Current density Definition and 200 Threads

In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In SI base units, the electric current density is measured in amperes per square metre.

View More On Wikipedia.org
Recent contents Top users
  1. H

    Quick question about current density

    Homework Statement Homework Equations J=I/A The Attempt at a Solution I was just looking at the solution for this, and I was confused because they seemed to use different ways of finding the area. For finding J2, they took the surface area of the end of the cable, pi(r3^2-r2^2), but for...
  2. C

    The units for current density don't check out

    In my lectures the equation for current density was given as: J=n*q*vd where: n = the number of electrons per unit area q = electron charge vd = drift velocity of electrons If you rewrite this equation as: J=\frac{N}{A}*q*\frac{dr}{dt} where: \frac{N}{A} is the number of electrons per unit...
  3. D

    How Do You Calculate Electrical Current Density with Complex Integrals?

    Homework Statement Hi. I'm having some trouble calculating the electrical current density, which in my case is given by: \sigma =\frac{{{e}^{2}}}{4{{\pi }^{3}}}\int{\left( -\frac{\partial f}{\partial \varepsilon } \right)\tau \cdot \mathbf{v}\cdot \mathbf{v}}\,dkHomework Equations Lets...
  4. S

    Complex current density of sphere confusion

    Hello, I am a bit confused on how to get this into the proper form, $$ \begin{eqnarray} \vec{J} &=& \vec{v}\rho \\ &=& (\vec{\omega} \times \vec{r}')\rho_o \Theta(R-r') \\ &=& \omega r' \sin(\theta')\rho_o \Theta(R-r')[\cos(\phi')\hat{y} - \sin(\phi')\hat{x}] \\ &=& \vdots \\ J_x + i J_y &=&...
  5. jegues

    Physical Electronics: Uniform Current Density

    Homework Statement Typical semiconductor fabrication technologies employ copper (ρ ~ 15.7nΩm; μr ~1) as the interconnect material. A process is designed for a clock frequency of 1GHz, has interconnect cross sections ranging between 35nm x 70nm and 0.18um and 90nm. Quantitatively determine...
  6. C

    Current Density of water through a pipe

    Homework Statement (a) Water flows through a pipe of radius 4 cm at a rate of 3.5 m/s. Suppose each water molecule is singly ionized (highly unrealistic). What is the electric current density associated with the flow of these ions? b) What is the electric current in the pipe? Homework...
  7. C

    Relationship between current and current density for a volume conductor

    (I'd like to preface this with the warning that the following question may be a very dumb one.) My understanding is that current density (or flux) \vec{J} = \vec{J}(x, y, z) is the rate of flow of charge (or the current) per unit area. (Units of \frac{\text{C/s}}{\text{cm}^2} .) Say...
  8. D

    Find Magnetic Field of Infinite Slab with constant current density

    Homework Statement Find the magnetic field from an infinite slab with constant current density, Jo, in the x direction. ρ(z) = ρ1 x_hat for -b<z<b ρ(z) = 0 for |z| >= b Homework Equations Ampere's Law. The Attempt at a Solution I draw a rectangular prism inside the slab with...
  9. H

    Reversal of limits of integration in the derivation of probability current density

    In working out the derivation of the probability current density, I see (based on the definition of j(x,t)) that the limits of integration are changed from d/dt∫(b to a) P(x.t) dx = iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](b to a) to d/dt∫(b to a) P(x.t) dx =...
  10. N

    Is it specific capacitance (Csp) is proportional to current density?

    I've run the experiment. By varying the current and fix the mass of the electrode, I found out that the specific capacitance (Csp) is increased when applied current (I) is increased. By using this formula, Csp = 4I / [M*(dV/dt)], where I is the applied current, M is the mass of both...
  11. F

    Vector potential with current density

    Homework Statement Hey, I got the current density \vec{j}=\frac{Q}{4\pi R^2}\delta(r-R)\vec{\omega}\times\vec{r} and now I should calculate the vector potential: \vec{A}(\vec{r})=\frac{1}{4\pi}\int\frac{j(\vec{r})}{|r-r'|}. Homework Equations The Attempt at a Solution here my attempt...
  12. H

    Total current with nonuniform current density

    Homework Statement J=J(r)(θhat), J(r)=(3ITr2)/R3 a)total current of the disk? b)J(r) was brought by a charge disk spinning at ang vel. ω, find the surface charge dens σ(r)? Homework Equations J=I/πr2 I=∫Jda J=vσ The Attempt at a Solution a)I assumed I would have to integrate J(r)da from 0 to...
  13. E

    Can velocity and wavefunction help prove Probability Current Density?

    hello, everyone. I have a question about Probability Current Density. I read a book which says that Probability Current Density equals velocity multiply wavefunction^2 .How to prove it? thank you!j=v*ψ^2. best wishes!
  14. S

    Using Current Density to find Total Current

    Homework Statement Suppose a wire has a radius R and a current density of J = I_0 \frac{x^2} {R^4}\hat{k}. Taking the wire to have cylindrical geometry, calculate the total current flowing down the wire, defined as I = \int J \cdot \vec{dA} . Homework Equations J = I_0 \frac{x^2}...
  15. P

    Current density and drift velocity

    Homework Statement 1. A copper wire 2 mm in diameter carries a 4 A current. Determine the current density in the wire, drift velocity of the electrons and the mean time between collisions. Assume that each copper atom contributes one free electron. Hint: you may need some additional parameters...
  16. P

    Surface current density problem

    Homework Statement A static surface current density Js(x,y) is confined to a narrow strip in the xy-plane In this static problem ∇ ⋅Js = 0. Show that the line-integral of Js along any cross-section of the strip will yield the same value for the total current I. (The direction of dl in these...
  17. C

    Current density of discrete charges in 1D space

    Hi guys I am new here. I was asked by my professor a problem: a positron-electron pair is produced at the leftmost position of a 1D circular loop of radius R. e+ moves along the bottom hemisphere and e- moves along the upper one. They are confined in the circular loop and perform circular...
  18. A

    Surface current density problem

    The surface current density, K, is defined as the the current through a unit width perpendicular to the flow. In particular: K = v\cdotσ where σ is the surface charge density. Now I have a little trouble understanding this formula intuitively. Can someone describe in pictures how it is...
  19. M

    Current density, drift velocity and electric field

    Homework Statement A) A current I flows along a straight wire of cross-sectional area A. If the unit vector I denotes the direction of current flow, write down the expression for the current density J (assuming it to be uniform throughout the wire ) and give its SI units. B) (This isn't...
  20. J

    Current density from charge density?

    In statistical mechanics, a probability current (http://en.wikipedia.org/wiki/Probability_current) can be derived from the probability amplitude via ψ*ψ,i - ψψ*,i (i=x,y,z) ...and it would be nice or any number of reasons to be able to do the same thing with a non-probability...
  21. R

    Current density inside superconductors

    Homework Statement consider an infinite superconducting slab of thickness 2d (-d<=z<=d), outside of which there is a given constant magnetic field parallel to the suface. Hx =Hz=0 hy= H0 (some value for z<d and z>-d) , with E vector= D vector=0 everywhere. compute H vector < J vector inside...
  22. G

    Where Can I Find Exchange Current Densities for Chromium?

    Hi folk, I am new to electrochemistry and I am currently trying to find values for the exchange current densities of a range of pure metals. I have had some success from books such as the encyclopedia of electrochemistry of the elements, however I can't seem to find any values for chromium. Can...
  23. J

    Two closely related questions about current density

    *The problem statement The second question kinda builds on the first and I am not too confident my solution to the first is correct. 1: A disk has a uniform surface charge density and is rotated at a rate 'w'. Find 'K'. 2: A uniformly charged sphere ('ρ') is spun. Find the current...
  24. A

    Designing a simple magnetic field gen with a straight wire. Need current density

    Homework Statement Need to design a simple magnetic field generator of radius a= 2mm. The solid metal wire must carry a current density, jw, uniformly distributed over its cross section. The current density that must be found must have a magnetic field at a radial distance of r= 8mm from the...
  25. J

    Circular ring in xy-plane with current, find current density

    Homework Statement Consider a circular ring of wire of radius a that resides in the x-y plane through the origin. The center of the ring coincides with the origin and you can regard the thickness of the wire to be infinitesimal. a. Given that a current I flows in the ring, find an...
  26. A

    Current density and drift velocity

    Homework Statement J = ne(v). (yes. it's a vector equation and I haven't indicated that, but just ignore that. It's not important to my question.) Let's say you have some positive ions traveling downward, and some negative ions traveling upward. The electric field is downward. Let's say...
  27. B

    What is the Role of J in Dynamic Ohm's Law?

    Homework Statement What is J in Ohms law in dynamics? Homework Equations Ampères law: \nabla \times H = J_f + \partial_t D = J_f + \partial_t ( \epsilon_0 E + P) \nabla \times H = \nabla \times (\mu_0^{-1} B - M) = \nabla \times (\mu_0^{-1} B) - \nabla \times (M) = \nabla \times (\mu_0^{-1} B)...
  28. L

    Help deriving expression of current density

    Hey I got an assignment where I have to get an expression of the current density to be: j = -e\int \frac{dk}{4\pi ^{3}} v_{x}f(k) It says k_{x} >0 underneath the intergrale. The current is flowing to the right (velocity of v_{x} > 0) Where f(k) is the fermi-dirac distribution function...
  29. F

    Quantum current density in general relativity

    Hi All, As shown here http://en.wikipedia.org/wiki/Klein–Gordon_equation#Gravitational_interaction one can modify the derivative operator in the Minkowski Klein-Gordon equation to generate the GR case for an arbitrary metric. My question is, what would the quantum current density j...
  30. N

    What are (a) the current density and (b) the electron drift speed?

    Homework Statement "The current in a 1.70mm x 1.70mm square aluminum wire is 1.70 A. What are (a) the current density [in MA/m^2] and (b) the electron drift speed [in micrometers/second]?" Homework Equations J = I/A The Attempt at a Solution I plugged in the values for current...
  31. G

    Current Density of Circular Current Loop (Jackson)

    Hi, I was reading through Jackson's Electrodynamics trying to reason through example 5.5 for the vector potential of a circular current loop of radius a centered at the origin. I pretty much understand everything except when he defines the current density as J_{\phi} = I\sin \theta'...
  32. L

    Why Does Current Density Point Downwards in a Magnetic Field?

    Homework Statement Heres the problem: Homework Equations F=BIL F=qvB The Attempt at a Solution I really don't know where to start. Can you guys give me a hand. Maybe a link to a web page explaining. I understand if it were convention current flowing through the 'pipe' it would experience a...
  33. B

    Proving that J[transverse] + J[longitudinal] = J, where J = current density

    Homework Statement see attached .pdf Homework Equations see attached .pdf The Attempt at a Solution see attached .pdf Question: am I wrong for using, {{\bf{J}}_\ell } \equiv - \frac{1}{{4\pi }}\nabla \int {\frac{{\nabla ' \bullet {\bf{J}}({\bf{x'}})}}{{\left| {{\bf{x}} -...
  34. J

    Current Density: Homework Statement & Stuck Solution

    Homework Statement In attachment The Attempt at a Solution I'm stuck.
  35. H

    How Do You Calculate the Constant C in a Cylindrical Wire's Current Density?

    Homework Statement A long, solid, conducting cylindrical wire of radius a has a current density J(r) = Cr and carries a total current I find a value for the constant C in terms of I and a Homework Equations J = I/A The Attempt at a Solution I believe that I need to...
  36. T

    Finding electric field intensity, power, current given current density

    Homework Statement Sheet of wire is biased with an electrical potential at each end of conduct current. Given current density, J, in wire: J=-x2y ax +xz ay + 2xyz az A)Continuity equation to prove its possible B) current along length of wire C) Electric field intensity E D) voltage drop...
  37. A

    Current Density and Electron Drift Speed

    Homework Statement The current in a 1.5 mm X 1.5 mm square aluminum wire is 1.10 A. What are (a) the current density and (b) the electron drift speed? Homework Equations current density: J = I/A drift speed Vd = J/ne The Attempt at a Solution It's asking for an answer in MA/m^2...
  38. 1

    How Do You Calculate Current Density in a Wire?

    Homework Statement A long straight wire with circular cross-section and a diameter of 5.10 mm is made of a metal with resistivity = 5.00×10-8 m. The wire carries a current of 28.5 A. Calculate the current density in the wire. Homework Equations J = i / A The Attempt at a Solution...
  39. D

    Volume integral of current density

    Hi. Can anyone tell me what the volume integral of the current density is? I find it strange, but G.D. Mahan uses it in his book on page 30. He claims that this is in fact the current. I have attached the particular page.
  40. M

    Finding current from current density of wire

    Homework Statement A cylindrical wire of radius 3mm has current density, J=3s |φ-\pi| z_hat. Find the total current in the wire. Homework Equations The Attempt at a Solution I believe all I have to do is integrate over the area, but for some reason I can't get it to work. Is the...
  41. O

    Current density and vector potential

    Homework Statement What current density would produce the vector potential A(r)=(-kmu/2pi)In(r/a) (in the z direction) where k is a constant, in cylindrical coordinates? Homework Equations The Attempt at a Solution i have done this three times and i get zero current...
  42. M

    What Is Probability Current Density in Quantum Mechanics?

    I'm going over the continuity equation and I'm having some problems getting an intuitive grasp of probability current density. I can't get an idea of what it is. I know the equation, but I don't really know what it means. Could anyone help me out? Cheers, Andrew
  43. S

    Current Density: Research by Mechanical Engineering Student

    Hi I am a research student looking at electrical current flow through various materials although my undergraduate degree was in mechanical engineering so electrical stuff isn't my strong point. I believe that current flow will flow through the path that offers the least resistance, and is...
  44. D

    Induced Current Density On Disk Due to Changing Magnetic Field

    Homework Statement A very thin conducting disc of radius a and conductivity \sigma lies in the x-y plane with the origin at its center. A spatially uniform induction is present and given by B=B_0 cos\(\omega t \)\hat{z}. Find the induced current density \vec{J} in the disc. Homework...
  45. C

    Current density in wires connected in series

    Homework Statement Wires A and B, having equal lengths of 40.0 m and equal diameters of 2.60 mm, are connected in series. A potential difference of 60.0 V is applied between the ends of the composite wire. The resistances of the wires are 0.127 and 0.729 , respectively. Determine: (a)...
  46. R

    Is Probability Current Flow Visualizable?

    Is probability current flow of probability density? I really haven't been able to visualise it properly.
  47. Y

    Ohm's Law in a sphere with current density

    Homework Statement Two concentric metal spherical shells of radius a and b, respectively, are separated by a weakly conducting material of conductivity sigma. (a) If they are maintained at a potential difference V, what current flows from one to the other? (b) What is the resistance between...
  48. S

    Divergence of mass current density

    Hi, i thought a while about the meaning of the following expression \delta t \, \cdot \, \mathrm{div} \, \vec j_m(\vec r,t) \qquad \mathrm{with} \qquad \vec j_m(\vec r,t) = \rho_m(\vec r,t) \cdot \vec v(\vec r, t)Does it indicates the mass, which is produced / annihilated in the Volume...
  49. R

    What is the correct equation for displacement current density?

    Hi, just to check which equation for Jd (the displacement current density) is correct: 1) Jd = ε0εr(dE/dt), or 2) Jd = ε0(εr-1)(dE/dt) 1) came from the fact that Jd = ε(dE/dt) and ε=ε0εr 2) came from differentiating P = ε0(εr-1)E (since Jd=dP/dt). It's only a minor thing but in a...
  50. M

    Eigenvalues and eigenvectors of the momentum current density dyadic

    Homework Statement What are the eigenvalues and eigenvectors of the momentum current density dyadic \overleftrightarrow{T} (Maxwell tensor)? Then make use of these eigenvalues in finding the determinant of \overleftrightarrow{T} and the trace of \overleftrightarrow{T}^2 Homework...
Back
Top