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{-5[&|$Nqs c*'G{v6>S0jzt!_-#CAf/,`" Which is obtained by using a U substitution. The force corresponding to this potential is Get solutions Get solutions Get solutions done loading Looking for the textbook? 30 623-627 You are integrating with respect to $r'$, so the $r$ comes outside the integral and you get (in polar coordinates): $\frac{ \sigma}{4\pi \epsilon_o} \sum_{l = 0} ^{\infty} \frac{1}{r^{1+l}}\int p_l(\cos \phi) \left( r' \right)^l r'dr'd\phi.$. 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. However, I hit a moderate snag that I was not able to reason out. 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. -? 40A?qP Plzs~@} $Y_$5zY QDq3Zk'%Dyhiy
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F'=p?[5%ztV}%#cUaDg{Y #knhqVlZ]-e%0Ir6G9 Effect of coal and natural gas burning on particulate matter pollution. Books that explain fundamental chess concepts, What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. The differential Voltage from a differential ring of charge with radius $r$ is: $$dV = \frac{1}{4 \pi \epsilon_o} \frac{dq}{ \mathscr{R}}$$, $$ \Delta V(z) = \frac{ \sigma}{2 \epsilon_o}\int_0^R \frac{ r dr}{\sqrt{r^2 + z^2}} = \frac{ \sigma}{2 \epsilon_o} \left( \sqrt{R^2 + z^2} - |z| \right)$$. For page To finddQ, we will need $dA$. 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. 6 0 obj ^4+N{.8Ocz8(8An h} !4_c~yatAyg9Vs;Bv!StHd7,=x;HsJ|DeX]=OO9wSs If we bring a charged particle from infinity to a point in this field, we need to do some work. Okay, Now find the approximate value. https://www.miniphysics.com/uy1-electric-field-of-uniformly-charged-disk.html. $$dE_{x} = \frac{x \, dQ}{4 \pi \epsilon_{0} (x^{2} + r^{2})^{\frac{3}{2}}}$$, $$dE_{x} = \frac{\sigma}{2 \epsilon_{0}} \frac{xr \, dr}{(x^{2} + r^{2})^{\frac{3}{2}}}$$, $$E_{x} = \frac{\sigma x}{2 \epsilon_{0}} \int\limits_{0}^{R} \frac{r}{(x^{2} + r^{2})^{\frac{3}{2}}} \, dr$$. Is it as simple as. What is $V$ relative to? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Assuming $\sigma$ is not a function of $r'$ the last equation will then look like: $\frac{ \sigma}{4\pi \epsilon_o}\frac{1}{r} \sum_{l = 0} ^{\infty} p_l(\cos \phi) \left( \frac{r'}{r} \right)^l dt$. }Yo;g7L4@:k"MOOX#\.^1c7 cp5nN4\IMt
@8P&A""-8YFdsF3kj(6W|p>p IN1'!}Y It only takes a minute to sign up. Administrator of Mini Physics. endobj B pl+1 -P.(cose), (1) 0 for coefficients Be to be determined. His teacher replied that we can find the potential on the axis of this plate using electrostatic concept. What point should I expand my taylor series about? endstream Are there breakers which can be triggered by an external signal and have to be reset by hand? << /Length 5 0 R /Filter /FlateDecode >> Thanks for your reply. endobj >> /Font << /TT1 8 0 R /TT9 18 0 R /TT10 19 0 R /TT4 11 0 R /TT2 9 0 R /TT8 Dec 5, 2009. 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. (i.e., what is your ground potential?) >> 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. Next: Electric Field Of Two Oppositely Charged Infinite Sheets, Previous: Electric Field Of A Line Of Charge. Assume . 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. It seems you should expand the integrand in terms of Legendre polynomials. 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. Even so, it is very unlikely that you will be able to get the solution in a closed form. However that is something I already considered. Electric field off axis inside a charged ring. Wendy is very large. 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. Physics Ninja looks at the electrical potential V produced by a charged disk with a uniform charge distribution. Deduce the electric potential $V(z)$ along the z-axis. However that is something I already considered. Expand the potential at $p'$ in terms of Legendre polynomials $P_l(\cos\theta)$ for $\rho < R$ and $\rho > R$. J. Phys. true /ColorSpace 7 0 R /SMask 20 0 R /BitsPerComponent 8 /Filter /FlateDecode 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. Something can be done or not a fit? _g$!v_Qr3K? )B@ip@M 3~-;6i W/"f,+dfF]:} Making statements based on opinion; back them up with references or personal experience. << /Length 13 0 R /Type /XObject /Subtype /Image /Width 1026 /Height 900 /Interpolate In the Math section, I would use a little more care in defining terms. he was interested in knowing the potential due to the circular disc on its axis and the edges . Is Energy "equal" to the curvature of Space-Time? Also, what makes an angle with the $z$-axis? >@'>.]T 5 0 obj 3C Any help would save me so very much. It's then just a matter of "pulling out" as many terms as you like, like: $\frac{ \sigma}{4\pi \epsilon_or}\int r'dr' + \frac{ \sigma}{4\pi \epsilon_o r^2}\int r'^2\cos(\phi)dr'd\phi$. I suggest evaluating the potential first and then obtain the field by taking a derivative. [D>vIW-*`8^Jlp j7;3Q(6(\>uPn8x{w6+s|p/(}`09?T(]o (Kdj:.Sent:PDg{ ta'Gy9I[?)S8[p2B!V"4?4t/p{!WWkS=&! Thanks for contributing an answer to Mathematics Stack Exchange! Asking for help, clarification, or responding to other answers. 12 0 obj The field from the entire disc is found by integrating this from = 0 to = to obtain. endobj 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. J3DzGz_271sro1")""E3M5QEslHvmWuaS,5.QqN 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 I think you can see that the off axis solution: V disk[x, y, z] depends in general on x,y, AND z. 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. 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 . MathJax reference. 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. (a) Argue that the potential in the region r > R takes the general form V(r,0) = . It may not display this or other websites correctly. Now, he asked his teacher about the potential on the circular disc due to the flow of charge. Wite B in terms of V, and you'll eliminate the term kQ/a? Should I expand it about u=0 (r >> R) or about u=1 (r=R)? Click both.] How does the Chameleon's Arcane/Divine focus interact with magic item crafting? Is there any reason on passenger airliners not to have a physical lock between throttles? fhs nvHLgK98+_q`qkWd$iYh-Yq8FwUPHygM,`5=9ls_Bu^vr>\]\"#SJ/g%vb8wszk CGAC2022 Day 10: Help Santa sort presents! To find dQ, we will need dA d A. 3xtK x@(mB
[hoN+5!93~l (1.6.11) E = 2 0 ( 1 cos ) = 2 0 ( 1 x ( a 2 + x 2) 1 / 2). I agree (I am a physicist, too). 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 . To learn more, see our tips on writing great answers. Home University UY1: Electric Field Of Uniformly Charged Disk. The rubber protection cover does not pass through the hole in the rim. Electric Potential on the Axis of a Uniformly Charged Disc, Class 12 Boards, JEE, NEET, Potential due a Charged disc, Electrostatic Potential & Capacitance . 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. [Live it up! Imagine moving a +q test charge around the disk with uniform + at various x,y,z values off the z axis. There's the distance from the point on the surface of the disc being integrated to the field point, call this $\mathscr{R}$. 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. You are using an out of date browser. In this case, we have a charged disc, with radius R and charge Q. 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? 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. Hint. $\int_0^R \left( \frac{p}{r} \right)^l dr$? Connect and share knowledge within a single location that is structured and easy to search. Why does the USA not have a constitutional court? If you spot any errors or want to suggest improvements, please contact us. O>d>'$ H@~u(/YSNa`sB!Mp*8G6- H@$FW 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. Here are the equations and results I have. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Wendy is very large. An insulated disk, uniform surface charge density $\sigma$, of radius R is laid on the xy plane. Homework Statement. 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. As another example, let's calculate the electric potential of a charged disc. *))f%g&X Would salt mines, lakes or flats be reasonably found in high, snowy elevations? 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 UI#*%*>l# Does the collective noun "parliament of owls" originate in "parliament of fowls"? 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. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The potential on the axis of a uniformly charged disk is 544 kV at a point 1.27 m from the disk center. 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. Consult with Jackson's EM book or hopefully, Wiki. 2 0 obj HINTS: (i) Treat as a 2D problem. ?eQn ;!r-PTh{YQ@dF+G]CxItQzUimqdgg06m~vrgMI;|j.]R
g y]l> Deduce the electric potential $V(z)$ along the z-axis. 4 0 obj Qh}@
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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 The electric field produced by an infinite plane sheet of charge can be found using Gausss Law as shown here. 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. 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. How is the merkle root verified if the mempools may be different? %PDF-1.3 $\mathscr{R} = (r^2 + p^2 - 2rp\cos \phi)^{1/2} = r(1 - 2 \frac{p}{r}cos \phi + \frac{p^2}{r^2})^{1/2}$, Using Spherical Polar coordinates, << /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 7 0 R How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? 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 Okay, Now find the approximate value. JavaScript is disabled. >> 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. Does a 120cc engine burn 120cc of fuel a minute? ,{* pM%F@i9 Let us assume that the charge is distributed uniformly through the surface of this disc and we are . Binomial series expansion of a trinomial? This creates an infinity. 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. Any plane through the z-axis will do take . Potential of a charged disc with radius R, and charge Q along its axis, z distance from its center. There's the distance from the origin to the field point, call this $r$. VC+qjxNfh6s@d/6R?IXh&1H"pyTOJ&'JbbmWG
wIO}PmS]D!LeD = Q R2 = Q R 2. 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. In this video you will know about complete derivation of Electric Field inside and outside the uniformly charged cylinder @Kamaldheeriya Maths easyThis is m. Now. 5502 to get an approximation for the potential to any accuracy you desire. Wrong direction in electric field of a linear charge. 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: $$dV = \frac{ \sigma}{2 \epsilon_o} \frac{r dr}{ \mathscr{R}}$$. And there's the distance from the origin on the disc to the point being integrated, call this $r'$. Calculating Force between point particle and Spherical Object, Calculating the potential generated by a specific distribution of charge. 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. stream stream 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. Not everyone who can possibly help you is a physicist who understands that you mean $V$ when you write $\Delta V$. Figure 25.15 shows one such ring. 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. For a uniform infinte line charge, the potential at a distnace r is given by equation 3.3 as . Next consider . How did muzzle-loaded rifled artillery solve the problems of the hand-held rifle? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. JI=#DvcvN("5}d(lg0t[^THvFn_c]GdW\sD{#,g? << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 612 792] :r)B,ou
/j!;7<=9o&h Un)7DM;!z{R \$%`>t0j(D4s[$? Any plane through the z-axis will do take . Use MathJax to format equations. A charge distributed uniformly over a disc will produce an electric field. The best answers are voted up and rise to the top, Not the answer you're looking for? Your solution to the 1st part looks OK, just figure out what quantity the function represents. G. Notify me of follow-up comments by email. Izx+6pJBvvN#X*'shs lUcd2`[f]Y
cA Ktd;oJAIT rlC;jR-@j_$DQ for a general surface or volume element $dt$. The mathematical calculation of the off-axis electrostatic potential created by a uniformly charged disk is of great interest to many scientific disciplines. for the point on the z-axis, this is pretty easy. l7I|
e JVD={?FP^ ,jBtLPanR! 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. Why does the distance from light to subject affect exposure (inverse square law) while from subject to lens does not? This falls off monotonically from / ( 2 0) just above the disc to zero at infinity. The electric field at the same point is 417 kV/m. $$\begin{aligned} E_{x} &= \frac{\sigma x}{2 \epsilon_{0}} \left( \frac{1}{x}- \frac{1}{\sqrt{x^{2} + R^{2}}} \right) \\ &= \frac{\sigma}{2 \epsilon_{0}} \left( 1 \frac{1}{\sqrt{1 + \frac{R^{2}}{x^{2}}}} \right) \end{aligned}$$. How to use a VPN to access a Russian website that is banned in the EU? 7(O Next consider an off axis point $p'$, with distance $\rho$ from the center, Making an angle $\theta$ with the z-axis. Note that dA = 2rdr d A = 2 r d r. % HINTS: (i) Treat as a 2D problem. 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 . Minor typo. C(f]B36E:fufz7u,7IPUmJeE&w9{pHACJ}w(ftYiOE'ZIrLE4*,gauB|id5wL;awb1hNG (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. 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. Why the $\Delta V$? ]QRo n!li>S@6OWDqjKUk2e839D; For a better experience, please enable JavaScript in your browser before proceeding. This page titled 1.6E: Field on the Axis of a Uniformly Charged Disc is shared . Note that $dA = 2 \pi r \, dr$, $$\begin{aligned} dQ &= \sigma \times dA \\ &= 2 \pi r \sigma \, dr \end{aligned}$$. x
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