Electric field Definition and 1000 Threads

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. T

    Electric field outside 2 same charge parallel plates

    Homework Statement Given 2 positively charged parallel plates with equal surface charge densities, calculate the electric field at a point outside the the parallel plates. Homework Equations E= (surface charge density) / 2(relative permittivity) for a single sheet. The Attempt at a Solution...
  2. T

    Is it a magnetic or an electric field that causes induction

    Is it a magnetic or an electric field that causes induction in the antenna wiki says that: The electric field (E, green arrows) of the incoming wave pushes the electrons in the rods back and forth, charging the ends alternately positive (+) and negative (−). enter image description here...
  3. D

    Magnitude of the Electric Field at the Following Distances

    Homework Statement The figure below shows a spherical shell with uniform volume charge density ρ = 1.87 nC/m3, inner radius a = 15.0 cm, and outer radius b = 2.60a. [Reference Picture] What is the magnitude of the electric field at the following radial distances? Homework Equations...
  4. G

    Electric field integral: Convergence where ρ is nonzero

    Hi. I know how to use Gauss' Law to find the electric field in- and outside a homogeneously charged sphere. But say I wanted to compute this directly via integration, how would I evaluate the integral...
  5. N

    Using Gauss' Law to Calculate electric field near rod.

    Homework Statement No variables, just a conceptual question. Homework Equations Flux = EA = Q/ε The Attempt at a Solution Given a uniformly charged rod of FINITE length, could we use Gauss' law for electric flux to calculate the field at a point p a distance x away from the rod, so long as the...
  6. B

    Determine work done by electric field

    Homework Statement Given electric field ##\vec E = 6x^2\hat i +6y\hat j+4\hat z## v/m Find ## V_{MN}## if both M and N separate by M(2,6,-1) and N(-3,-3,2) Homework Equations The Attempt at a Solution here i find ##V_{MN}## by unit vector from N to M is ##\frac 1 {\sqrt (115)}(5\hat i +9\hat...
  7. Philosophaie

    Electric Field and Electric Dipole Moment for a Dipole

    The Magnetic Dipole Moment for a Magnetic Field for a dipole oriented on the x-y axis is: ##\bar m = |m| \hat z## The Magnetic Field is: ##\bar B = \frac{\mhu_0}{4 * \pi * |\bar r|^5} * 3 * \bar r * (\bar m . \bar r) - \bar m * |\bar r|^2## Vector Potential is: ##\bar A = \frac{\mhu_0}{4 * \pi...
  8. P

    Electric field above an off-center finite line charge

    Homework Statement There is a finite line charge with length L = 1 meter and linear charge density λ = 1*10^-16 C/m. Point P is h = 70cm above the line charge and distance x from the right end of the line charge. The magnitude and direction of the electric field at point P must be found. The...
  9. B

    Gaussian beam spherical mirror reflection question

    Homework Statement Gaussian beam of radius R_i and beam width w_i, The beam is reflected off a mirror with a radius of curvature R = R_i and the reflectivity of this mirror is given as rho(r) = rho_0*exp(-r^2/a^2), where r is the radial distance from the center of the mirror and a is a...
  10. P

    Calculate strength of the electric field at indicated point

    Homework Statement https://imgur.com/a/wpir4 [/B] a. What is the strength of the electric field at the position indicated by the dot in the figure? Use the following values: q1 = 1.09 nC, q2=0.93 nC, d1=2.49 cm, d2=6.9 cm, d3 = 4.27 cm. b. What is the direction of the electric field at the...
  11. T

    Electric field inside hollow conductor with a charge

    Ok, this might be a really dumb question, but I still am asking it: I was reading about gauss' Law when it comes to a hollow conductor with a (say) point charge inside it, and it seems intuitive to me that, in electrostatic equilibrium, the charges rearrange themselves to cancel the electric...
  12. T

    Electric field inside non-conducting spherical shell

    Homework Statement Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...
  13. Epoch

    Electricity: electric field in a point Between Two Charges

    Homework Statement I've seen many books writing the cosine rule like this: a^2 = b^2 + c^2 - 2bc cos A My electricity textbook for an electric field in a point between two charges says this: E resultant = root[E1^2 + E2^2 + 2*E1*E2*cos(angle between E1 and E2)] In the first equation it is -2...
  14. M

    Strength of electric field given potential difference

    Homework Statement What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1.50×104 V? Homework Equations ΔV = qΔU ΔV = -∫E⋅dl E = kq/r2 The Attempt at a Solution I am not sure where to...
  15. T

    Rotating a spherical conductor in an Electric field

    Hi, I recently came across the familiar image of a metal sphere in an electric field: https://i.stack.imgur.com/x58Ia.jpg I noted how the free-charges on the surface of the sphere align with the electric field lines as opposite charges are attracted. Then I wondered, 'what if the sphere was...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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...
  21. 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...
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. 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...
  28. 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...
  29. 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...
  30. 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...
  31. 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...
  32. 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...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. 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...
  38. 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...
  39. 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...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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...
  45. 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...
  46. 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...
  47. 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...
  48. 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.
  49. 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...
  50. 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?
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