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. Brendan Webb

    Electric Field of Equilateral Triangle

    Homework Statement Consider an equilateral triangle of side 15.6cm. A charge of +2.0μC is placed at one vertex and charges -4μC each are placed at the two. Determine the electric field at the centre of the triangle. Homework Equations E=kQ/r^2 The Attempt at a Solution I am hoping someone...
  2. Iftekhar Uddin

    How an Electric Field is affected by an Insulator

    I looked through this forum post for an answer to my problem. It gave me enough insight to try and come to some conclusions but I'm still confused on some parts here and there about how I got my final answer. 1. Homework Statement A uniformly charged, straight filament 7.70 m in length has a...
  3. C

    Electric Field of Line Charge with Displaced Origin

    Homework Statement Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. Determine a. The electric field produced by the charge distribution Q at points on the positive x-axis where x > a. b. A point charge q is then placed at x = a + r. Determine force on q due to Q...
  4. R

    Magnitude of electric field at point A using components

    Homework Statement https://imgur.com/gallery/YwCap In side are image of figure, and questions.Homework Equations E = kq/r^2 The Attempt at a Solution So I have an electric field where the y compontents cancel. I have 2Ecos(∂) = E (Electric field at point A) - 2 because there is a top and...
  5. L

    Can E=V/d be used to calculate the electric field of a dipole?

    This is from a lab where my team found the equipotential lines from the electric field of a dipole. The information I was given to calculate the magnitude of the electric field seems too simple, and for some reason I'm expecting this to be more complex. So, this is my attempt at double checking...
  6. A

    Breakdown voltage of humid air in uniform electric field

    Could anyone please let me know if breakthrough spark can happen, or, in general, what will happen in the below system? Note 1: the dielectric layers have a much higher breakthrough voltage than humid air. Note 2: the intensity of the electric field that develops in the flow of the humid air is...
  7. A

    How can I relate the electric field to potential in a parallel plate capacitor?

    I want to calculate Electric field inside and outside a capacitor(two parallel conductor plates and in between a dielectric) which is fed by an AC voltage source. My problem is I do not know how can I relate the electric field to the potential in a capacitor. I got confused about the derivative...
  8. T

    Electric field (in)dependent of distance?

    Hi guys, I was reading about electromagnetism, specifically about the application of Gauss' Law to an infinite charged sheet, and how its electric field doesn't depend on the distance from the sheet. I think I have finally managed to wrap my mind around the concept intuitively, based on one of...
  9. K

    Gradient, Electric Potential, and Electric Field

    Hi guys! I was wondering about the relation between the Gradient, Electric Potential, and Electric Field. I know that if you take the Gradient of a scalar field, you get a resultant vector field in which the vector points in the direction of greatest increase when you take a infinitesimally...
  10. R

    Simple Electric field question -- Charged sphere

    Homework Statement A sphere with a charge of -3.5 x 10^-9 C and a radius of 1.0x10^-2 m is located at the origin of a coordinate system. What is the electric field 1.75 x 10^-2 m away from the center of the sphere along the positive y axis? Homework Equations e = kQ/r^2 The Attempt at a...
  11. D

    Electric Field of a cube with a rod

    Homework Statement The electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude ##3 \frac{N}{C}## and directed outward from the axis of the rod. (a) How much charge per unit length exists on the copper rod? (b) What would be the electric flux through a cube of...
  12. T

    Electric field of a ring:integrate over dq or ds?

    Hi people, I was reading on my textbook on electromagnetism (Halliday) about using integral to field the electric field of a charged ring (1D) at a point P located on an axis perpendicular to the ring's plane. The ring is uniformly charged. The book (and my professor) both breakdown each element...
  13. RJLiberator

    EM: Electric field, Two thin rods uniform line charge

    Homework Statement Two identical thin rods of length L carry the same uniform line charge distribution (charge per unit length) of . If the two rods are collinear (aligned along the same line), with a distance of d between their nearest ends, calculate the Coulomb force (magnitude and...
  14. D

    Electric field of a positive plate

    Homework Statement There is a large positively charged plate whose charge density is ##\sigma = 2.0 × 10^{-5}\frac{C}{m^2}##. What is the electric field at a point P, that is not enclosed between the plates. Homework Equations For an infinite sheet: $$\vec E = \frac{\sigma}{2\varepsilon_0}\hat...
  15. K

    Deriving the energy density of the Electric Field

    Homework Statement Taken from Purcell Problem 1.33 Consider the electric field of two protons a distance b apart. The potential energy of the system ought to be given by U=∫E2dv. Let E1 be the field of one particle alone and E2 that of the other. Evaluate ε0∫E1⋅E2dv. Set one of the protons...
  16. D

    Particle traveling towards a plate with an Electric Field

    Homework Statement From a distance of 10 cm, a proton is projected with a speed of ##v = 4.0 × 106 \frac{m}{s}## directly at a large, positively charged plate whose charge density is ##\sigma = 2.0 × 10^{-5} \frac{C}{m^2}##. (See below.) (a) Does the proton reach the plate? (b) If not, how far...
  17. N

    Finding the Charge on an Ion in a Zero Electric Field

    Homework Statement A proton is at the origin and an ion is at x1 = 6 nm If the electric field is zero at x2 = -3 nm , what is the charge on the ion? Homework Equations for ion The Attempt at a Solution https://imgur.com/ryyuQBq I just have used all my attempts besides one. So I...
  18. D

    Electric Field between Two Thin Conducting Plates

    Homework Statement Two thin conducting plates, each 25.0 cm on a side, are situated parallel to one another and 5.0 mm apart. If ##10^{-11}## electrons are moved from one plate to the other, what is the electric field between the plates?Homework Equations $$\vec E(P) = \frac{1}{4\pi...
  19. L

    Jackson's 6.4 - Uniformly magnetized conducting sphere

    Homework Statement A uniformly magnetized and conducting sphere of radius R and total magnetic moment m = 4\pi MR^3/3 rotates about its magnetization axis with angular speed \omega. In the steady state no current flows in the conductor. The motion is nonrelativistic; the sphere has no excess...
  20. E

    Electric field outside conductor surface

    I'm confused as to how this expression E= (δ/εo) can't be used to calculate the electric field of a perfectly flat part of a surface even farther from just above the surface.If you just extend the same cylindrical Gaussian surface used for this proof, wouldn't the field stay the same no matter...
  21. B

    Electric field in an infinite layer

    Homework Statement In the layer ##0<z<a## there is a uniform and constant density of charge ##\rho>0##. In the layer ##-a<z<0## the density of charge is ##\rho<0##. What is the total electric field in the space?The Attempt at a Solution By the Gauss law I find that if ##z \geq a## or ##z \leq...
  22. Z

    Angle between 2 charged spheres hanging from string

    Homework Statement Two positively charged metal spheres are suspended from the same hook by light strings of equal length, making an angle of 10.0◦ with each other. The charges carried by the spheres are as shown in the diagram. After that, the spheres are brought in contact briefly, then...
  23. B

    Electric field generated by ions in a box

    Homework Statement A ionized gas (overall neutral) is in a cylindrical box with radius ##R## and ##h<<R##, with is main axis along ##\hat{z}## (there is acceleration of gravity ##\vec{g}=-g \hat{z}##). The ions are points: some of mass ##M## and charge ##q>0## (heavy positive ions) and some of...
  24. R

    What is Electric Field on a grounded structure?

    Suppose we have an energized conductor say 10m above the ground, my understanding is that E Field at the ground will be 0 v/m. My question is, if we have say 8m tall steel tower approximately 3m from the energized conductor and grounded. What is the electrical field on this grounded steel...
  25. G

    A positive charge Q is located at the origin....

    <Moderator's note: Moved from a technical forum and therefore no template.> Hi, I've been doing this excersice but I'm not quite sure about my answer It says: A positive charge Q is located at the origin of a three-dimensional coordinate system. Consider and imaginary square surface of side...
  26. rumborak

    Magnetic field = electric field in some reference frame?

    This Wikipedia article https://en.m.wikipedia.org/wiki/Relativistic_electromagnetism seems (to me) imply that there is always a frame of reference in which a magnetic field can be rather viewed as an electric field modified by relativistic considerations. Is that always true? That is...
  27. H

    Electric field generation between anode and cathode

    Hi I'm running an experiment where I want to see the electrical field generated when I energise a submerged anode (an array consisting of 4 x stainless steel tubes spaced equidistance apart) and cathode array (similar to the anode) upstream and downstream of the flowing water tank (glass sided...
  28. K

    Electric Field Lines: Charge Movement and Conductor/Insulator Interactions

    1. The problem statement "If charges are free to move, the field lines will straighten and shorten as the charges move together" 2. Questions in relation to statement Are there any cases in which charges aren't free to move between two charged objects such as between conductors or insulators...
  29. Pushoam

    Electric field inside a cavity in a dielectric

    Homework EquationsThe Attempt at a Solution A)[/B] In the spherical cavity, let me have a Gaussian Spherical Surface around the center. Applying Gauss' s Law for dielectrics, ##\oint _S\vec D⋅ d \vec a = Q_{f_{en}} ## Due to the symmetry of the problem and ## Q_{f_{en}} =0## , ## \vec D = 0...
  30. Pushoam

    Electric field due to a uniformly polarized cylinder

    Homework Statement Homework EquationsThe Attempt at a Solution Uniform polarization : ##σ_b = \vec P ⋅ \hat n ## Taking ## \vec P = P \hat x ~and ~ \hat n = \hat s ~, ~ σ_b = P \cos \phi ## Let's take a strip of width R dΦ at an angle Φ. This strip will be equivalent to a rod of linear...
  31. R

    Electric field of an infinitely long charge carrying wire

    Homework Statement Find the electric field of an infinitely long straight wire of charge ## \lambda## C/m at a point ##r= ix+jy## Homework Equations ##\int E.da = \frac {Q}{\epsilon_0}## ##E= \frac{\int dq}{4\pi\epsilon_0 r^2} ##r The Attempt at a Solution Drawing a cylindrical gaussian...
  32. Pushoam

    Sketching the electric field of a bar electret

    Homework Statement Homework Equations ##σ_b = \vec P ⋅\hat n The Attempt at a Solution The polarized system could be transformed into two charged discs S1 and S2 of radius a kept at a distance L. The discs S1 and S2 have surface charge densities -P and P respectively. A) For L>>a, In...
  33. A

    Electric field in leaky capacitor model

    Hi everyone. I need to calculate E-field(AC source / DC/ point charges) in leaky capacitor( epsilonr= a dielectric with relative permittivity and finite conductivity). But I do not how to calculate or write the equations for them. any idea or reference is very welcome.
  34. E

    Electric Field Intensity of a line on bisecting plane

    Homework Statement A very thin, finite, and uniformly charged line of length 10 m carries a charge of 10 µC/m. Calculate the electric field intensity in a plane bisecting the line at ρ = 5 m. Homework EquationsThe Attempt at a Solution Not sure why I'm not getiting this but I've been at this...
  35. spareine

    Sketch of the electric field of a laser beam

    I am trying to sketch the electric field E in snapshot of a linearly polarized laser beam. Is it correct that the E vectors bend from vertical to longitudinal near the cylindrical surface of the beam, and that all field lines within a half wave segment are closed loops?
  36. C

    Electric field strength between charged plates help

    Homework Statement Homework EquationsThe Attempt at a Solution E=kq/d2 how do I involve the kinetic energy K in the equation?
  37. C

    Electric field strength between charged plates

    Homework Statement Homework EquationsThe Attempt at a Solution E=kq/r2 so when the distance increase E should decrease? I know this is wrong, but can someone explain why? Thanks
  38. A

    Understanding Electric Field Lines: An Introduction to E Bar and Tangent Vectors

    Hi, I'm reading the textbook and there is my image. http://imgur.com/a/9BqHm It says "The field vector E bar is tangent to the electric field line at each point". I might want to ask what "tangent" means in this sentence? Sorry to ask that stupid question.
  39. A

    Electric field of AC source

    Hello everybody I got really confused. I want to calculate the Electric-Field of an alternating current source( Sine(wt)). I do not know what is its equation. I need to run it in Matlab to get a result. Can you please give me some hints? I need to write the equation to calculate the E-field in...
  40. S

    Electric field above the centre of a rectangle

    Homework Statement Exercise in integration: Using the Electric Field E of a straight line segment of charge, find the electric field at height 10 cm above the centre of a rectangle of sides 10cm and 20 cm carrying charge density 4 μC/m2. Homework Equations µ=Q/L µ = charge density Q = total...
  41. P

    Charged sphere and charged conducting shell

    Homework Statement A + q = 5 pC charge is uniformly distributed on a non-conducting sphere of radius a= 5 cm , which is placed in the center of a spherical conducting shell of inner radius b = 10 cm and outer radius c = 12 cm. The outer conducting shell is charged with a -q charge. Determine...
  42. R

    Electric Field of a Charged Sphere?

    Homework Statement A sphere of radius R has total charge Q. The volume charge density (C/m^3) within the sphere is ρ = ρ_0 (1 - r/R). This charge density decreases linearly from ρ_0 at the center to zero at the edge of sphere. a. Show that ρ_0 = 3Q/πR^3. b. Show that the electric field inside...
  43. SetepenSeth

    Electric field in the center of an arc

    Homework Statement Consider a conductor wire with a charge Q uniformly distributed, shaped in the form of an arc of radius R and amplitude 2A (were A is a given number between 0 and π). Find the value of the electric field in the center of the arc. Homework Equations ##E(P)= \int K_e...
  44. C

    Which point has the strongest electric field strength in this scenario?

    Homework Statement Homework EquationsThe Attempt at a Solution I tried to use the formula: F=kq1q2/r2 So at point B, the electric field strength is( 2kQ/r2) - (-kQ/r2)= 3kQ/r2 At A: (2kQ/r2)+(-kQ/r2)=kQ/r2 At C: -(2kQ/r2)-(-kQ/r2)=-kQ/r2 So B is the strongest? Is there an easier way to do it?
  45. Arup Biswas

    Electric Field Behavior Between Charged Parallel Plates

    One side of a plate has a uniform positive charge density. Two of those plates are placed parallel to each other in a distance away, with their charged side facing each other! The electric field between is zero then! If we put a charge there it will feel no force? I think if the charge is put...
  46. R

    Explanation on the Electric Field in Griffiths' Textbook

    Hi. I'm going over the discontinuity aspects of the electric field as we cross the surface charge. A pillbox Gaussian surface was drawn and the electric field for "below" is throwing me off. Can someone explain why the electric field is pointing in the same direction from both sides of the...
  47. Arup Biswas

    Why is the electric field inside a conductor zero?

    It can be mathematically shown by Gauss's law that it is true but physically how? In case of a symmetrical conductor(Eg Sphere,Cyllinder) there are charges uniformly distributed and field of one charge cancels out the opposite charge's field! But which are not symmetrical, for them what makes...
  48. A

    How can two equal and opposite forces produce motion? [EM]

    I am having hard time understanding the definition of work done to move a charge in an electrostatic field book says that if charge A and B sitting at some position and now if I move the charge say A towards B from arbitrary direction that force required is exactly equal and opposite to the the...
  49. R

    Magnitude of the electric field

    Homework Statement http://imgur.com/a/g5acE # 34 A plastic rod of length L = .24 cm is uniformly charged with a total charge of 12 x 10^-6 C. The rod is formed into a semi circle with its center at the origin of the xy plane. What are the magnitude and direction of the electric field at the...
  50. R

    Find the electric field at the origin

    Homework Statement Given two charged particles: 1) 5x10^-9 C, (-.03 m, 0 m) 2) -20x10^-9 C (.04 m, .02 m) find the electric field at the origin.Homework Equations F = (kQq)/r^2 E = (kQ)/r^2 The Attempt at a Solution So I know since 1)'s charge is plus, its field vector is ( (8.99x10^{-9})...
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