E-field Definition and 189 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. Drakkith

    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...
  2. K

    E-field, force, & changing sign of charge (grade 12)

    Homework Statement a) Find the net electric field at a point b) Find the net force experienced by a charge of -1.2 x 10-5 C placed at that point c) What would happen if the charge changed signs? Homework Equations FE = qε The Attempt at a Solution a) Solved: 6.7 x 104 N/C [E 63° N] b) FE =...
  3. G

    Finding E-field at a point away from a line charge

    Homework Statement A line charge with a uniform linear charge density Lambda lies along the x-axis and extends from -∞ to 0. Determine the X-component, and Y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis. Homework Equations dE= (k*dq/r^2)* r(hat)...
  4. D

    Electric field inside and around a hollow sphere

    Hi everyone, I am wondering if anybody could help me out. For my study I got the following question but I got stuck in part C (see image below). I Found at A that due to symmetry all components which are not in Ar direction will get canceled out I found at B that there is only charge density at...
  5. Alex_Neof

    Calculating the E-Field inside and outside a sphere.

    Homework Statement Consider a sphere of radius ##R##, with a charge density ##\rho(r)=\frac{\alpha} {r^2},## with ##\alpha## a constant. Use Gauss' law to calculate the electric field outside the sphere at a distance ##r## from the sphere's centre (ie. ##(r > R)## and inside the sphere (ie...
  6. HaLAA

    Python Using VPython program to calculate the E-field

    Homework Statement Charge a ring of radius R=5.0cm laying in the x-y plane to 50nC. Create a VPython program that will allow you to calculate the E-field due to the ring anywhere in space. Homework Equations E_ring=kQz/(R^2+z^2)^(3/2), point P above the xy-plane The Attempt at a Solution...
  7. H

    Is E-field in pn-junctions changing linearly with bias?

    Hi guys, there are a lot of textbooks and articles describe the electric field in depletion region at thermal equilibium, but very few of them tell what happens to the field under bias. I am wondering if the electric field in the depletion region simply changes linearly with reverse bias? Or if...
  8. B

    E-field of cylindrical conductor above infinite ground plane

    Homework Statement Find the electric field between the conductor and ground. The conductor is at: Potential = +V0, radius a distance d from the ground plane. Homework Equations I used image theory to create a conductor at -V0 at distance -d from the ground plane. Laplace's equation: ∇2V = 0...
  9. M

    Problems of E-field of a Continuous Charge Distribution

    dE = ke(dq/r2) How to change to complicated equation in the following picture?
  10. A

    E-field and charge density outside two coaxial cylinders

    I am working on a problem of electrostatics, and I am having troubles in trying to figure out one part of it. 1. Homework Statement It consists of an inner solid cylinder of radius ##a## with a voltage ##V_A##, and an outer coaxial cylindrical shell of inner radius ##b## and outer radius ##c##...
  11. T

    A non-conducting sphere, e-field and potential.

    Homework Statement A non-conducting sphere of radius R has volume charge density ρ = B/r. for r<R and ρ = - for r>R. B is a constant. a) Calculate E-field for r>R. b) Calculate E-field for r<R. c) Calculate potential for r>R. d) Calculate potential for r=R. e) Calculate potential for r<R...
  12. BiGyElLoWhAt

    Carrier particles and E-Field Propagation

    A thought experiment that is a consequense of a question someone asked in my particle physics class: We place an isolated electron. We wait 10 years, and place a half ring of electrons (spaced far apart from each other, but uniform) 10 LY away from our central e. Will our charges move? If so...
  13. T

    Is There an Experimental Apparatus to Determine Photon Propagation Mechanism?

    When we dissect the photon we find an electric field and a magnetic field according to Maxwell. In order to determine the propagation mechanism of a single photon through the fabric of space-time, is there an experimental apparatus designed to determine which field may plow the path, in order...
  14. A

    Help visualizing E-field between moving magnets

    I'm doing my best at learning electricity & magnetism for the first time and I could use some help. Let's say I have two horizontal bar magnets moving horizontally towards each other at constant velocity. The changing B field should induce an electric field gradient in the perpendicular...
  15. D

    Problem 2.4 Griffiths E&M 3rd ed -- E-field above a square loop

    Homework Statement The problem states, "Find the electric field a distance z above the center of a square loop (sides of length a) carrying a uniform line charge λ. " The hint says to use the result of example 2.1. Example 2.1 is a similar problem, but instead of a square loop you are asked...
  16. Zaent

    Direction of E-Field in 3d space

    Homework Statement I am trying to find the direction of an E-Field from a given E-Field vector in 3d space. If I have an electric field vector of (-1i, -2j, 3k), the magnitude of the field is sqrt(-1^2 + -2^2 + 3^2) = 3.74, but how do I find the direction? Homework Equations tan(y/x)? The...
  17. N

    Varying current inducing E-field: example 7.9 in Griffiths

    Homework Statement Look at the attached file. 1) Why does Griffith simply say that the E-field of the amperian loop is parallel to the axis of the wire? 2) And how come ##\int \vec{E} \cdot d \vec{l} = -E(s) l ## ? Shouldn't it at least be ## E(s) 2l## ? Why the minus sign and ##l## instead...
  18. A

    E-Field & Voltage: Coulomb's Law & Integration Explained

    1. Looking to find E-field and Voltage (in pic) 2. Coulomb's Law, E=q0V, E=integralde 3. Basically i tried to split the quarter ring into halves and then integrate. It worked i got the right answer. But my professor did it in 1 step? Something about just integrating over DV? I don't get how or...
  19. A

    E-field vanishing *at* the surface of a conductor

    Suppose we apply a uniform field to an infinite conducting slab (i.e. like an infinite parallel plate capacitor, but the interior is included as part of the conductor). What is the resulting field? The simple answer is that a surface charge develops on the boundary planes of the conductor so as...
  20. A

    Silicon in an External E-Field

    Hello! I was wondering what would happen if you placed a piece of undoped Si in an external electric field (say, between the plates of a capacitor) under illumination. Would it generate current? I'm essentially trying to understand if a large enough external electric field could split an...
  21. E

    Help finding the voltage in a uniform E-field

    Homework Statement Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. What is the voltage across an 8.67-nm-thick membrane if the electric field strength across it is 9.16 MV/m? You may assume a uniform E-field. Homework Equations...
  22. E

    Help finding the electric feild strength in a uniform E-field

    Homework Statement The voltage across a membrane forming a cell wall is 78.7 mV and the membrane is 8.52 nm thick. What is the electric field strength? (The value is surprisingly large, but correct.) You may assume a uniform E-field. Homework Equations E=-Vd The Attempt at a Solution...
  23. F

    E-field in a cylinder with a hole parallel to its axis

    Homework Statement A long insulating cylinder of radius R1 has a cylindrical hole parallel to the axis of the cylinder. The radius of the hole is R2, and the distance from the centre of the cylinder to the centre of the hole is a. There is a uniform fixed charge per unit volume ρ throughout...
  24. A

    Is Charge Density Zero for a Uniform E-field in y-direction?

    Homework Statement I have a function for an E-field E(x,y,z,t)=E_o\cos(k(x-ct))\hat j and I need to find the charge density... Homework Equations \vec \nabla \cdot\vec E=\frac{\rho}{\epsilon_o} The Attempt at a Solution When I compute the dot product of gradient operator with...
  25. A

    Calculating electric potential from constant E-Field

    Hey, folks. I've typed out the question here. I hope you don't mind my just linking this (if that's against the rules or something, I'll type it out). I'm still pretty confused about what to do. I assume, as usual, it's probably something... well... stupid—but I can't figure out what. Thanks...
  26. L

    Question about the E-field along center axis of charged ring

    http://www.physics.udel.edu/~watson/phys208/exercises/kevan/efield1.html I'm having trouble understanding the derivative notation. I know that "dE" and dQ" have to do with the derivative, but what exactly does that mean in the context of this problem? For some reason I find it difficult to...
  27. J

    Explanation of E-field torque and initial angle

    Homework Statement Hello, A dipole moment is placed in a uniform electric field oriented along an unknown direction. The maximum torque applied to the dipole is equal to 0.1 N.m. When the dipole reaches equilibrium its potential energy is equal to -0.2 J. What was the initial angle between the...
  28. K

    Why Is the Electric Field Stronger at Sharp Edges on Conductors?

    Hello everyone, Could someone explain or direct me to some detailed explanations as to why is the electric field at a conductor greatest where the curvature is sharpest? I just can't seem to grasp this concept. I understand sharp edges do have this property so is this that there is more...
  29. C

    E-field & hollow non-conducting sphere

    I know that the E-field around a hollow non-conducting sphere charged with Q charge comes immediately from Gauss' Law but I'm wondering what the situation is if we somehow go inside the material, we make a very small hole through the material of the sphere and go inside it. What would there be...
  30. K

    Why Does the Escape Velocity Decrease as Mass Increases in an Electric Field?

    Upon applying the method of finding escape velocity to the E-field, I end up with: \sqrt{\frac{2kQq}{rm}} What I don't understand, conceptually, is why escape velocity decreases as mass increases, in the electric field. What property is actually taking place here?
  31. F

    E-field Perturbation of 2D rotor. Show Y_10 couples ground state?

    Homework Statement Consider a molecule with an electric dipole moment d. The Hamiltonian of a molecule in the external electric field E is: \hat{H} = \frac{\hat{L^2}}{2I} - dE \cos{\theta}, where the polar angle \theta characterises the orientation of the molecule. (We have chosen the field...
  32. M

    Tricky problem - Find E-field of a sheet of charge

    Homework Statement Consider a uniformly charged, infinitesimally thin rectangular sheet with total charge Q extending from x = 0 to x = -w and from y = 0 to y = L. Find the electric field at an arbitrary distance x along the positive x-axis. Homework Equations Superposition; E =...
  33. E

    Calculating E-field and potential of a charged ring

    Hello folks! I've been trying to calculate the E-field of a charged ring. It seems well documented for a symetric point(a line from the center etc.) but what I'm interested in is say if I'm slightly of the center of the ring, how can I make a more general equation? I've tried calculating...
  34. D

    Finding scalar potential from E-field and vector potential

    Homework Statement Hi. This one I really am lost on :/ In my mind it seems rather easy, but I still can't figure it out. I have been given the E-field: \mathbf{E}\left( t,\,\,\vec{r} \right)=\frac{\kappa }{{{\varepsilon }_{0}}}\left[ \begin{matrix} ctx+{{x}^{2}}-{{y}^{2}} \\...
  35. O

    E-field polarization in the direction of propagation, TEM, TE, TM

    I read that for a plane wave E, B and k are always perpendicular to each other but then in a TM mode I have electric field in the direction of propagation. This means this TM and TE modes I cannot have in free space? Can I have them in a laser? If I can have some E-field in the direction of...
  36. K

    E-field from Time Varying B-field of Current wire

    Homework Statement Time Varying Current carrying wire creates time varying magnetic field.How can we analytically calculate electric field at distance r from the time varying current carrying wire? I(t) is time varying current where α , β are angle of two ends of current carrying wire...
  37. F

    Why does the E-field of radiation vary with inverse distance?

    Feynman_Lectures_on_Physics_Volume_1_Chapter_28 In 28-2 Radiation Feynman starts talking about the third term of Eq. 28.3 and why that it varies with the inverse of the distance. On page 28-4 he says that the unit vector e'r is pointed to the apparent position of the charge. I understand...
  38. U

    Capacitance and E-field of a parallel plate capacitor

    Homework Statement The Attempt at a Solution I know that the E-field is definitely affected by the presence of the space charges. Since one side is positive, the positive charges in the air get pushed towards the negative plate. so Enet = Eplate - Echarges But the thing is...
  39. L

    Why does the E-field inside a cylinder =0?

    Homework Statement Figure 24-32 shows a section of a long, thin-walled metal tube of radius R, carrying a charge per unit length  on its surface. Derive expressions for E in terms of distance R from the tube axis, considering both (a) r > R and (b) r < R. Plot your results for the r = 0 to...
  40. D

    Finding E-field within a semiconductor.

    Homework Statement rho(x) = 0 for x >= Xo and x <= -Xo rho(x) = ρ1 for 0< x < Xo rho(x) = -ρ1 for -Xo < x < 0. The last two rho's are constants. Electric field = 0 for x> Xo and x < -Xo. Find E for -Xo< x < Xo Homework Equations I used the ∇. E = ρ / epsilon The Attempt at a Solution...
  41. J

    E-field between two concentric cylinders (not homework)

    Hi, I have a question. Suppose you have two concentric cylinders of radii a and b with opposite uniform surface charges, line charges or something to that effect. Now, I know (or was told) that the E-field between the two, that is for a<r<b, is equal to the field from the inner cylinder (radius...
  42. A

    Why does net charge always reside on the surface of a conductor?

    If you place a conductor in an external E-field the charges inside it will move so as to cancel off the field making the field inside the conductor zero. My question is: Is this also true if you place some net charge on a conductor? Will the field inside it then still be zero? The net charge...
  43. S

    Questions about the Potential and E-Field directions of P-N junction

    Hi, on re-visiting some basic ideas about PN junctions, I found I am confused with the depletion region diagram: I understand that the depletion region originated from the diffusion current at the local contact of the p and n type material, the electrons diffuse from the n type to p type...
  44. X

    Calculating work from E-Field Graphs

    Homework Statement a)Calculate the work performed by an external agent to move a charge of -0.39x10^-12 C from `i' to `b' http://capa-new.colorado.edu/msuphysicslib/Graphics/Gtype54/prob04a_threeqcontour.gif Hint: The equipotential lines shown are separated by 1 kV. Work to move a charge is...
  45. T

    Can the magnetic field from a single charge be converted into an electric field?

    Consider the following "classical" example: ^{}_{} A system Σ' moves away from a system Σ with relative velocity v in the direction of z'z axis (their origins concur at time t=t'=0). A charge q is located in the origin of Σ' and moves along with it, while an observer sits at (0,yo,0) in Σ. The...
  46. A

    E-Field Attenuation: Causes & Effects

    Do electric fields attenuate in space? If so what causes the attenuation?
  47. M

    Paschen's Law and E-field between spheres

    I am reading up on Paschen's Law and came across some papers measuring breakdown voltage between two identical spherical electrodes. I've read in a couple places that the electric field is uniform when the gap distance is no larger than the radii. Why is that? It seem to me that the field...
  48. A

    Working w/ Complex representation E-field

    Often a time varying E-field is represented in complex format. I have a simple E-field (uniform in space) given by \vec{E}(t)=E_o\cos(\omega t)\cdot\hat{k} or equivalently, the real part of \vec{E}(t)=E_o e^{\omega t}\cdot\hat{k}. We know the potential is the negative gradient of the...
  49. S

    What is the ratio of the voltmeter readings in this E-field scenario?

    Greetings everyone, While I was studying on my own using MIT OCW, I came across the following document. In that document in the last part you are asked to calculate the ratio of the reading of the two voltmeters positioned to the left and right of the loop. I did some work on them but I am...
  50. K

    Time-retarded E-field and Gaussian surface integral

    If I have an oscillating charge inside of a sphere, will the integral of E(t), where t=proper time of the sphere, over the sphere's surface area result in a value of electric flux equal to the value of the charge?
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