# What is Electric field: Definition and 999 Discussions

An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges, or from time-varying magnetic fields. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.
Electric fields are important in many areas of physics, and are exploited practically in electrical technology. In atomic physics and chemistry, for instance, the electric field is the attractive force holding the atomic nucleus and electrons together in atoms. It is also the force responsible for chemical bonding between atoms that result in molecules.
Other applications of electric fields include motion detection via electric field proximity sensing and an increasing number of diagnostic and therapeutic medical uses.
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The derived SI units for the electric field are volts per meter (V/m), exactly equivalent to newtons per coulomb (N/C).

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1. ### I Work done by electric field of an irregularly shaped conductor

I am trying to wrap my head around something and would be grateful for some insight. Specifically, why the different electric fields along different paths to different areas of an irregularly shaped conductor don't impart different energies to inflowing particles. Say we have a negatively...
2. ### How do we know the point of 0 electric field is on the axis?

In many homework problems I've encountered, they all seem to assume the electric field = 0 point is along the axis of the two charges. Intuitively it kind of makes sense, but I'm looking for a solid justification for it. In other words, why can't it be off the axis of the two charges? When...
3. ### I Thought I Understood Gauss' Law (Sheets)

We know Gauss's law for an infinite sheet yields ##\textbf{E}=\frac{\sigma}{2\varepsilon_{0}}##. This is relatively elementary and I completely understand the derivation. This is also valid when looking at a parallel plate capacitor (the electric field is additive between the plates yielding...
4. ### (Help) Surface charge density (σ) for particle to hit plate...

I don't know if i'm exactly right. But I started with x(time) = V cos θ t which = (6810 m/s) cos (69.1°) (11.4 * 10^-3 s) is ... 27.69 m & since Electric field due to uniformly charge surface is represented by... E = (q * σ)/(2 * ε_0 * m), and since acceleration (a) can be expressed as F/m...
5. ### Electric field strength and direction problem (need help)

E1= 9.0 x 10^9 * 10 x 10^-9 / (0.045)^2 = 45000. x cos(153.43)= E2= 9.0 x 10^9 * 10 x 10^-9 / (0.02)^2= 22500 x cos(180)= E3= 9.0 x 10^9 * 5.0 x 10^-9 / (0.04)^2= 28125 x cos(90)= ? Enet= ?
6. ### Electric field on the axis of a ring-shaped charged conductor

Hello. I was wondering why do we not multiply cos(alpha) by 2. I believe we should do this since the y-components of the electric field cancel out, meaning there would be 2 x-components of the electric field(at least I think so). Currently, this derivation/answer only considers one horizontal...
7. ### Electric Field of two charges

I have attached an image of what *I think* the electric field looks like. Would this be correct? I am convinced about everything here, apart from the ones on the far right. All the other ones loop from the +ve charge to the -ve charge, but where do the grey lines on the right loop to (the ones...
8. ### E&M: Forces resulting from Charges at the Corners of a Cube

My first attempt at solving: I divided up the point charges based on the radius away from point A. 1 charge was s*sqrt(3) away, 3 charges were s*sqrt(2) away, and 3 charges were s away from point A. q remained constant. Therefore, my F_total was: F_total = k * [(q^2 /...
9. ### I Simple electromagnetic wave including delay

I want to derive the electric and magnetic field at a point around an infinitely long wire which carries a sinusoidal alternating current. And I want the answer includes the phase delay according to the limited speed of propagation of the wave. Surely the answer must satisfy the Maxwell's...
10. ### I In ##\nabla\cdot\vec{E}## why can ##\nabla## pass through the integral?

We have $$\vec{E}(\vec{r})=\frac{1}{4\pi\epsilon_0}\int_V\frac{\rho(\vec{r}')}{\eta^2}\hat{\eta}d\tau'\tag{1}$$ A few initial observations 1) I am using notation from the book Introduction to Electrodynamics by Griffiths. When considering point charges, this notation uses position vectors...
11. ### I Electrical breakdown in air in the presence of a single charge

Suppose there is an electric charge of 350 micro coulombs in space. The electric field at a distance of less than one meter will be more than 3,000,000 volts/meter considering that this field is greater than the electric breakdown of air and the charge has no place to discharge, what happens...
12. ### I Looking for knowledge and insight about Magnetohydrodynamics and a simple setup to observe the phenomenon

I have been reading about Magnetohydrodynamics and would like a bit of insight from anyone who has any knowledge on the subject. If I understand correctly when a conductive fluid is in motion it produces an electric field, and motion can be generated using a few methods one of which is a...
13. ### A Electric field of infinite sheet with time dependent charge

Consider infinite charged sheet in xy plane and suppose that charge is gradually and uniformly removed from the sheet. Electric field outside the sheet obviously do not depend on x and y variables, thus the Maxwell equation divE=0 reduces to the simpler form ∂Ez/∂z=0, this means that z component...
14. ### I The electric field due to a dipole

and Can someone explain how they made these equations like this? How did the radius become that equation? What formulas from algebra did they applied? I'm looking at these formulas and I don't understand how r=z+1/2*d
15. ### B Measuring electric field vs magnetic field

Hello. Sorry. I am not a physicist and I have very superficial knowledge of the subject. I would like to ask a question about the practical field. I only have a device that measures the electric field. When I measure the signal coming from a cell phone tower before it is reflected from a metal...
16. ### Find the Electric field due to an electric dipole at the origin

Question : I have tried to solve but I struggle with this part: Any help would be appreciated.
17. ### B Why can only the electric field (E) be measured?

I would like to consult with you about something. Mobile phone towers transmit at relatively high frequencies. From a health perspective, on the internet :) all measurement values are interpreted in microteslas. However, with the Wavecontrol probe (WPF8) I have, only the electric field (E) can...
18. ### I How is Potential Difference Created across a Resistor?

In a simple circuit consisted of a battery and a resistor, how is potential difference actually established on the resistor? My understanding is that battery creates the electric field which propagates through space at the speed of light. Resistor is put inside this field and therefore...

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20. ### Electric field in nonmagnetic material given a magnetic field

Hello, I am stuck on a problem that I don't quite understand, which looks like this: "Given a nonmagnetic material with the magnetic field H = 50⋅exp(−100⋅x)⋅cos(2π⋅10⁹⋅t − 200⋅x)⋅ŷ determine the electric field strength E" I don't understand how I am supposed to find the solution for this...
21. ### Does a linearly time varying B create changing E?

As accelerated charges produces time varying electric field which produces time varying magnetic fields and so on. I know there is something wrong with my argument, I can't point it out. Please be kind to help.
22. ### Electric field near conducting shell

How would I do this question? I am having trouble figuring out what the radius is meant to be, why is it not 3R?

24. ### Finding electric field between two conducting plates using Gauss' law

This picture is from Sears and Zemansky's University Physics. It considers ##S_1## as a gaussian surface then it finds electric field between two plates. The only thing that I cannot understand is why it doesn't consider the electric field due to negative charges on other plate. Then electric...
25. ### A Electric field vs coupling between transmission lines

Hello All, I'm trying to create equation which can describe relation between electric fields of three coupled-lines and coupling between them. Let we say that, we have thee lines having infinit length which are placed above ground plane in distance h. The distance between coupled lines is...
26. ### Confused about direction of electric field

TL;DR Summary: I am studying a book and at some point i couldn't able to understand a topic about Electric field hi All, Currently I am reading a book "Matters and interactions". In chapter 18 - Page 724 author asked reader to do the exercise about the electric field in the wire. here are...
27. ### I Parallel Capacitor safety at 10 micron plate spacing

Hi all. This might be a complex thread or line of questioning if the first question passes the human safety test. I was advised to post at undergrad level. I myself am a layperson without an education in physics/maths so if anyone would find the patience to explain answers in terms a layperson...
28. ### B How is surface charge accumulated?

let's discuss copper wire all along so we only focus on the specific wire. Let's discuss 2 cases(case 1 is hopefully correct, so if it is, would be good to mention it). I'm sorry that this text got so bigger(didn't expect it), but wanted to mention my thought process. Somehow, none of the...
29. ### B Electric Flux - confused about integrating over a tilted area

I have been thinking today about electric flux and it got me (as always) into confusion. I love to dig deeper and sometimes, I deviate from the truth. Let's consider the tilted surface where Electric field is passing by. I'm attaching the image as well. I know that to calculate flux, we must do...

Let a = distance between the charge on the left to the third bead. Since the electric field is equilibrium, we equate the electric field emanating from the left charge to the right charge at the location of the third bead. I want to try to find the ratio of d with a. E=E Kq/(d-a)^2 = K*3q/a^2...
31. ### I Do Electric field lines propagate by themselves away from a charge?

I'm trying to understand how kink would be formed for only electric field for now. Let me share my pictorial understanding. Here is the Link. Moderator's note: The use of external image servers is not allowed. Please upload all images to PhysicsForums. Note that I'm not looking for...
32. ### Find the magnitude of the electric field at point P

There are two identical spheres with the same charge that are the vertices of an equilateral triangle. ##+3 \mu C## will exert an outward electric field, which is drawn in the FBD below (see the attached pic), Since the horizontal force components (1x and 2x) are equal and opposite at point P...
33. ### Capacitor 1/3 filled with a dielectric

My attempt would be to calculate the electric fields of the vacuum and dielectric part seperately and then use superpositioning to obtain the full solution. However, I don't see an ##x##-dependency coming along that path. The assignment suggests that there must be one though. Unfortunately, this...
34. ### B Exploring the Electric Field of a Moving Charge

How does an electric field of a moving charge, for example a moving electron, inside a wire looks like? Does it looks like this with distorted circular radial lines?
35. ### Electric field amplitude question regarding intensity calculations

My question is specifically with calculating the intensity. The book solution is I=P/(4*pi*r^2) but would this not give me a weaker electrical amplitude in the final calculation after plugging it in to I=(1/2)*√(ε0/μ0)*(E02) ?
36. ### B Seeing both B field lines and E field lines at the same time

After watching this clip Electric Field Lines Lab I wonder if it is possible to see both electric field lines and magnetic field lines at the same time by swapping the two nails in the video with two bar magnets, as the conductors as we understand bar magnets are metals and metals are good...
37. ### Divergence of the Electric field of a point charge

Hi, unfortunately, I am not sure if I have calculated the task correctly The electric field of a point charge looks like this ##\vec{E}(\vec{r})=\frac{Q}{4 \pi \epsilon_0}\frac{\vec{r}}{|\vec{r}|^3}## I have now simply divided the electric field into its components i.e. #E_x , E-y, E_z#...
38. ### I Electric Field Shielding by Conducting Sheets

Dear Experts, When a thin conducting sheet with no charge on is placed at a certain distance from a point charge, does it shield the electric field caused due to the point charge from reaching the other side of the sheet. As an extension of that idea, when a conducting sheet or slab is placed...
39. ### A Two level system in a thermal noise electric field

Hello! I have a 2 level system with a dipole moment d. I want to simulate numerically the evolution of the system under an external sinusoidal electric field (far off resonant). This is straightforward using SE. However I also have on top of that another electric field, created by a coupling of...
40. ### Understanding the energy of a dipole in a uniform electric field

Griffith's E&M problem 4.7 asks to calculate the energy of a dipole in a uniform electric field and I ended up getting a different answer than the one given. I thought that calculating the energy/work done to construct the dipole is the same as dragging two point charges where one is d apart...
41. ### I Units of q in Electric Field Equation

Quick and possibly stupid question, but in the equation for calculating the electric field: ##{\mathbf E} = \frac{1}{4πe_0}\frac{q}{r^2} \hat {\mathbf r}## What unit is ##q## in? Coulombs? Although now that I think more on it I suppose it also depends on the units you're using to calculate the...
42. ### A Two level system under electric field without RWA

Hello! I have the following Hamiltonian: $$\begin{pmatrix} 0 & -\Omega\sin(\omega t) \\ -\Omega\sin(\omega t) & \Delta \end{pmatrix}$$ where ##\Delta## is the energy splitting between the 2 levels, ##\Omega## is the Rabi frequency of the driving field and ##\omega## is the frequency of the...
43. ### Electric field generated by solenoid

The formula we are given is E=(1/2r)(alpha)R^2(muo)Ioe^-(alpha)t. However, I am struggling to figure out what each of the symbols stands for in the formula...can someone help me out? Like super confused on what alpha is in this case.
44. ### Electric field at the center of the equilateral triangle

I've found the distance from each point to the center, which is equal to r=20x1.732/3 = 11.55 cm. I find out that E2 and E3 due to -4µEyC on x-direction canceled each other. The E2y = E3Y = EY = E2Ycos60 = E2/2 = [(KQ2)/r^2]/2 So the net E-field: E = E1 +E2y+E3Y =kQ1/r^2 + [(KQ2)/r^2]/2 +...
45. ### Electric Field due to a disk of radius R in the xy-plane

Hello, This question, which I found in various electricitiy and magnetism books (e.g. Introduction to electrodynamics grif.). There are many variations of this question, I am mainly interested in the following setup of it: -Suppose there is a charged disk of radius R lying in the xy-plane, and...
46. ### A (nonconservative) electric field is induced in any region in which...

TL;DR Summary: A (nonconservative electric field is induced in any region in which) A. there is a changing magnetic flux B. there is a changing magnetic field C. the inductive time constant is large D. the electrical resistance is small E. there is electrical current there can be more than one...
47. ### Electric Field Inside Cylindrical Capacitor

we know that flux is equal to the area integral of electric field dotted with dA and we can set this equal to charge enclosed divided by epsilon naught. Thus, in this case, the integral simplifies to E * A = (q_enclosed)/(ε_naught) when we choose a cylindrical gaussian surface with radius of r...

49. ### Magnitude of the Line Charge Density of a Power Line

Okay so I am a little confused as to where I made a mistake. I couldn't figure out how to program Latex into this website but I attached a file with the work I did and an explanation of my thought process along the way.
50. ### Struggling With Part C of Electric Field Calculation

I've figured out parts A and B but I'm struggling with Part C. I used the equation V = kQ1/r1 + kQ2/r2 where Q1 = -4.4e-12C ; k = 8.98755e9 r1 = 0.026 m Q2 = 27.4e-12 and r2 = .051-.026 My answer (8.329 V) is wrong but I have no idea why. Please help if you can.