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.
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...
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
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...
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...
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...
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...
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...
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...
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...
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?
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...
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} -...
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...
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 !
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...
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...
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?
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...
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!
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...
Since sphere is made of l.i.h material, $$\vec{J_f}= \sigma \vec{E}$$
We compute electric field E using
$$\vec{E} = -\nabla V$$
$$= -\nabla \left(V_0cos\theta\right)$$
$$= -\frac{\hat\theta}{r}\frac{{\partial}}{{\partial\theta}}\left(V_0cos\theta\right)$$
$$\vec{E}=...
I first took out the variation of conductivity along the radius of cylinder.Also we know that J=sigmaE.Therefore i have to find variation of E also.But how will i find that as potential is also not given.Help.
While I was going through "Introduction to Electrodynamics" by David J. Griffith I see the line "Current is a vector quantity". But we know it doesn't obey the vector algebra (addition ). Then how it can be a vector?... Please help me
Dear Sirs,
Maybe this is general knowledge, but I couldn't find the answer where I looked, so please bear with me.
Consider a circuit consisting of a mechanical generator (some spinning magnets and coils) and a wire across the generators output. At some point the wire gets hot and starts a...
Homework Statement
[/B]
Let us assume that neutral atoms or molecules can be modeled as harmonic oscillators in some cases. Then, the equation of the displacement between nucleus and electron cloud can be written as
$$\mu\left(\frac{d^x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x\right)=qE.$$
where...
In order to check if a quantum particle crosses a barrier or not, isn't calculating ##|\psi(x)|^2## enough in that particular region ? Why do we need to calculate probability current density for that matter?
I am confused by the definition of current density in Maxwell electrodynamics. Perhaps someone can help me out?
As I understand it, the current density function can be written as
$$ \vec{J} = \rho \vec{v}_S$$
where ρ is the charge density function and v_S is the continuous source charge...
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...
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 ?
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 (...
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...
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...
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!
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...
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...
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##...
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...
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...
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...
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...
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?
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...
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...
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...
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}}...
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)...
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...
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...