$$ The $z$-component of this electric field is The ratio $\dfrac{{{\rho }_{1}}}{{{\rho }_{2}}}$ can be: In the given figure, the particles have charge, \[{{q}_{1}}=-{{q}_{2}}=100nC\text{ }\]\[\text{and }{{q}_{3}}=-{{q}_{4}}=200nC\],and if the distance, \[a=5.0cm\]. for JEE 2022 is part of JEE preparation. Suppose, we wish to find the electric field at a point $(0,0,z)$. The charge of this element is $\sigma dx dy$. However, since you are asking for a more formal answer, I will write one. Imagine sitting very close to the sheet. Why don't you do the computation? Correctly formulate Figure caption: refer the reader to the web version of the paper? $$ The first derivation is incorrect because we assume the sheet of charge to be infinitely thin and the surface you are using to apply Gauss Law is also infinitely thin, and so the Gaussian surface must either contain the charged sheet (as it does in derivation 2), or it doesn't contain the second sheet, in which case $Q_{enc}=0$ and so Gauss Law doesn't do anything for us, since we just get $0=0$. But for a non conducting sphere, the charge will get distributed uniformly in the volume of the sphere. Why does the equation hold better with points closer to the sheet? to us, but not w.r.t. The charge enclosed is the same in both pictures, and the flux is 2EA in both pictures. However, how do we know the. Electric field due to conducting and non-conducting plates. Of course, if it were a conductor, then there must be an equal amount of charge on the right surface of the conducting plate. Work them all out and show that in the small $z/a$ limit, $E_x$ and $E_y$ vanish, while $E_z$ goes to $\frac{\sigma}{2\epsilon_0}$. For a better experience, please enable JavaScript in your browser before proceeding. Japanese girlfriend visiting me in Canada - questions at border control? I'm trying to derive the electric field due to a single large, thin, non-conducting plate at a point (see figure). Thus, when we are sitting close to the sheet, the field takes the form you described above. You are using an out of date browser. In this limit, we find Integrating this over the sheet, we find the total electric field at $(0,0,z)$ as @Prahar Could you please give me a more formal explanation? The Earth is big w.r.t. Charges $25 \mathrm{Q}, 9 \mathrm{Q}$ and $\mathrm{Q}$ are placed at point $\mathrm{ABC}$ such that $\mathrm{AB}=4 \mathrm{~m}, \mathrm{BC}=3 \mathrm{~m}$ and angle between $\mathrm{AB}$ and $\mathrm{BC}$ is $90^{\circ} .$ then force on the charge $\mathrm{C}$ is: Why must electrostatic fields at the surface of a charged conductor be normal to the surface at every point? However, since you are asking for a more formal answer, I will write one. move in very close to the sheet. LET'S LEARN PHYSICS. By symmetry, this electric field will point solely in the $z$-direction. dE = \frac{1}{4\pi \epsilon_0} \frac{\sigma dx dy}{x^2 + y^2 + z^2 } Inserting a dielectric in a parallel-plate capacitor, MOSFET is getting very hot at high frequency PWM. $$ since both are in same direction they are added and we get option 'b'as answer. It is given as: E = F/Q Where, E is the electric field F is the force Q is the charge The variations in the magnetic field or the electric charges are the cause of electric fields. In order to obtain the constants I used three things: 1) the fact that the electric field outside the plate is symmetrical w.r.t the plate (and not just constant) 2) Gauss law where the two bases of the Gaussian cylinder/box are outside the plate 3) Gauss law where one base is inside the plate and the other . Electric Field Due To Infinite Plane Sheets(Conduction and Non Conducting) -Derivation. I don't really get the analogy you gave above. Irreducible representations of a product of two groups. For a given closed surface . Finding the general term of a partial sum series? I had read that thread before posting but was unable to find the exact reason as to why the Gauss Law application in the 1st derivation was incorrect. Electric field of not-grounded conducting plate with a given potential? Is it appropriate to ignore emails from a student asking obvious questions. MathJax reference. The equation F = qE determines the force, where F and E are vector variables, and q is a scalar number. This would give E = 0 inside, and E = / 0 outside Share Cite Just because I'm closer, it doesn't mean the sheet is any bigger. So, the value of electric field due to it will be different from the value of electric field for conducting sphere. Compute the electric field at a general point $(x,y,z)$ in space-time. It only takes a minute to sign up. where $\sigma$ is the surface charge density. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Let us now take the limit of small $z$. What is the electric field in a parallel plate capacitor? This electric field will have in general all 3 - components $(E_x, E_y, E_z)$. Connect and share knowledge within a single location that is structured and easy to search. to us, but not w.r.t. Direction of electric field at points on boundary between two dieletrics. The question you must always ask when you use the word "big" is "big with respect to what?" I computed the field at $(0,0,z)$ so that I have enough symmetry to say $E_x = E_y = 0$ even for a finite plate. Why doesn't the magnetic field polarize when polarizing light. How many transistors at minimum do you need to build a general-purpose computer? Electrical Force And Its Characteristics 15,399 Stay tuned with BYJU'S for more such interesting derivations in physics, chemistry and maths in an engaging way with video explanations. A charged particle having a charge "q" is placed close to a non conducting plate having charge density "d". Really nice explanation! What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. The Earth is big w.r.t. The Question and answers have been prepared according to the JEE exam syllabus. Suppose, we wish to find the electric field at a point $(0,0,z)$. dE_z = \frac{1}{4\pi \epsilon_0} \frac{\sigma z dx dy}{\left( x^2 + y^2 + z^2 \right)^{3/2}} Use logo of university in a presentation of work done elsewhere. THE BOOK says this: "With twice as much charge now on each inner face, the new surface charge density (s) on each inner face is twice s1. A similar thing happens here. The electric field due to ONE plate is E1 = s/epsilon0. One more thing - your proof calculates the field at $(0,0,z)$ - does this work for other points too? Since electric field is a VECTOR, the NET electric field is: E = E1 + E2 = 2 X s/epsilon0. What is the formula for an electric field? And the voltage between the plates is 28 volts. make the sheet very very large. The UNIFORM electric field between the leaves would have a magnitude of. $$ where $\sigma$ is the surface charge density. CGAC2022 Day 10: Help Santa sort presents! A similar thing happens here. To find the electric field, consider a small element on the sheet located at $(x,y)$ of area $dx dy$. dE_z = \frac{1}{4\pi \epsilon_0} \frac{\sigma z dx dy}{\left( x^2 + y^2 + z^2 \right)^{3/2}} The work done by the field in the above process is: NEET Repeater 2023 - Aakrosh 1 Year Course, To Measure the Thickness of a Given Sheet Using Screw Gauge, Potential Energy of Charges in an Electric Field, Calculating the Value of an Electric Field, Difference Between Electric Field and Magnetic Field, Relation Between Electric Field and Electric Potential, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. 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If charge A, B, C, D, E and F are \[2\mu C\], \[2\mu C\], \[2\mu C\], \[-2\mu C\], \[-2\mu C\] and \[-2\mu C\] respectively. Thanks for contributing an answer to Physics Stack Exchange! Hence, the flux is the integration of electric field vectors and area vectors. Could an oscillator at a high enough frequency produce light instead of radio waves? Why is this integral for a uniform electric field of a charged plate not evaluating correctly? I would like to know which method is correct, and why is the other method wrong? Z13 Physics Y Kumar Dehradun. Electric field due to negatively charged plate towards that plate and is equal to sigma/ 2ephslanot.electic field due to positively charged plate is away from it and is equal to Sigma/2 ephslano. The electric field due to the OTHER is the same: E2 = s/epsilon0. How does the Chameleon's Arcane/Divine focus interact with magic item crafting? Connecting three parallel LED strips to the same power supply. Central limit theorem replacing radical n with n. Asking for help, clarification, or responding to other answers. This equation holds well for a finite nonconducting sheet as long as we are dealing with points close to the sheet and not too near its edges. $$ The magnitude of the electric field at $(0,0,z)$ due to this element is then (treating the element as a point charge) What properties should my fictional HEAT rounds have to punch through heavy armor and ERA? The electric field between two plates: The electric field is an electric property that is linked with any charge in space. Electromagnetic radiation and black body radiation, What does a light wave look like? Electric field due to a large, non-conducting plate and factors of 2 [closed], Help us identify new roles for community members. How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Imagine sitting very close to the sheet. make the sheet very very large. The only dimensionless number that I can construct using $z$ is $\frac{z}{a}$. 2022 Physics Forums, All Rights Reserved, Problem with two pulleys and three masses, Newton's Laws of motion -- Bicyclist pedaling up a slope, A cylinder with cross-section area A floats with its long axis vertical, Hydrostatic pressure at a point inside a water tank that is accelerating, Forces on a rope when catching a free falling weight. Why is the overall charge of an ionic compound zero? Now, there are two ways to make this small -. I computed the field at $(0,0,z)$ so that I have enough symmetry to say $E_x = E_y = 0$ even for a finite plate. Find the force of attraction between them? $$ Why is it that potential difference decreases in thermistor when temperature of circuit is increased? This electric field exists even if the plates are not conducting. 1 For a non-conducting sheet, the electric field is given by: E = 2 0 where is the surface charge density. Test your Knowledge on Electric field intensity due to a thin uniformly charged infinite plane sheet If the plate were a conducting plate (part of a capacitor), would it still be valid to consider the effect of the electric field due to the left side, on any point towards the right in derivation 2 (since electric field does not exist within the volume of the conductor, and therefore cannot propagate through it)? The best answers are voted up and rise to the top, Not the answer you're looking for? Electric field lines fall within a circle? This equation holds well for a finite nonconducting sheet as long as we are dealing with points close to the sheet and not too near its edges. Expressing the frequency response in a more 'compact' form. However, $z$ is a dimensionfull quantity, and you can't discuss the largeness or smallness of dimensionfull quantities, only dimensionless numbers. Also It would be greate if anyone can comment on how to find the electric field by directly solving the poisson equation. This would give E = 0 inside, and $E = \sigma/\epsilon_0$ outside. Why don't you do the computation? By symmetry, this electric field will point solely in the $z$-direction. It only takes a minute to sign up. Let us now take the limit of small $z$. So, when I say, $z$ is small, I really mean $\frac{z}{a}$ is small. How is the merkle root verified if the mempools may be different? @Prahar Could you please give me a more formal explanation? 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. Connecting three parallel LED strips to the same power supply. As far as you are concerned, the sheet is infinite because you can't see the edges. Thank you! 428 . To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The distance between the plates in the diagram above is 0.14 meters. Better way to check if an element only exists in one array. rev2022.12.11.43106. When discussing the electric field due to a sheet, the size of sheet is compared to our distance from the sheet. If the area on both plates is 1m^2 then calculate the value of electric field at (a) to the . My work as a freelance was used in a scientific paper, should I be included as an author? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. E_z = \frac{\sigma}{ \pi \epsilon_0} \tan^{-1} \left[ \frac{a^2}{z \sqrt{ 2a^2 + z^2 } } \right] Does integrating PDOS give total charge of a system? Is there something special in the visible part of electromagnetic spectrum? I have another query. Formulas used: So if it were a conducting plate, can we say that each side of the plate produces an electric field E = /20, and that the net E at any point will be equal Enet = /20 + /20 (since both sides produce an outward electric field?). Use MathJax to format equations. Inside the plate, the field contributions cancel $\vec{E}_{in} = \frac{\sigma}{2\epsilon_0}\hat{x} - \frac{\sigma}{2\epsilon_0}\hat{x} = 0$. In this limit, we find The only dimensionless number that I can construct using $z$ is $\frac{z}{a}$. For a non-conducting sheet, the electric field is given by: $$E = \frac{\sigma}{2\epsilon_0}$$ $$ Integration of the electric field then gives the capacitance of conducting plates with the corresponding geometry. I understand why the approximation worsens near the edges (because symmetry fails and causes fringe effects) but why is the approximation better near the sheet? Volt per meter (V/m) is the SI unit of the electric field. How could my characters be tricked into thinking they are on Mars? $$ Proof that if $ax = 0_v$ either a = 0 or x = 0. Maybe one that uses symmetry? to apply Gauss's theorem we require the direction of electric field at P for this purpose we consider two small surface elements S 1 and S 2 the same distance from O as shown in the figure 2.12 the components d . Definition of Gaussian Surface $$ Why doesn't the method of images work for this problem? But, here's the important thing. If not then what method would I use to find the electric field in this case. Find the electric field at points: Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ${{\rho }_{1}}$ and ${{\rho }_{2}}$ respectively, touch each other. Help us identify new roles for community members. At a different point, there is no symmetry, so $E_x , E_y \neq 0$ which only makes the computation more complicated. We didn't really care if $z$ itself is small (that sentence doesn't even make sense). Electric Field Intensity Due to Non-Conducting Sphere The charge on the conducting sphere get distributed over the surface. The electrons are attracted to the plate with the opposite charge. If there are any complete answers, please flag them for moderator attention. I only to described the simplest possible case to explain my point. How many transistors at minimum do you need to build a general-purpose computer? The electric field between parallel plates is influenced by plate density, which determines how large the plate is. E_z = \frac{\sigma}{ \pi \epsilon_0} \tan^{-1} \left[ \frac{a^2}{z \sqrt{ 2a^2 + z^2 } } \right] Integrating this over the sheet, we find the total electric field at $(0,0,z)$ as The question you must always ask when you use the word "big" is "big with respect to what?" Point charges $+3.0\mu C$ and $+7.0\mu C$ are located at the origin and at the point (0.5m, 0) respectively in the x-y plane. 4 . Counterexamples to differentiation under integral sign, revisited. The $z$-component of this electric field is $$ The magnitude of the electric field at $(0,0,z)$ due to this element is then (treating the element as a point charge) To learn more, see our tips on writing great answers. Using Gauss's law derive an expression for the electric field intensity due to a uniform charged thin spherical shell at a point. Please help the asker edit the question so that it asks about the underlying physics concepts instead of specific computations. Note also that if this were a conductor, then the electric field would be zero inside the material and Derivation 1 gives the correct answer. The electric field from a thin conducting large plate is Ei = qi / (2Ae_0) in direction outward, from each side of the plate. For negative charge the . Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. The charge of this element is $\sigma dx dy$. Classic electrostatics image problem surface charge. Just because it. It may not display this or other websites correctly. the sun. Just because it. By the gauss law, flux is charge divided by absolute permittivity. If you are close to the sheet, the edge effects are negligible. otherwise you'll need to know the dielectric constant of the material.) How can I use a VPN to access a Russian website that is banned in the EU? Thus, the electric field is any physical quantity that takes different values of electric force at different points in a given space. Make $a$ large compared to $z$, i.e. Then P is . Homework Statement. We get that the y-component of the electric field due to just this little chunk of our plate, the electric field in the y-component, let's just call that sub 1 because this is just a little small part of the plate. So I would say that your mistake is that you did NOT draw the electric field going to the right inside the material in your first figure (Derivation 1). Compute the electric field at a general point $(x,y,z)$ in space-time. Both the statements above are completely equivalent. Can a prospective pilot be negated their certification because of too big/small hands? $$ At a different point, there is no symmetry, so $E_x , E_y \neq 0$ which only makes the computation more complicated. If the sheet on the left is non conducting and have a uniform charge density 3 (sigma) and the one on the right is conducting and has a uniform charge density (sigma). Thank you! PSE Advent Calendar 2022 (Day 11): The other side of Christmas. I only to described the simplest possible case to explain my point. Is this an at-all realistic configuration for a DHC-2 Beaver? the sun. What are the x components of force? Images produced by myself using this website. The best answers are voted up and rise to the top, Not the answer you're looking for? Thanks for the reply @Qmechanic. One more thing - your proof calculates the field at $(0,0,z)$ - does this work for other points too? Why does the equation hold better with points closer to the sheet? What is the probability that x is less than 5.92? I don't really get the analogy you gave above. Electric field due to conducting and non-conducting plates, A very large nonconducting plate lying in the xy-plane carries a charge, electric field due to thin sheet (non conducting) and conducting plate why it is different, Electric Field Due To Infinite Plane Sheets(Conduction and Non Conducting) -Derivation, Electric field due to conducting and non-conducting sheet | JEE & NEET. A charge in space is carried by an electric field that is linked to the charge. 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. Why does my stock Samsung Galaxy phone/tablet lack some features compared to other Samsung Galaxy models? E = V/d. Maybe one that uses symmetry? Now, there are two ways to make this small -. Are defenders behind an arrow slit attackable? Examples of frauds discovered because someone tried to mimic a random sequence. Both the statements above are completely equivalent. Why is the y-component of electric field of a uniformly-charged disk near its center the same as that of infinite sheet of charge? $$ Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. $$ How to get the electric field strength of a plate as approximation of a sphere. JavaScript is disabled. This electric field will have in general all 3 - components $(E_x, E_y, E_z)$. Just because I'm closer, it doesn't mean the sheet is any bigger. If you are close to the sheet, the edge effects are negligible. So, when I say, $z$ is small, I really mean $\frac{z}{a}$ is small. Consequently if we take case of finite disk the following is the resulting integration. As an alternative to Coulomb's law, Gauss' law can be used to determine the electric field of charge distributions with symmetry. $$ A point charge q moves from point P to a point S along a path PQRS in a uniform electric field E pointing parallel to the x-axis. Give reason. The electric field is created by the movement of electrons within the plates. Direction of electric field due to infinite charged sheet: Suppose is the surface charge density on the charge sheet and at point P we have to find the intensity of electric field . Gauss's law and superposition for parallel plates. (i) Outside the shell (ii) Inside the shell Easy View solution > Two parallel large thin metal sheets have equal surface charge densities (=26.410 12c/m 2) of opposite signs. E = F/q. What we really care about is if $z/a$ is small. Can we keep alcoholic beverages indefinitely? Why is the field inside a capacitor not the sum of the field produced by each plate? 11 : 56. electric field due to thin sheet (non conducting) and conducting plate why it is different. Note also that if this were a conductor, then the electric field would be zero inside the material and Derivation 1 gives the correct answer. Your proof shows that in the limit, the magnitude of the field approaches the formula I gave. E_z = \frac{\sigma}{ \pi \epsilon_0} \tan^{-1} \left[ \frac{1}{(z/a)\sqrt{ 2 + (z/a)^2 } } \right] = \frac{\sigma}{2\epsilon_0} + {\cal O}(z/a) How can I fix it? We didn't really care if $z$ itself is small (that sentence doesn't even make sense). I've referred some textbooks, and they say that the result of the 2nd derivation is correct. Two infinite sheets of charges are placed parallel to each other. For a non-conducting sheet, the electric field is given by: $$E = \frac{\sigma}{2\epsilon_0}$$ Consider a square sheet with edges located at $(a,0)$, $(-a,0)$, $(0,a)$ and $(0,-a)$. How is dielectric constant both $E_{net}/E_o$ and $/_o$? Connect and share knowledge within a single location that is structured and easy to search. This equation holds well for a finite nonconducting sheet as long as we are dealing with points close to the sheet and not too near its edges. This creates a force between the plates. It is then definitely true, that when we are closer to the sheet, in comparison, the sheet has "grown bigger" and therefore can essentially be considered as an infinite sheet and the edge effects can be ignored. It is then definitely true, that when we are closer to the sheet, in comparison, the sheet has "grown bigger" and therefore can essentially be considered as an infinite sheet and the edge effects can be ignored. Using both equations, we can determine the electric sheet due to the charged sheet which will also give us the relation between electric field and distance from the sheet. We assume positive charge in the formulas. mathOgenius. Electric field due to plate = d/2epsilon hence force = Eq = dq/2epsilon . E = r 2 o = 0 = R d ( 2 + r 2) 3 / 2 The coordinates of P, Q, R and S are (a,b,0), (2a,0,0), (a,-b,0) and (0,0,0). You can keep the Gaussian surface inside the material, but there IS an electric field in there, just as you've drawn in the Derivation 2. Make $a$ large compared to $z$, i.e. 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. Your proof shows that in the limit, the magnitude of the field approaches the formula I gave. rev2022.12.11.43106. I have spent HOURS on the internet but the sites I have found do not clearly distinguish between PLATES and CONDUCTING PLATES. Make $z$ small compared to $a$, i.e. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centre of the spheres is zero. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. move in very close to the sheet. What we really care about is if $z/a$ is small. Work them all out and show that in the small $z/a$ limit, $E_x$ and $E_y$ vanish, while $E_z$ goes to $\frac{\sigma}{2\epsilon_0}$. As far as you are concerned, the sheet is infinite because you can't see the edges. At what point in the prequels is it revealed that Palpatine is Darth Sidious? Fair enough. electric field due to non conducting plate / sheet (in English ) 78 views Jan 1, 2021 this video drives an expression for electric field due to infinite long uniformly charged. An electric field is an area or region where every point of it experiences an electric force. $$ I understand why the approximation worsens near the edges (because symmetry fails and causes fringe effects) but why is the approximation better near the sheet? Why does the equation hold better with points closer to the sheet? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. The field between plate A and plate B is */*0 if they are charged to some extent, and 0 if they are not. Is it correct to say "The glue on the back of the sticker is dying down so I can not stick the sticker to the wall"? What is the electric field in a parallel plate capacitor? Can I change any equation/assumption in the wrong method to arrive at the right result? Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Why does my stock Samsung Galaxy phone/tablet lack some features compared to other Samsung Galaxy models? Is the electric field at the edge of a uniformly charged disk infinite? Thanks for the answer, @xXx_69_SWAG_69_xXx! Hebrews 1:3 What is the Relationship Between Jesus and The Word of His Power? It is equal to the electric field generally, the magnitude of the electric field from this point, times cosine of theta, which . dE = \frac{1}{4\pi \epsilon_0} \frac{\sigma dx dy}{x^2 + y^2 + z^2 } Make $z$ small compared to $a$, i.e. Japanese girlfriend visiting me in Canada - questions at border control? However, how do we know the. Since it's a nonconducting plate, the charge sits only on the left surface and there is indeed an electric field inside the material (we're ignoring dielectric effects here, right? At what point in the prequels is it revealed that Palpatine is Darth Sidious? As you mention in the question the second derivation is what gives us the correct answer for Electric Field due to this large-thin sheet, and is how its done in most all textbooks. What happens if you score more than 99 points in volleyball? How do I put three reasons together in a sentence? Consider a square sheet with edges located at $(a,0)$, $(-a,0)$, $(0,a)$ and $(0,-a)$. Of course, if it were a conductor, then there must be an equal amount of charge on the right surface of the conducting plate. But anyways I managed to solve it. That's exactly right for regions outside the conducting plate. Inconsistent image charges: what happens when three conducting planes meet? Prove that isomorphic graphs have the same chromatic number and the same chromatic polynomial. $$ To find the electric field, consider a small element on the sheet located at $(x,y)$ of area $dx dy$. in this video, we will study about electric field due to #conducting_and_nonconducting_sheet *all doubts explained success router | physics by sanjeet singh | sanjeet singh iit (ism). But, here's the important thing. Fair enough. Is it possible to hide or delete the new Toolbar in 13.1? Thus, when we are sitting close to the sheet, the field takes the form you described above. (3D model). Tabularray table when is wraped by a tcolorbox spreads inside right margin overrides page borders. 7 07 : 40. When two plates are placed next to each other, an electric field is generated. Is the EU Border Guard Agency able to tell Russian passports issued in Ukraine or Georgia from the legitimate ones? I'm solving it using 2 methods, and arriving at a different answer using both. 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. E_z = \frac{\sigma}{ \pi \epsilon_0} \tan^{-1} \left[ \frac{1}{(z/a)\sqrt{ 2 + (z/a)^2 } } \right] = \frac{\sigma}{2\epsilon_0} + {\cal O}(z/a) Making statements based on opinion; back them up with references or personal experience. When discussing the electric field due to a sheet, the size of sheet is compared to our distance from the sheet. However, $z$ is a dimensionfull quantity, and you can't discuss the largeness or smallness of dimensionfull quantities, only dimensionless numbers. An electric field is defined as the electric force per unit charge. 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