What is Electric field: Definition and 1000 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. Biker

    Calculating the work done in an electric field

    Homework Statement It is not an actual questions, Just misconceptions For example, Lets find the work done over a distance in an electric field Homework Equations v = PE/q E = F/q F = k q1 q2 /r^2 W = fd The Attempt at a Solution I didn't study calculus yet but I am going to because I need to...
  2. S

    Thin rod w/linear charge density, dipole moment

    Homework Statement A thin rod of length 2L has a linear charge density that isλ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero. Given E = −kλ0/L(d/(L−d)−ln(d−L)+d/(L+d)+ln(L+d)) for a point P that is...
  3. S

    Electric Field along bisector of charged line (w/error)

    Homework Statement You wish to determine the electric field magnitude along the perpendicular bisector of a 230-mm line along which35 nC of charge is distributed uniformly. You want to get by with a minimal amount of work, so you need to know when it is sufficient to approximate the line of...
  4. T

    A Charged Conductive Plate with a Charged Plane

    Homework Statement In the "Before" scenario, there is conductive plate in electrostatic equilibrium with uniform surface charge density +η (the plate has some thickness but the width and length are significantly larger). In the "After" scenario, an infinite plane of negative charge with fixed...
  5. S

    Magnitute and Direction of Electric Field Based on Particle

    Homework Statement A positively charged particle initially at rest on the ground accelerates upward to 180 m/s in 2.70 s .The particle has a charge-to-mass ratio of 0.100 C/kg and the electric field in this region is constant and uniform. What are the magnitude and direction of the electric...
  6. person_random_normal

    Energy stored in electric field

    I know that energy stored in electric field / unit volume = 1/2 ε E2 so can I say that for any configuration calculating ∫ ½ ε E2 over whole space - gives me the potential energy stored stored in the system for instance for → Q1 °...
  7. Titan97

    A conducting shell kept in a uniform electric field

    Homework Statement Find the force that tries to rip apart a conducting shell into two halves about its equator when kept in a uniform electric field of magnitude ##E##. Homework Equations Gauss Law: $$\nabla\cdot\vec{E}=\frac{\rho}{\epsilon_0}$$ I think Laplace equation might also be...
  8. D

    Electric Field between two Charges

    Homework Statement A positive charge of 3 microCouloumbs is at the origin. A negative charge with the same magnitude is 8 m away along the x direction. a) What are the magnitude and direction of the electric field at the points between the two charges, 2, and 4, and 6m from the positive charge...
  9. A

    Approximations used in solving for the electric field

    Homework Statement Suppose we have a rod of length L oriented on the z-axis so that the bottom end is at z= - L/2 and the top end if at z = L/2. Furthermore, the rod is uniformly charged with charge density 'λ'. Now we are interested in finding the electric field at a point x away from the...
  10. P

    High electric field / droplet levitation

    Dear All, I know this may sound a bit of a broad approach for a question but I would like to know what equipment I would need to create a very high electric field in order to levitate a non-highly conductive droplet (from water to water + salts but not metallic, in the milli-microscale). I will...
  11. 1

    What does divergence of electric field = 0 mean?

    Homework Statement I just want to focus on the divergence outside the cylinder (r >R) Homework Equations The Attempt at a Solution For r > R, I said ∇ * E = p/ε But that's wrong. The answer is ∇ * E = 0 I'm confused because there is definitely an electric field outside the cylinder (r...
  12. S

    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...
  13. S

    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...
  14. S

    Electric field lines from a metal shell and sphere

    Homework Statement A metal sphere of charge +6μC is surrounded by a metal shell of net charge +6μC. Which of the following diagrams represents the electric field lines of the system? Homework EquationsThe Attempt at a Solution The correct answer provided by my teacher is a figure with 12...
  15. D

    Transfer of kinetic energy from particle to electric field

    If an electron in an excited wave form passes thru an electric field , can it lose kinetic energy in doing so.?
  16. L

    Electric field at a point inside of a uniformly charged ball

    As the name of the thread says, I am wondering what would the amount and the direction of the electric field at some point in the uniformly charged ball of radius R(it has a constant charge volume density) be at the distance r from the centre of the ball. Does anyone know what would they be? I...
  17. C

    Electric field in the vicinity of an antenna

    I don't know why I was persuaded that in the free space, the electric field of an EM wave is always orthogonal to the direction of propagation. I've recently read my old textbook, and found that this is true only when the wave is far from the emitting source. But if I've understood right the...
  18. K

    Is this how to attempt this problem on electric field strength

    Homework Statement Two parallel plates at -50kV and 100kV have separation 35cm. a proton is placed between the plates. calculate the electric field strength between the plates Homework Equations E=v/d The Attempt at a Solution 100kV--50kV=150kV 150x10^3/0.35=428571.4N/C
  19. A

    Deriving electric field with given potential

    Homework Statement Given that the potential of dipole is equal to: V(\vec{r})=\frac{\vec{p}\vec{r}}{4\pi\epsilon_0 r^3} show that the electric field is equal to: \vec{E}(\vec{r})=\frac{1}{4\pi\epsilon_0}(\frac{3(\vec{p}\vec{r})\vec{r}}{r^5}-\frac{\vec{p}}{r^3}) Homework Equations...
  20. C

    Electric field inside a conductor

    Suppose there is a metal disk with an initial excess of charge represented by the four red electrons. Naturally, they reach their equilibrium position on the surface. After this, a new electron (the green one) is added exactly at the center. The repelling forces from the red charges cancel each...
  21. F

    Calculating Electric Field at Multiple Points in a Charged System

    Homework Statement In the figure (attached), find the magnitude and direction of the electric field at points A, B, C and D. Homework Equations E = kQ / r^2 The Attempt at a Solution I'm just a little lost with the directions/if I need to be including angles so for point A: E = k 7.5e^5C /...
  22. Icy98

    Movement of electron in an electric field

    Homework Statement An electron has an initial velocity of 5.00 x 10^6 m/s in a uniform 2.00 x 10^5 N/C strength electric field. The field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron...
  23. L

    Overall Electric flux of a rigid body

    When we looked at some closed surface, we defined the overall electric flux of that surface as the sum of all infinitesimal fluxes of all the infinitesimal surfaces that make the quoted closed surface. Does that change if we do not have a closed surface, but a rigid body such as, let's say, a...
  24. A

    Electric Field distribution around two-conductor cable

    What is electric field distribution around two conductor cable connected to DC power supply? Assume power supply is isolated and not grounded. Assume cable is straight. Case 1: no current runs through the cable. One wire is positive, another – negative. Negative or zero? If we think in terms of...
  25. K

    I Electric Field and manifolds

    This is from Jackson, "Electrodynamics" a field is a fuction mapping phi: M -> T, x -> phi(x) from a base manifold M into a target manifold T. field X: R3 * R1 -> R3 x(r,t) ->X(x)I think this is eucledian R4 to R3 so I wonder why Jackson explained this with the concept of manifolds? Is it...
  26. M

    How do you find electric field given only time and distance?

    Homework Statement Two charged plates are 2mm apart. An electron escapes from the negatively charged plate and reaches the positively charged plates in 1.2x10^-8 seconds. Find the electric field between the plates. Homework Equations E=V/d eV= + or - 1.6x10^-19 C The Attempt at a Solution...
  27. B

    Solve Gauss' Law Question: Find Max Acceleration of Two Balls

    Homework Statement Consider two balls of equal radii and masses but opposite charges, distributed uniformly over their volumes. Initially, the balls are at rest and far away from one another. Due to the Coulomb attraction, the balls start moving towards each other. The balls can be treated as...
  28. Dimani4

    A Fermi energy Ef changes with applied electric field?

    Hi people, I don't understand why when we apply the electric field to the metal Ef remains the same. Ef as translation energy of electrons remains the same but we accelerate the electrons with applied electric field so the translation energy increases too? In other hand according the formula...
  29. M

    Charged mass hanging in electric field

    Homework Statement My teacher came yesterday, and put in the board one exercise, just the scheme, not aditional data, i have one picture of the scheme Homework Equations The given E its mean to electric field The Attempt at a Solution I need some help, go get the right way into problem [/B]
  30. Titan97

    Calculating Induced EMF in a Circular Region with Decreasing Magnetic Field

    Homework Statement In the below figure, magnetic field is decreasing at a rate of 1.5T/s in a circular region of radius 2m. EMF developed in the rod will be? Homework Equations $$V_{\text{induced}}=-A\frac{\mathrm{d}B}{\mathrm{d}t}$$ The Attempt at a Solution I tried using induced electric...
  31. H

    Direction of electric field

    Homework Statement beam of protons moving in +x direction at speed v electric field is perpendicular to magnetic field magnetic field in +y direction no deflection What direction/sign has the electric field? Homework Equations not looking for numerical solutions The Attempt at a Solution...
  32. Physics Dad

    Electric Field Strength - Assignment Question

    Homework Statement The Nucleus of a helium ion contains two protons approximately 5x10-15m apart. They can be considered to be surrounded by one orbiting electron approximately 5x10-11m away. Calculate the following: a) The electrostatic force between the two protons b) The electrostatic...
  33. P

    Electric Field Homework: Rank Protons by Acceleration

    Homework Statement The figure below shows five protons that are launched in a uniform electric field E (green). The magnitude and direction of the launch velocities are indicated. Rank the protons according to the magnitude of their accelerations due to the field, greatest first. Justify...
  34. B

    Electric field between inner and outer cylinder

    Homework Statement A capacitor is constructed of two long concentric metal cylinders, each having length of 1.0 meters. The inner cylinder has a radius R1 = 1.0 cm, and the outer cylinder has a radius R2 = 1.25 cm. The hollow space between the two cylinders is filled with nylon having a...
  35. Drakkith

    Conductor in an External Electric Field

    I just had a test question in my E&M class that asked what would happen to a conductor when placed in an external electric field. One of the "correct" answers was that all of the free electrons would move to the surface of the conductor. I understand that the free electrons would rearrange...
  36. K

    Electric Field Divergence Solution for Moving Source Charge

    I would like to know what is the solution for the divergence of the electric field if the source charge is moving.
  37. C

    Finding the magnitude and direction of the electric field

    Homework Statement 13. Find the magnitude and direction of the electric field at P due to the two charges shown. Homework EquationsThe Attempt at a Solution I have attached both the question, which involves a diagram, as well as my attempt at the answer below. My first question is regarding...
  38. E

    Static magnetic field from time-varying electric field

    Hello! In this thread, in this answer, my statement "A time-varying electric field creates a magnetic field which is time-varying itself" was refuted. Because I never observed this before, I would like to discuss about it. As far as I know, Maxwell's equations are valid always together, that...
  39. J

    I What is the resolution to the problem with E cross B field and E>B?

    I have been unable to find a satisfactory explanation of this problem, elsewhere. Consider an uniform electric field, E, along the y axis. Consider also a uniform magnetic field, B, along the z axis. If we release a particle (charge=q, mass=m) at rest on the origin at time t=0, what will be...
  40. B

    Proof that disk of charge = point charge when very far?

    Homework Statement Take the expression 21.11 (pictured below, specifically the bottom one) for the electric field above the center of a uniformly charged disk with radius R and surface charge density σ, and show that when one is very far from the disk, the field decreases with the same square...
  41. P

    The approximate orientation of an electric field

    Homework Statement On the image, the left stick has a positive charge and the one of the right has a negative one. (Unirformed charge for each) Give the approximate orientation of the electric fields at the points A, B, C, D by using cardinal orientation. http://imgur.com/uWW7JJH [Image...
  42. K

    Magnitude of the electric field across cell membranes

    Homework Statement The electric potential difference across a neuron cell membrane is 0.070 V. The thickness of the membrane is 5.0 x 10-9 m. a) Find the magnitude of the electric field across the membrane. Describe any assumptions you are making. Homework Equations ε = V/r The Attempt at...
  43. F

    Integration to find Electric Field at a point P -- dQ or dq?

    Hey everyone, So I've been learning about electric fields and all that good stuff. So now the question arises, what is the electric field at a point P away from an object (say a rod or a ring) at a distance D away? So we know E=Kq/r2 or E=KQ/r2 . The difference between q and Q: q the charge for...
  44. K

    Electric Field Effect on Quantum Well

    Hello everybody ! Recently i heard that, application of an electric field onto a quantum well tilts the quantum well and changes its 2-D density of states to 3-D bulk density. Is this true..? Can anybody give some more information or reference on this..? Thanks for any Help.
  45. henrco

    Find the rms electric field strength of a given EM wave

    Hi, I was able to correctly calculate the answer to part 1 below but the answer to part 2 is incorrect and I cannot see the error of my ways... any help gratefully received. 1. Homework Statement An electromagnetic wave has an intensity of 127 W/m2. 1) Find its rms electric field strength...
  46. S

    Gauss's Law and Electric Field Question.

    Homework Statement figure shows, in cross section, a plastic, spherical shell with uniform charge q=16e and radius R. A particle with charge Q = 5e is at the center.What is the electric field (magnitude and direction) at (a) point P1 at radial distance a from Q My question is at the point P1...
  47. S

    How Do You Calculate the Electric Field at the Origin with Three Charges?

    Homework Statement Three charges q1=+2Q q2=-2Q q3=-4Q. are each a distance d from the origin. What is the magnitude and direction of the electric field at the origin. I'm getting confused by not having d specified as a number. Homework Equations E = Σ kq/r2 The Attempt at a Solution I've...
  48. I

    Electric field outside a gaussian surface

    Hello If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...
  49. C

    Calculating Electric Field of Two Charged Particles on the y-axis

    Homework Statement Two 1.00µC charged particles are located on the x axis. One is at x = 1.00 m, and the other is at x = -1.00 m. Determine the electric field on the y axis at y = 0.400 m Homework Equations Electric Field = ke * q / r^2 3. The Attempt at a Solution I know the x-components...
  50. B

    Thought experiments about Gravitational Waves

    Imagine a mass that disappeared from space. I know that it is impossible, but imagine it is sucked by a wormhole or it just disapperars. Will we detect ONE gravitational wave only? Like a pulse and nothing else? Now the other way around. A mass appears from nothing. Then we will detect one...
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