# What is Current density: Definition and 199 Discussions

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.

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1. ### I Deriving expression for resistance in terms of current density

Is there a way to obtain equation 9.42 (I is current, j is current density, and sigma is conductivity) in the following image (from Modern Electrodynamics by Andrew Zangwill, the part on electromotive force) besides using V=IR and substituting the line integral of j/conductivity for V? The...
2. ### Calculate the probablity density and current density of a wavefunction

i have use time evolution operator to get the wavefunction at any time "t" as Ψ(x,t) = U(t,t1) * Ψ(x,t1) but i don't know how to calculate next part of the question
3. ### A A question about current density in finite element analysis

I know that if there is only one conductor providing the current density, then the current density can be used. But if you apply Maxwell's equation when there are multiple current sources, I don't know which value to use. This is not an analysis using a tool, but a problem when I develop the...
4. ### A Relationship between magnetic potential and current density in Maxwell

I am currently studying to solve Maxwell's equations using FEM. I have a question about Maxwell's equations while studying. I understood that the magnetic potential becomes ▽^2 Az = -mu_0 Jz when the current flows only in the z-axis. I also understood the effect of the current flowing in a...
5. ### Total Josephson current through junction with magnetic field

Hello there, I am given a diagram of a Josephson Junction like so: With a magnetic field ##B = \mu_oH## in the z-direction. I'm reasonably sure ##d_x,d_y,d_z## are normal lengths, not infinitesimal lengths although that is up for debate. Using the above equations I rearrange the expression...
6. ### Impact of AC effects on current density analysis of pcb for 50-60Hz

Hello , I was looking into current density analysis of a PCB that handles distribution of AC power . from ansys and cadence sites , i realized by current density they refer to DC IR drop that is a pure ohmic analysis that doesn't take into consideration the AC effects . And in order to take this...
7. ### Green's reciprocity theorem about current density and magnetic field

I have to prove three equations above. For first two equations, I've been thought and made reasonable answer by using a definition of the electricfield. However, for third, I can't use a definition of a magnetic field due to the cross product Like J_2 X J_1 X (r_2 - r_1). I think three of 'em...
8. ### Current vs Current Density vs Magnetic Field

If I want to carry 10 A through an 8 AWG wire, I understand that there will be a specific magnetic field around the wire which will decrease as I move outward from the wire radially. Let's consider the center of that wire as coordinates (x,y)=(0,0). An object located at (0,10) would see a...
9. ### How is the current density solved for in an electrolyzer unit?

Hydrogen production rate is typically measured in current density, but what is the area in which the current is divided by to find such a value?
10. ### B How to find the current density in an alkaline electrolyzer?

To my understanding, current density is simply the current flowing through the alkaline electrolyzer divided by the area (the units for current density are A/m^2). But what would the area be in this situation? Is it the area of the electrodes or maybe the area of the electrolyte solution or...
11. ### Current density in a wire that is being used to charge a capacitor

Somehow this answer is incorrect , but i realize that even numbers are hipothetical , 45 coulumbs is too much charge , what is wrong in my calculations?
12. ### Ohm's law, current density, free & bound charge

Hello, I wonder if you could give me some advice to how solve this question. What I was thinking to solve it was to determine J by using Ohms law, ## \vec J = \sigma_{\alpha} \vec E ## I already determined the E field for for the sphere, I got it from a) ("a)" was to determined all the bound...
13. ### Conservation of charge with Dirac delta

Hello, I was reviewing a part related to electromagnetism in which the charge and current densities are defined by the Dirac delta: ##\rho(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} - \underline{x}_n(t))## ##\underline{J}(\underline{x}, t)=\sum_n e_n \delta^3(\underline{x} -...
14. ### Magnetic field generated by a current in a wire - special relativity

First I wrote in ##S'##, by using Gauss theorem $$\int_{\Sigma} \underline E' \cdot \hat n d\Sigma = \frac Q {\varepsilon_0} \rightarrow E'(r)2\pi rH=\frac{\lambda'H}{\varepsilon_0}$$ $$\underline E'(\underline r)=\frac{\lambda'}{2\pi\varepsilon_0r}\hat r$$ Its components are...
15. ### I Is the current density operator derived from fundamental considerations?

Hello, I found this article. In equation (1) the authors wrote that the current operator is given by : ## - \frac{\delta H}{\delta A} ##. I just would like to know if this relation is a just definition or if it can be derived from more fundamentals considerations ? Thanks !
16. ### Finding the conduction current density

The current density is given by the formula ##J_e = (n\mu_n + p\mu_p)qE = \sigma E; \sigma \text{=conductivity}## ->eq1 The resistivity of intrinsic germanium is 60 Ohm-cm, the equation 1 becomes ##J_i=n_i(\mu_n + \mu_p)qE## ->eq2 ##J_i=60 \text{ ohm-cm} ## Applying the standard equations...
17. ### Bound Bulk Current Density and Surface Current Density

Hi there, I've worked through most of this question but I'm stuck on the final part, showing that total bulk current ##I_B## is equal and opposite to total surface current ##I_S##. I calculated ##\vec H## the normal way I would if I was looking for ##\vec B## in an infinitely long cylindrical...
18. ### Electric current is not a vector while electric current density is a vector

Why is electric current not a vector while electric current density is a vector? What's the intrinsic difference between the two through that surface integral?
19. ### I Probability current density of a stationary state

I have written a finite difference program to solve 1D time-independent Schrodinger equation. It seems to work correctly for harmonic oscillator, particle in a box, etc. But I can't figure out how to calculate the probability current density. It should be constant, but what is it? The program...
20. ### Determine the magnetic field inside and outside the cable using Ampere's law

My attempt: I realized after i had tried to solve the problem that the current must be constant in the cables. But no information about where the cables has radius a and b is given so how would I go about to find an expression for the current? Thanks in advance!
21. ### Magnetic field of a rotating cylinder with permanent polarization

I am struggling to get my work to match the posted solutions to this problem. I understand part (a) but can’t get the integral to work out for (b). I know I have to use Biot-Savart and add up the components from the the surface and volume currents. The cylinder is very long, so I need to make a...

29. ### Solving Schrodinger's Equation with a weak Imaginary Potential

Homework Statement A particle of energy E moves in one dimension in a constant imaginary potential -iV where V << E. a) Find the particle's wavefunction \Psi(x,t) approximating to leading non-vanishing order in the small quantity \frac{V}{E} << 1. b) Calculate the probability current density...
30. ### The relationship between initial and final current density

Homework Statement Homework Equations ##J=\frac{I}{A}## A=π r2 The Attempt at a Solution Since I is constant and the diameter is doubled , A2 = π (##\frac{2D}{2}##)2 A2 = 4 A1 J2 = I/(4A1) = J1 /4 → (E) Is my answer correct ?
31. ### An interesting question about the divergence of a current density

Hi, maybe as you know ##\nabla. J = -\frac {\partial p} {\partial t}## where J is current density p is charge density. But also we know current density flux outward the circuit is 0 because current density does not flow out of circuit an this actually volume integral of ##\nabla. J## is zero (...
32. ### Resistance, current and current density

Homework Statement A coaxial cable consists of a core cylindrical wire and a coaxial cylindrical shell, as illustrated in the Figure below. Consider a cable made of copper, which has resistivity of ρ=1.70×10−8Ω·m. Thecorewirehasaradiusof r =1.0mm. Theinnerradiusofthe 1 outer shell is r = 5.0...
33. ### Vector potential of a plate with a uniform, time-harmonic current density

Hi all, i tried to do this question but got stuck on the last point . Can anyone help me please? The general form of vector potential: I got the answer for A1 vector potential but don't know what assumptions i need to get the expression for the A2. Does anyone know how one can derive it...
34. ### Calculate magnetic potential of a given current density

Hello, I'm current studying magnetostatics and I'm struggling to understand the equation for A. Here is the equation from Griffith in the attachment. My confusion is, if the object is a cylinder and the current density is a function of s, J(s), then how would I write r-r'? Thank you!
35. ### Current Density between two infinite plates

Hi, I'm studying the "Child Langmuir law". We have a grounded cathode that is an infinite plane with free electrons, and an anode with a positive voltage V. The text says that the current density J is constant between the two plates for the "Charge conservation principle". I was not able to...
36. ### Magnetostatics - Magnetic field of a nonuniform current slab

Homework Statement A thick slab in the region 0 \leq z \leq a , and infinite in xy plane carries a current density \vec{J} = Jz\hat{x} . Find the magnetic field as a function of z, both inside and outside the slab. Homework Equations Ampere's Law: \oint \vec{B} \cdot d\vec{l} = \mu_0...
37. ### Current Density and Charge Density in a loop of Wire

I am trying to formulate the Current Density for a Loop of wire with a diameter,d, current,I, and an cross-sectional Area of the wire ##\pi(d/2)^2##. With spherical coordinates (radial, azimuthal, polar) ##\bar j## = ##\frac{I}{\pi(d/2)^2}*cos \theta *sin \phi \hat x##...
38. ### A Difference between conduction & convection current density?

Hello Everyone, Could anyone please explain the difference between the conduction current density (J=σE) and the convection current density (J=ρvd)? I really appreciate any examples or applications to further elaborate these two theories. Note: vd is the particles' average drift velocity...
39. T

### How to Calculate Current Density (Petri Dish/Graphite 0.7 mm)

Hello all, I have a petri dish 8.7 cm in diameter filled with 20 mL of TSB media. I have set up a .7mm graphite at the 0cm mark of the diamter and measured current at 4.6Volts over the entire distance of the petri dish (8.7cm) with .5 cm step sizes. For example: When the probes are 1cm apart I...
40. ### Relationship between line current & surface current density

Homework Statement In a configuration having axial symmetry about the z axis, a line current I flows in the −z direction along the z axis. This current is returned at the radii a and b, where there are uniform surface current densities Kza and Kzb , respectively. The current density is zero in...
41. ### Find Reliable Current Density Sensors for Aluminum Foil Treatment

Hi all, don't know if this is the appropiated place to search. I am trying to find a supplier for a current density probe (Hall sensor or similar) to measure the current density in a tank where an aluminum foil is treated to form electrolitical capacitor. Im searching for this in Europe and USA...
42. ### Importance of Current density?

Why we do use electrical current density in place of total electrical current? Actually I want to know what is the advantage of using electrical current density?
43. ### What does Griffith mean by this hint? [Electrodynamics]

I was solving the problems given by Griffith in his book 'Introduction to Electrodynamics' and stumbled across this question. "Because sigma (conductivity of the medium) is a function of position, the equation 7.5 does not hold" --i get this point; current density isn't constant and so its...
44. ### Current density of specific configuration

Homework Statement Two hollow metal spheres (left one has radius of 0.7 meters and right one has radius of 0.4 meters) are half-submerged in the sea water with specific conductance of γ = 4 S/m. Distance between their centers is much greater than their radii dimensions and equals 60 meters...
45. ### Electric field in a wire with same current as another wire

Homework Statement For what electric field strength would the current in a 2.0-mm-diameter nichrome wire be the same as the current in a 1.0-mm-diameter gold wire in which the electric field strength is 0.0095 N/C? dn = .002m dg = .001m Eg = .0095 N/C ρn = 100 * 10-8 Ωm ρg = 2.44 * 10-8 Ωm...
46. ### Magnetostatics force equation for continuous current density

In Jackson, the following equations for the vector potential, magnetostatic force and torque are derived##\mathbf{m} = \frac{1}{{2}} \int \mathbf{x}' \times \mathbf{J}(\mathbf{x}') d^3 x'## ##\mathbf{A} = \frac{\mu_0}{4\pi} \frac{\mathbf{m} \times \mathbf{x}}{\left\lvert {\mathbf{x}}...
47. ### Interpret current density in plasma as material property?

Homework Statement An electromagnetic wave propagates through a gas of N free electrons per unit volume. Neglecting damping, show that the index of refraction is given by n^2 = 1 - \frac{\omega_P^2}{\omega^2}, where the plasma frequency \omega_P = \sqrt{\frac{Ne^2}{\epsilon_0m_e}}.\quad(1)...
48. ### Varying Charge Densities with Constant Current Density

1) If I vary charge densities, but keep current density constant, do I get any sort of electromagnetic wave? 2) If the answer to question 1 is no, then if I vary charge densities, but keep current density constant, could I conceivably have a two isolated "open circuit" current elements of...
49. ### A Relativistic conduction current density?

Hello, I am an electrical engineer rather than a physicist, however, I am trying to understand the physics of a twin wire transmission line in terms of the charge and current density. Let's say we have a lossless, infinite length, twin wire transmission line, a step current is induced into the...
50. ### Is the current density a vector?

In Newtonian physics, is the current density, usually called j, a vector? Namely, is it a polar vector in the sense of a tensor of rank 1?