# What is E-field: Definition and 188 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. ### A Induced dipole moment (adiabatic) following the rotating E-field

Hello! Assume I have a 2 level system, where the 2 levels have opposite parity. If I apply an electric field, I will get an induced dipole moment. For now I want to keep it general, so the induced dipole moment can be very large, too. Let's say that I start rotating this electric field in the...
2. ### Chapter 2 Griffiths EM Problem: E-Field from a charged ring

Hi. I have solved the problem below as shown in the attached image. However I'm at a loss to figure out where I am making a mistake, and I know it is indeed a big goof up. Requesting guidance over identification and rectification of this big goof up. (Edit- I can solve this problem in the...
3. ### E-field of solid sphere with non-uniform charge density

Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below? However, from integrating the density and then plugging it into Gauss's law, I get the exact same thing, except a 15 instead of a 5. Could any please help point out if there is an...
4. ### Going From EMF to Faraday's Law to find E-field in my HW problem

Ok, so I understand how to find dphi/dt that is integral of -d/dt(B "dot" da). In this case I find a Phi that is a constant in space in time which causes me confusion in next step. Edit: dphi/dt is constant... Grithff's then says E field same as a Mag field above center of circular current. He...
5. ### Electrostatic vs DC Conduction Simulations for E-field Analysis

Hi, I am doing e-field simulations and have came across two types; electrostatic and dc conduction. I know that electrostatic means there is no changing field so I'm just hoping for discussion on when one is more appropriate than the other and when one definitely should or should not be used.
6. ### I Estimation of E-field strength at a distance from dipole antenna

Hello everyone, I was asking myself about electric field strength estimation at a distance d from - in my case - a half wave dipole antenna. There are pretty much a lot of information about this on internet or in books but still, there are a few things that are confusing to me that I would...
7. ### Optical vs Static Dielectric Constant for E-field Simulation

I am just learning about e-field simulations and I came across two different types of dielectric constants: optical and static. I'm unsure which to use and in which cases. I would like to simulate e-field intensity to help ensure I'm always below the dielectrics breakdown strength.
8. ### Engineering I can't understand the question -- Calculate the E-field in the electron cloud around a heavy atom's nucleus

I tried to use the formula for electric field intensity but I feel like something is missing.
9. ### E-Field immediately outside a charged conductor

Griffith's says this, and I'm not exactly sure why... If you had a solid, spherical, and externally induced conductor... Does this mean that IMMEDIATELY outside, when you're infinitesimally close to the surface, E looks like this? If you surround the entire conductor with a Gaussian surface...
10. ### Spherical charge distribution to generate this E-field

A spherical volume charge (R<=1cm) with uniform density ρv0 is surrounded by a spherical surface charge ( R=2cm) with charge density 4 C/m2. If the electric field intensity at R=4cm is 5/Є0 ,deterime ρv0
11. ### Find the charge distribution from the given E-field (spherical)

a) Static charge distribution should result in a static electric field? Legitimacy should be checked with curl of E = 0? b) Using the second equation should give is the answer?
12. ### Simulating the E-field distribution using the charge distribution

Hello everyone, I am new to this site so I hope this is the right place to ask this. I understand simulating electric field intensity using electrostatics because E=V/d makes sense to me. I do not understand how to consider e-field intensity using charge distribution. When is charge...
13. ### Calculating Angle Between E-Field and Current Vectors in Anisotropic Mat.

In a certain anisotropic conductive material, the relationship between the current density ##\vec j## and the electric field ##\vec E## is given by: ##\vec j = \sigma_0\vec E + \sigma_1\vec n(\vec n\cdot\vec E)## where ##\vec n## is a constant unit vector. i) Calculate the angle between the...
14. ### Calculating E-field Through Layers w/ Diff. Permittivities & Conductivities

I'm trying to understand how the total electric field changes as it passes through layers with different electrical permittivities and conductivities (as shown in the linked figure). The rectangular prism layers are assumed to be very thin. The conductivities ##\sigma## and relative...
15. ### Do moving electrons also create an E-field?

Hello guys, i get a little bit confused about the fact ,that static electrons produces E-Fields and after they moves one speaks only about the magnetic field .But what happens with the E-field in a moving ensemble of electrons?I mean,the E-field should also exists .It doesn't...
16. ### E-field at the origin from two point charges

Using superposition and "breaking up" the vectors into three components ax, ay, az on points should solve the task. For Q1 there is no effect on x-axis. On the y-axis the distance from Q1 to origin is 2. Using coulombs law will give us -> (-Q/4) * k , where k is the constant 1/(4*pi*e0). On...
17. ### Dielectric interface plate capacitor at angle alpha

Consider a plate capacitor with a dielectric interface (\epsilon = \epsilon_0*\epsilon_r, thickness=d) tilted at the angle \alpha . Outside the interface \epsilon = \epsilon_0. Without dielectric interface is the field \vec{E}=E_0*\vec{e_z}. Determine the E-field inside and outside the...
18. ### Find the E-Field between plates when given only given part of the total voltage

I'm really unsure about how to solve this because I am not given the total voltage between the plates. The voltage given (693V) is at a point that is 7.85 cm away from the zero volt plate. If I was given the total voltage between the complete distance between the plates (10 cm), then I could...
19. ### Finding the launch velocity of a point charge in a e-field

I'm not sure how to proceed with this, but here are my findings/hypothesis: First we find the electric field contributed by the plate with ##E=\frac{\lambda}{2\pi r\epsilon_{0}}## where r=2? After finding out the electric field, is it safe to assume I can find the acceleration of the point...
20. ### Calculate linear charge density of rod & mag. of E-field at point

Here is my work done for this problem, along with a diagram of the situation. I'm not worried so much about the arithmetic because our tests are only 50 min long so the problems they give us do not require heavy integration or calculus, but you need to know what goes where in the formula. That...
21. ### E-field from one end of an infinite non-conducting rod

Homework Statement Homework Equations dE= k dq/r2 The Attempt at a Solution [/B] I started off taking a derivative of q(x). dq = -qo/l ⋅ e-x/ldx Then, I decided that r was the distance x along the rod + .02m. r=(.02+x) Following that, I plugged everything into the formula: dE = k⋅qo/l...
22. ### Amplitude of a mass joined to a spring in the presence of an E-field

Homework Statement A block of mass m having charge q placed on smooth horizontal table and is connected to a wall thorough an unstretched spring of constant k . A horizontal electric field E parallel to spring is switched on. Find the ampliture of the shm by the block. Homework Equations kx=...
23. ### Use Gauss' Law to find E-field, tricky problem

Homework Statement A) use gauss's Law to determine the electric field at all values of radial distance (0<r<infinity) from the center of a non-uniformly charged cylinder that is very very long and lies along the x-axis. The cylinder carries excess charge per volume ρ=[a]r^2 (the [] are supposed...
24. ### Electron brought to rest by the E-field, potential difference question

Homework Statement An Electron with an initial speed of 500,000m/s is brought to rest by an electric field a)did the electron move into a region of higher or lower potential? I b) what was the potential difference that stopped the electron? Homework Equations ΔV=ΔU/q ΔU=-W The Attempt at a...
25. ### Conducting Sphere With Cavity E-field / Gauss' law

Homework Statement You have a conducting sphere that is in equilibrium, it has a cavity in it with positive charge +q. If you bring another charge +q2 near the outer edge of the conductor does the total surface charge on the wall of the cavity, q(int) change? There is an image attached that...
26. ### E-field generated by constant current in a circular loop

Homework Statement Discussions of the possibility of a tangential E-field external to a current-carrying conductor must include a voltage source and a return path. Here the problem is reduced to (we believe) the simplest possible geometry. Assume that a circular conducting loop has constant...
27. ### Ion craft using magnetic field instead of E-field

Hello folks, I did some research and I know a charged particle in a coil magnetic field travels along the lines of the coil. My thoughts are having a vertical cylinder and having charged ions flow down. 1. How can I figure out how much velocity the charged ions would have. 2. Would it...
28. ### Problem in electrostatics: E-field near 2 point charges

Homework Statement Refer the image. Homework Equations kq1q2/r^2 = F Potential energy = kq1q1/r The Attempt at a Solution Obviously since both charges are unequal in magnitude option a is incorrect. Calculating field at large distance r, E = kq1/r^2 - kq2/r^2 = kq2/r^2 Also potential energy...
29. ### I What's the effect of E-field for an electron in a solid?

Could an uniform external electrical field make an electron jump to a higher energy level?
30. ### Unpolarised light: Orientation of the E-field

Homework Statement How does this picture represent a unpolarised light?Homework EquationsThe Attempt at a Solution [/B] I thought light waves were perpendicular to the direction of propogation so if it has diagonal components then isn't that not perpendicular to the wave direction If it is...
31. ### B Integration Bounds for E-field Calcualtion

Hi guys. I’m looking at the brute force way at getting the E-field for a uniformly spherical charge distribution. The location of the E-field of interest is anywhere outside of the sphere. Here are some images Everything makes sense. I’m just not sure why the bounds for ‘s’ where z-r to...
32. ### Electrostatics: calculating the E-field of a line charge

Hey guys, could anyone tell me if set up this integral correctly? Thanks in advanced!
33. ### Finding Total Charge from E-field

Homework Statement A static charge distribution has a radial electric field of magnitude ##E = \alpha \frac{e^{-\lambda r}}{r} ## where λ and α are positive constants. Calculate the total charge of the distribution. Homework Equations Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot d\vec{S}##...
34. ### E-field from uniformly distributed charges on sphere?

So if I have a sphere of uniform charge distribution, the electric field at one point away from the circle would be affected by ALL individual charges distributed across the circle, right? From the picture I drew, there would only be a net effect of E-field in the X direction because there...
35. L

### How to determine the direction of the E-field of an EM wave

Homework Statement Consider a wave vector which hits a plain boundary between water and air. The wave vector hits the boundary with an angle α1 measured from the vertical axis. The magnetic field amplitude has a y-component only. Also, notice: The z-axis is the horizontal axis, the x-axis is...
36. ### Finding the magnitude of electric field

Homework Statement A uniform electric field exists in the region between two oppositely charged parallel plates 1.59 cmapart. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate in a time interval 1.50×10−6 s . Find the...
37. ### E-Field Through Copper Wire given drift velocity

Homework Statement If the magnitude of the drift velocity of free electrons in a copper wire is 7.84×10-4 m/s, what is the electric field in the conductor? (Also gives chart that states that the resistivity of Cu is 1.7×10-8 Ωm) Homework Equations [/B] vd=(qEτ)/me (where τ is avg. time...
38. ### Estimate the E-field required to ionize Hydrogen

Homework Statement Estimate the E-field required to ionize Hydrogen in a time comparable to the time taken for the electron to orbit the nucleus. (n=1 ground state) (hint: relate the required E field to the energy of a charged particle) Homework Equations F = mv^2/r (rotational) F = Ze^2/Kr^2...
39. ### Potenital of a cylindrical, linear dialectric in a E-Field

Homework Statement A very long cylinder of linear dialectric material is placed in an otherwise uniform electric field ##E_0##. Find the resulting field within the cylinder. (The radius is ##a##, the susceptibility ##X_e##, and the axis is perpendicular to ##E_0##) Homework Equations Boundary...
40. ### How can voltage drop be zero if E-field isn't?

Hi. I learned that in an ideal conductor in a circuit, the voltage drop is zero. But how does this agree with the basic definition of voltage $$U_{AB}=\int_A^B \vec{E}\cdot d\vec{s}\enspace ?$$ The electric field inside a conductor only vanishes in static conditions, but in an electric circuit...
41. ### Direction of dipole moment in e-field of another dipole

Homework Statement Hi everybody! I'm trying to solve a problem about dipoles, but there is something I don't quite get about it. Well, first here is the problem: An electric dipole ##\vec{p}_1## is placed at the zero-point and shows in the z-direction. A second electric dipole ##\vec{p}_2##...
42. ### I Why is the E-field inside a solid conducting sphere zero?

The common explanation is this: If the conductor has a net charge, then the charges repel each other until they arrange themselves symmetrically around the outside of the sphere, and if you do the math the electric field will cancel out everywhere inside the conducting sphere. Alright, but what...
43. ### B Question about the math involved in E-field calculations

When calculating the electric field from a point above a line of charge using coulomb's law, the integral that comes up is of the form \int { \frac { dx }{ { x }^{ 2 }+{ a }^{ 2 } } } . But if the point we were asked for is right in the middle, the horizontal (cosine) components cancel out...
44. ### I How are Mixed State Ammonia Molecules Separated by an E-Field?

I am working on a paper about Ammonia masers. It looks like Ammonia molecules are usually found in a superposition of even and odd parity states that are eigenstates of the inversion potential. That is the double well potential of the Nitrogen to tunnel through the Hydrogen plane. If it...
45. ### I Relationship between E-field and Probability Amplitude of Waves

Electromagnetic waves can be classically described by Maxwell's equations. Photons can be described by probability waves.In this case, what is the relationship between the electric field and the probability amplitude? Are they directly proportional to each other? What about the fact that one...
46. ### E-field of a moving charge at constant velocity

I came upon this page that provides the answer: http://farside.ph.utexas.edu/teaching/em/lectures/node125.html But I can't figure out what gamma(u) is. Could anyone help?
47. ### Can Fa = -Fb Solve E-Field Problem Faster Than Calculating at Part 1?

Homework Statement Homework Equations kq/r^2=E λ=q/L The Attempt at a Solution λ=8μC/1=8μC/m dq=λdx dE=k(dq)/(√(x^2+2^2))^2 dE=kλdx/(x^2+4) ----------------------------------------------- for x-direction dEx=dEcosθ=(2kλdx)/(x^2+4)^(3/2) Ex =2kλ∫dx/(x^2+4)^(3/2) =2kx[x/4(x^2+4)^(1/2)] (from...
48. ### E-field of a Semi-spherical charge distribution with a hole

Homework Statement Using direct integration, compute the electric field at the point (0,0,Z) of a semi-espherical (z > 0) charge distribution of radius R < Z and density ##\rho=constant## having a spherical hole of radius ##r_h<R## centered at (0,0,##r_h##). Homework Equations Coulomb's law...
49. ### Magnitude of the E-Field at the center of curvature

Homework Statement A circular rod has a radius of curvature R = 8.11 cm, and a uniformly distributed positive charge Q = 6.25 pC and subtends an angle theta = 2.40 rad. What is the magnitude of the electric field that Q produces at the center of curvature? Homework Equations E = kQ/r^2 6.25 pC...
50. ### Negative and Positive E-Field Components

Homework Statement In the diagram below, each division on the horizontal axis (the displacement s) is 0.10 m while each division on the vertical axis (the electric potential V) is 1.0 V. What is the electric field component along the displacement axis s in each of the regions specified below...