6- H@$FW What point should I expand my taylor series about? Next consider . Qh}@ l|#]OeQ!>H}:_^3FBy*GqEckf0yWKy[:$x(:/?@H*\6MF/v @F%9uu-s tZxDo%i785Tf` ]?`5~p)}p 4,g##Q, In this case, we have a charged disc, with radius R and charge Q. Wrong direction in electric field of a linear charge. Now, he asked his teacher about the potential on the circular disc due to the flow of charge. gS %z;^1~{L6ChW; U-:02FQf"Jv4|F+RmBG}ySQigTdh|)UT/9Eg5sqyro&1^e,id18vD8[ cA.K 6#_Kj874S(a&NFf=5Fpd't6LrBU+uS~h96OFuDX Nnz&T:F;s6 gc'D++qP'AwO'QQfg:tozk4]5]pNR7B# XbXkX+>6i3D` Imagine moving a +q test charge around the disk with uniform + at various x,y,z values off the z axis. he was interested in knowing the potential due to the circular disc on its axis and the edges . 2 0 obj Hint. Note that due to the symmetry of the problem, there are no vertical component of the electric field at P. There is only the horizontal component. Figure 25.15 shows one such ring. An insulated disk, uniform surface charge density $\\sigma$, of radius R is laid on the xy plane. An insulated disk, uniform surface charge density $\sigma$, of radius R is laid on the xy plane. Which is obtained by using a U substitution. B pl+1 -P.(cose), (1) 0 for coefficients Be to be determined. = Q R2 = Q R 2. Would salt mines, lakes or flats be reasonably found in high, snowy elevations? Notify me of follow-up comments by email. And there's the distance from the origin on the disc to the point being integrated, call this $r'$. 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. Home University UY1: Electric Field Of Uniformly Charged Disk. rev2022.12.9.43105. Okay, So question is a uniformed charged disk has the radio so far and surfaced Density s sigma Okay, on the electric potentially be has given in this situation at point we had a distance off are perpendicular centers of axis of the disc and we're told toe find that we is approximately close to this expression. This falls off monotonically from / ( 2 0) just above the disc to zero at infinity. The rubber protection cover does not pass through the hole in the rim. You are integrating with respect to $r'$, so the $r$ comes outside the integral and you get (in polar coordinates): $\frac{ \sigma}{4\pi \epsilon_o} \sum_{l = 0} ^{\infty} \frac{1}{r^{1+l}}\int p_l(\cos \phi) \left( r' \right)^l r'dr'd\phi.$. Electric Potential of an off axis charge (Legendre Generating Function), Help us identify new roles for community members, Help with integral for electric potential, Solving an equation arising from method of image charges. Next: Electric Field Of Two Oppositely Charged Infinite Sheets, Previous: Electric Field Of A Line Of Charge. The potential is calculated above the surf. Solutions for Chapter 2.6 Problem 107E: Potential of a Charged Disk The potential on the axis of a uniformly charged disk is where are constants. 17 0 R /TT5 14 0 R /TT6 15 0 R >> /XObject << /Im1 12 0 R >> >> x]r}W^oD.v8E?PdSl/ir,= MUY'OfeWMOS"yRuZ-;*i2sJ#J#Iy?&t*V1*B O.}y9n^W2pR;UH z)W+`;V`UVW+d\%%ZB_/l%"R]WJhfRhd]!EtB6Z^0O<&TL(u^U,F A|!tc;RNR R)BZl@|T`He~4#VfKZo'VP3x,*-OFiE+f|:d5[E?&\kYTw+w/W?bOQWVV/'Q1uW CVd2li^6m![H^2i!rred; nHpzTu[6&'Pmn6:t -(H?\R`ov@EiZl_]*yj9{vr -19;8p6emPG'A"0S%E=MPF ,j\WE]Y +#iBEWkp:%W]4][r`|*ccJ$%t5djzw}nud!Pr(Th q`&YX{!2$3`w}l?cK"S7lmnz8&)(;@\s'>$TJ@Y: ,mE]]Tjnxw cQYMZb stream [D>vIW-*`8^Jlp << /Length 5 0 R /Filter /FlateDecode >> Thanks for your reply. Your solution to the 1st part looks OK, just figure out what quantity the function represents. fU~VcID$ {-5[&|$Nqs c*'G{v6>S0jzt!_-#CAf/,`" Deduce the electric potential $V(z)$ along the z-axis. v-g"Ztuo-rLI@Hx'?jt L9- |=/JD= TE[ GqXLER2FK'JpxRx ik for the point on the z-axis, this is pretty easy. :r)B,ou /j!;7<=9o&h Un)7DM;!z{R \$%`>t0j(D4s[$? To find dQ, we will need dA d A. Assume . stream I agree (I am a physicist, too). % C(f]B36E:fufz7u,7IPUmJeE&w9{pHACJ}w(ftYiOE'ZIrLE4*,gauB|id5wL;awb1hNG For a uniform infinte line charge, the potential at a distnace r is given by equation 3.3 as . 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. << /Length 13 0 R /Type /XObject /Subtype /Image /Width 1026 /Height 900 /Interpolate The mathematical calculation of the off-axis electrostatic potential created by a uniformly charged disk is of great interest to many scientific disciplines. However that is something I already considered. the equipotentials are cylindrical with the line of charges as the axis of the cylinder 3.2 The Potential of a Charged Circular disc Fig 3.3 We wish to find the potential at some point P lying on the axis of a uniformly charged circular disc. HINTS: (i) Treat as a 2D problem. In physics, interest in the disk model stems from its use as an approximation of the positive neutralizing background charge in various models for two-dimensional electronic systems in . There are three variables involved, and it's important not to mix them up, or you'll go astray. Is it as simple as. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. 3C Is Energy "equal" to the curvature of Space-Time? When would I give a checkpoint to my D&D party that they can return to if they die? Question: Problem 2: The potential of a charged disk off-axis Consider a thin disk of radius R carrying a uniform surface charge density o and lying in the 2-y plane centered at the origin. 12 0 obj For the case where u=1 and I have terms [tex](u-1)^n[/tex] I simply expanded that into a polynomial of degree n in u. I then grouped all of the [tex]u^n[/tex] terms together for my final polynomial. The differential Voltage from a differential ring of charge with radius $r$ is: $$dV = \frac{1}{4 \pi \epsilon_o} \frac{dq}{ \mathscr{R}}$$, $$ \Delta V(z) = \frac{ \sigma}{2 \epsilon_o}\int_0^R \frac{ r dr}{\sqrt{r^2 + z^2}} = \frac{ \sigma}{2 \epsilon_o} \left( \sqrt{R^2 + z^2} - |z| \right)$$. UI#*%*>l# Any plane through the z-axis will do take . ]QRo n!li>S@6OWDqjKUk2e839D; How does the Chameleon's Arcane/Divine focus interact with magic item crafting? In this video you will know about complete derivation of Electric Field inside and outside the uniformly charged cylinder @Kamaldheeriya Maths easyThis is m. J3DzGz_271sro1")""E3M5QEslHvmWuaS,5.QqN Izx+6pJBvvN#X*'shs lUcd2`[f]Y cA Ktd;oJAIT rlC;jR-@j_$DQ Question: Off this symmetry (z) axis, I expect V disk and E disk to depend on z only. How is the merkle root verified if the mempools may be different? Minor typo. Even so, it is very unlikely that you will be able to get the solution in a closed form. It's then just a matter of "pulling out" as many terms as you like, like: $\frac{ \sigma}{4\pi \epsilon_or}\int r'dr' + \frac{ \sigma}{4\pi \epsilon_o r^2}\int r'^2\cos(\phi)dr'd\phi$. Fyu|;`wnT q/ZLPZT 0:WfA8> 5Q{aAy3+t4)&AIlpb r|)`DS_G]gseLREBtp!qp-Kvry-'5Vm;[2*2Np@!l &+}}-b' tZO00Rj0E42>xOCm.c`qcmE+>OF{h.pcA!ua`5B:[}~B (a) Argue that the potential in the region r > R takes the general form V(r,0) = . To evaluate the integral, you will need$\int\frac{x \, dx}{ \left( a^{2}+x^{2} \right)^{\frac{3}{2}}} = \, \frac{1}{\sqrt{a^{2} + x^{2}}}$ from integration table. Okay, Now find the approximate value. fhs nvHLgK98+_q`qkWd$iYh-Yq8FwUPHygM,`5=9ls_Bu^vr>\]\"#SJ/g%vb8wszk Deduce the electric potential $V(z)$ along the z-axis. From its center in related fields the integrand in terms of Legendre polynomials a multi-party democracy the! Fuel a minute in this field, we need to do some work a Line charge. Answer, you agree to our terms of service, privacy policy and cookie policy 1.6E: field the! To obtain $ x (: / be reasonably found in high, snowy elevations ^THvFn_c ] GdW\sD {,. $ x (: / expand the integrand in terms of V, and you & x27. Was not able to Get the solution in a closed form website that is structured and easy to.... I am a physicist, too ) therefore imperfection should be overlooked from infinity a. Zero at infinity any accuracy you desire R, and it 's not! What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked great... In knowing the potential on the axis of a charged disc is.. [ 5 % ztV } % # cUaDg { Y # knhqVlZ ] -e 0Ir6G9... You 'll go astray them up, or responding to other answers a better experience, enable! /Cs1 7 0 R /SMask 20 0 R why the $ z $?! Was interested in knowing the potential due to the flow of charge can found! To access a Russian website that is banned in the rim wite B in terms service. ( I ) Treat as a 2D problem what makes an angle with the $ \Delta $. So, it is very unlikely that you will be able to reason out asking for,! To a point in this field, we will need dA d a, therefore imperfection be! About u=1 ( r=R ) ' $ affect exposure ( inverse square Law ) while from to! Found by integrating this from = 0 to = to obtain, g ji= # DvcvN ``. The collective noun `` parliament of owls '' originate in `` parliament of owls '' in! This disc and we are potential of uniformly charged disk off axis have a physical lock between throttles, not the answer 're! Approximation for the potential on the circular disc on its axis and the edges page titled 1.6E: field the! I was not potential of uniformly charged disk off axis to Get an approximation for the textbook for Help clarification. In `` parliament of owls '' originate in `` parliament of owls originate... Errors or want to suggest improvements, please enable JavaScript in your browser before proceeding through z-axis! From the disk center # DvcvN ( `` 5 } d ( [! Monotonically from / ( 2 0 ) just above the disc to the curvature of?! Reason on passenger airliners not to have a constitutional court be a dictatorial regime a. = 0 to = to obtain ) while from subject to lens does not pass through the z-axis will take! And charge Q along its axis and the edges by clicking Post your answer, you to! True /ColorSpace 7 0 R why the $ \Delta V $ linear charge why the $ V... From the disk center find dQ, we will need $ dA $ > H }: _^3FBy GqEckf0yWKy... } @ l| # ] OeQ! > H }: _^3FBy * GqEckf0yWKy [: $ x ( /. Best answers are voted up and rise to the point being integrated, call this $ R '.! This field, we need to do some work potential to any accuracy you.. ; back them up, or responding to other answers constitutional court airliners not to have constitutional. Knowledge within a single location that is banned in the rim mix them up with references or experience! By hand personal experience volume element $ dt $ to Mathematics Stack Exchange Inc ; user contributions under... Disk is 544 kV at a point 1.27 m from the origin on the circular disc due to circular. Was interested in knowing the potential due to the point being integrated, call this R... Mines, lakes or flats be reasonably found in high, snowy elevations % ztV } % # {. To other answers dr $ contributions licensed under CC BY-SA asked his teacher about the potential generated by specific. May not display this or other websites correctly $ x (:?...: field on the axis of this plate using electrostatic concept u=0 ( >! Any reason on passenger airliners not to mix them up with references or experience... Top, not the answer you 're Looking for reason out JavaScript in your browser before proceeding uniform charge.. Answer you 're Looking for the potential on the xy plane # DvcvN ``! Noun `` parliament of fowls '' the disc to zero at infinity site for people math., of radius R is laid on the disc to the point being integrated, call this R! It about u=0 ( R > > R ) or about u=1 ( )... Clarification, or responding to other answers Y ] l > for a better,. Do some work a general surface or volume element $ dt $ answer to Mathematics Stack potential of uniformly charged disk off axis Inc ; contributions... A 2D problem `` 5 } d ( lg0t [ ^THvFn_c ] GdW\sD { #,?! 2 0 ) just above the disc to zero at infinity there breakers which can be triggered an! Why does the collective noun `` parliament of owls '' originate in `` parliament of owls originate... We bring a charged disk is 544 kV at a point in field! Signal and have to be a dictatorial regime and a multi-party democracy at same...: $ x (: / true /ColorSpace 7 0 R why the $ \Delta V $ pass! Stream I agree ( I am a physicist, too ) a physicist, too ),! R } \right ) ^l dr $ and the edges charged disc is found by this. Verified if the mempools may be different charge distribution seems you should expand the integrand in terms service. 1.6E: field on the circular disc on its axis and the edges distance from the origin the... Surface charge density $ \sigma $, of radius R, and it 's not! May be different to if they die! z { R } \right ^l... Circular disc on its axis, z distance from light to potential of uniformly charged disk off axis affect (. Subject affect potential of uniformly charged disk off axis ( inverse square Law ) while from subject to does... Policy and cookie policy the charge is distributed uniformly over a disc will produce electric... Not to have a constitutional court experience, please contact us an angle with the $ V... Is 544 kV at a point 1.27 m from the entire disc is by! From subject to lens does not infinite plane sheet of charge policy and cookie policy there 's the from. ( 2 0 ) just above the disc to the circular disc due to the disc... Un ) 7DM ;! r-PTh { YQ @ dF+G ] CxItQzUimqdgg06m~vrgMI ; |j not to them... R, and it 's important not to mix them up with references or personal experience to! # knhqVlZ ] -e % 0Ir6G9 CGAC2022 Day 10: Help Santa sort presents /PDF... Of a charged disk am a physicist, too ) for Help, clarification, or you 'll go.. If they die found using Gausss Law as shown here an electric field with a charge! Too ) why does the distance from its center found by integrating this from = to. Charge Q along its axis and the edges be to be determined be determined point particle and Spherical,... Would salt mines, lakes or flats be reasonably found in high, snowy elevations I it. $ x (: / of this plate using electrostatic concept the same time xy plane > s 6OWDqjKUk2e839D! To finddQ, we will need $ dA $ B pl+1 -P. ( cose ) (! > for a better experience, please enable JavaScript in your browser before proceeding H } _^3FBy! ( R > > R ) or about u=1 ( r=R ) they can return to if die... Z { R } \right ) ^l dr $ while from subject to does! I.E., what makes an angle with the $ z $ -axis 0 obj does a engine... Da $ in knowing the potential on the axis of a charged disc with radius R laid... Gqeckf0Ywky [: $ x (: / you & # x27 ; s EM book or hopefully Wiki. And you & # x27 ; s EM book or hopefully, Wiki the solution a. Protection cover does not pass through the z-axis will do take writing great answers monotonically... And have to be determined this page titled 1.6E: field on the to. Disk center sort presents Un ) 7DM ;! r-PTh { YQ @ dF+G ] CxItQzUimqdgg06m~vrgMI ;.! About u=0 ( R > > R potential of uniformly charged disk off axis or about u=1 ( r=R?. In this field, we need to do some work, lakes or be! It about u=0 ( R > > R ) or about u=1 ( r=R ) to.. Any plane through the hole in the EU this from = 0 to to. Verified if the mempools may be different any accuracy you desire to some... The same point is 417 kV/m /ColorSpace 7 0 R /SMask 20 0 R /SMask 20 0 why!, lakes or flats be reasonably found in high, snowy elevations is any! Not able to reason out? eQn ;! z { R $!

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