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. moeug1999

    Help! I'm Stuck on an Equation My Professor Gave Me

    My professor does not walk us through the problem. He literally just gave us an equation and that's it. I do not know how to do this problem.
  2. S

    I Electric Field Directly Ahead of or Behind a Moving Charge

    Since it is stated that ##E'_x = E_x##, I am going to set a special case where ##z' = z = 0##, ##E_x## in (5.10) reduces to, ##E_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{x^2}## However, ##E'_x## in (5.13) reduces to, ##E'_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{\gamma^2 x'^2}## There is an...
  3. jisbon

    Net electric field in a circle

    In this case, I know there won't be any net efield in the x direction because it cancels out with each other. The problem is dealing with the y axis. Am I supposed to presume an angle for each of them or what should I do instead? Thanks
  4. P

    Charged proton enters an electric field

    I tried to do Net force with electric field = E x q minus the gravitational force= mg. However, this gives me a negative net force suggesting the proton is moving downwards. I'm not sure this is correct as the initial velocity was horizontal. Was there no gravitational force before? Am I missing...
  5. jisbon

    Energy band gap when there is an electric field

    So I have just been taught this topic but this question seems to be one of a kind and I can't seem to figure it out. What I've learnt: When there is a positive electric field applied to the right, for example, the electrons that are free moving in a crystal (aka conducting band) will oppose...
  6. Decimal

    Spectral density of radiative electric field

    So I have to find an expression for ##\vec{A}(\omega)##, $$\vec{A}(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} \vec{A}(t)e^{i\omega t} dt.$$ This point is where my confusion comes up. In the answer sheet they integrate over the retarded time ##t_r##, so the integral is...
  7. H

    Electric field between two capacitor plates (proof)

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  8. D

    Electric field involving 4 point charges in a rectangle

    I am stuck on the following question (Image attached of my work) appears to make sense until i try to take a limit as c--->0 because the result should be 0. Am i missing something, if so can't you point me in the right direction. Thank you
  9. Z

    Find the electric field on the surface of a sphere using Coulomb's law

    Note that the solution is 5625 V/m in z direction which is found easier using Gauss' law, but I want to find the same result using Coulombs law for confirmation. Lets give the radius 0.04 the variable a = 0.04m. ##\rho## is the charge distribution distributed evenly on the surface of the...
  10. Saptarshi Sarkar

    Electric field inside a polarized dielectric sphere

    My attempt: I know from Gauss' law in dielectric ##\nabla .D = ρ_f## where ##D = ε_0E + P##, so as ##ρ_f = 0## (as there is no free charge in the sphere) => ##\nabla .D = 0## => ##ε_0\nabla .E = \nabla .P## from this I get ##E = \frac {-kr^2 \hat r} {ε_0}## But, I know that for a uniformly...
  11. S

    The electric field of a piecewise uniform 1D charge distribution

    This is not really homework, but I'm having trouble understanding it intuitively. I came across this when learning about the space charge layer of a diode. The solution I know simply uses the 1D form of Gauss's law: ##\vec{\nabla} \cdot \vec{E}## = ##\dfrac{\rho}{\epsilon_0}## becomes...
  12. Saptarshi Sarkar

    Calculating total charge when the electric field is given

    I first tried to use the Gauss' law equation E.A = q/ε0 to find the total charge enclosed. The answer came out to be q(enclosed) = 4πqε0e^(-4r). So for r approaching infinity, q(enclosed) approached 0. Next, I tried the equation ∇·E = ρ/ε0, calculated rho to be -4qε0e^(-4r)/r^2 and total...
  13. askcr9

    A slab? Infinite area? Electric field? Help please

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  14. Moara

    Electron moving inside a region of homogeneous electric field

    a) since the eletric field is perpendicular to the inicial velocity, the x component is constant, hence Vf.cos45=Vo. This gives Vf=0,6√2.C b) Ei=γi.Eo , γi=5/4 , Ef=γf.Eo , γf=5/(2√7) Finally, Ei+e.E.d=Ef. Apparently this is incorrect, why??
  15. N

    Relativistic motion of an electron in a uniform electric field

    dv/dt is the acceleration, so I thought I could find the acceleration from F = qE = ma = dp/dt. But this is a relativistic case, so the proper acceleration is a = F/mγ3, where v in the gamma is the v of the electron and F = eE. However, I'm not sure if this is correct, because the constant τ...
  16. N

    Electric Field of a Point Charge

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  17. BickySmalls

    What would happen to a charge that is placed in an Electric Field = 0?

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  18. Z

    Evaluate the electric field for two slabs of charge

    Thus I assume that one slab has positive charge Q1 and the other slab has negative charge Q2 = -Q1 There are 4 cases for the electric field: 1. x <= -a 2. -a <= x <= 0 3. 0 <= x <= a 4. a <= x The general case: Charge Density ##\rho = \frac {Q} {V}## Flux of E ##\phi_e = \oint \vec E \cdot d...
  19. E

    Electric field in a spherical shell

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  20. Z

    Find the electric field of a cylindrical charge

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  21. Diracobama2181

    Rigid Rotator in an Electric Field

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  22. bryanso

    Why is the Electric Field outside this wire not zero?

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  23. Moara

    Flux of Electric Field through a cone

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  24. binbagsss

    A Hamiltonian background magnetic field, perturbed by electric field

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  25. B

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  26. D

    Find the electric field inside and outside of a spherical shell superposition

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  27. adamaero

    Electric energy density in the dielectric of a coaxial cable

    V(ρ) = V_o*ln(ρ/0.0018)/ln(45/180) (Attached picture is where the unit vector of r is really ρ.) In cylindrical coordinates ∇V = ρ*dV/dρ + 0 + 0 ∇V =derivative[V_o*ln(ρ/0.0018)/1.386]dρ ∇V = V_o*0.0018/(1.386*ρ) E = V_o*0.0012987/ρ Work = 0.5∫∫∫εE•E dv Bounds: 0.0018 to 0.00045 m D = εE =...
  28. Jelsborg

    Electric field of a spherical conductor with a dipole in the center

    In a recent test we were asked to calculate the electric field outside a concentric spherical metal shell, in which a point dipole of magnitude p was placed in the center. Given values are the outer radius of the shell, R, The thickness of the shell, ##\Delta R## and the magnitude of the dipole...
  29. jisbon

    Find the velocity of a point charge in a ring of electric field

    Okay, I am not even sure how to startr with this question. But here's my theory: First I will need to the electric field produced by the ring using the formula: ##E = k\frac{\lambda a}{(x^2+a^2)^{3/2}}## After finding out electric field produced by ring, am I supposed to find out the...
  30. D

    How to show that the electric field inside a spherical shell is zero?

    Hi! I need help with this problem. I tried to do it the way you can see in the picture. I then has this: ##dE_z=dE\cdot \cos\theta## thus ##dE_z=\frac{\sigma dA}{4\pi\epsilon_0}\cos\theta=\frac{\sigma 2\pi L^2\sin\theta d\theta}{4\pi\epsilon_0 L^2}\cos\theta##. Then I integrated and ended up...
  31. D

    How to calculate the electric field at a point on the axis of two rings

    Hi! I need help with this problem. I tried to solve it like this: First I calculated the electric field of each ring: Thus the electric field at a point that is at a distance z from the ring is ##E=\frac{Qz}{4\pi\epsilon_0(z^2+r^2)^{3/2}}##, Thuss for the upper ring, the electric field would be...
  32. D

    Electric Flux through a circle

    Hi! My main problem is that I don't understand what the problem is telling me. What does it mean that the surface is a flast disc bounded by the circle? Is the Gauss surface the disc? Does that mean that inside the circle in the figure, there is a disc? Can you give me some guidance on how to...
  33. F

    Why is the magnitude of the electric field in a sphere the same?

    I was looking at a sphere that has a positive point charge at the center of a sphere with radius R. Now, I understand that the electric field is pointing outwards (in the direction of dA), so $$d\phi = EdA$$ However, I am told that since the magnitude electrical field is the same because the...
  34. K

    Electric field using Gauss's Law, but in open cylinder given only r?

    I have no idea how to approach the problem using Gauss's Law. I found the electric field using superposition, and it was incorrect. I am assuming you treat the wire as a continuous electric field, and then also treat the pipe as a continuous electric field. I solved for this using...
  35. jisbon

    Electric field of an infinite charged plate

    So I figured to get e-field at point (4,4,0), I need to find the resultant e-field from the negatively charged particle and the plate ##E_{resultant}=E_{particle}+E_{plate}## ##E_{particle}=\frac{kq}{d^2}=\frac{(9*10^9)(-2*10^-6)}{4^2}=-1125N/C## Now for the plate is where I'm confused. If this...
  36. D

    Amplitude of an oscillating electric field

    Homework Statement: The amplitude of the oscillating electric field at your cell phone is 4.0 μV/m when you are 10 km east of the broadcast antenna. What is the electric field amplitude when you are 20 km east of the antenna Homework Equations: electric field i've done E=##\frac A...
  37. D

    Electric field in the narrow wire

    i've started from this I1=I2 then I1= JA1=##\frac {E l} R## I2= JA2=##\frac {E_2 l} R## but can't get anything useful relating them. Am i forgetting any other useful formula? I get as result E4
  38. A

    Electric Field for the circular path of a positively charged particle

    Here is picture. Answers is A. My attempt was that I thought if i were to place a positive test charge then it would go from top to bottom if there was a positive charge in the center it was avoiding and a positively charged particle at the top, but an electron at the bottom so it would avoid...
  39. C

    Electric Field and Capacitance

    Question Part C Part D
  40. C

    Deriving an Expression for an Electric Field along the Z axis

  41. Yalanhar

    Electric Field due a charged disk

    Homework Statement: uniformly charged disk, radius r, with surface charge density ##\sigma## . I want to find the electric field along the axis through the centre of the disk at a h distance Homework Equations: ##dE=\frac {kdq}{r^2}## My Solution: ##dE=\frac {kdq}{r^2}## in this case r=s...
  42. Yalanhar

    Calculate the electric field due to a line of charge of finite length

    Homework Statement: A thin rod of length L and charge Q is uniformly charged, so it has a linear charge density ##\lambda =q/l## Find the electric field at point where is an arbitrarily positioned point. Homework Equations: ##dE=\frac{Kdq}{r^2}## A thin rod of length L and charge Q is...
  43. AndresPB

    Electric Field from its Potential of a Half Circle along its Z axis

    So I figured out the potential is: dV = (1/(4*Pi*Epsilon_0))*[λ dl/sqrt(z^2+a^2)] . From that expression: We can figure out that since its half a ring we have to integrate from 0 to pi*a, so we would get: V = (1/(4*Pi*Epsilon_0))*[λ {pi*a]/sqrt(z^2+a^2)] In that expression: a = sqrt(x^2+y^2)...
  44. N

    Find the Electric Field E using Gauss' Law

    I tried to work out both a) and b), but I am not sure if I am correct. I drew a picture with a sphere around q first with radius r and then with radius 3r. For a) ##E.A=\frac {q}{ε_°}## (when using Gauss' Law) Since ##A=4πr^2##, I substituted this in the equation and solved for E giving me...
  45. adamaero

    By using Gauss' law, can the electric field be p/(pi*ε*r^2)

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  46. S

    Electric field due to two positive charges

    I am having trouble solving the following problem. I am given two positive charges on the x axis: I know that the electric field strength at point P is ##E=150 \frac{V}{m}##, ##d=1.8m## and ##a=2.5m##. I want to find the charge of ##Q##. As far as I know, the electric field on the y-axis...
  47. R

    Electric field on a ring's axis

    The contribution coming from a little segment of the ring is ##d\vec{E}=\frac{dQ}{r^2}cos\theta \hat{z}##, assuming that the horizontal components cancel out. But how can we show that?
  48. navneet9431

    Would electric field exist if there were only one type of charge?

    I believe the answer is incorrect, reasons: The answer assumes that electric field will exist . But this is not the case , until and unless there is a bipolarity there cannot be an electric field ( in case of isolated charged objects, the field exists because the bipolarity is separated by a...
  49. Zahid Iftikhar

    Electric Field of a moving charge

    When a charge is at rest, it has an electric field only. When the charge starts moving , it is said to have accompanied a magnetic field. My question relates to its electric field while in motion. Does it still exist or not? I know in electron guns electrons are deflected while passing thru the...
  50. J

    Electric Field for Charge Distributions

    We are given: q1 = +2.0 x 10-5 C, q2 = q3 = -3.0 x 10-5 C, r31 = r21 = 2 m a) We start by finding the electric force between q3 to q1 and q2 to q1 FE31 = k * q1 * q3 / r312 FE31 = (9.0 x 109 Nm2/C2) * (+2.0 x 10-5 C) * (3.0 x 10-5 C) / (2 m)2 FE31 = 1.35 N FE21 = k * q1 * q2 / r212 Since...
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