Current density Definition and 189 Threads

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?

Homework Statement Current density is the amount of current per cross sectional of flow. I'm having trouble wrapping my head around this definition. Surface charge or volume charge I understand better since they are almost analogous to the density we all understand (amount of matter/charge...

Homework Statement Copper and aluminum are being considered for a high‐voltage transmission line that must carry a current of 51.4 A. The resistance per unit length is to be 0.176 Ω/km. Compute the magnitude of the current density for an aluminum cable. Homework Equations R\quad =\quad \frac {...

Homework Statement A beam contains 3.95×108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.64×105 m/s. What is the magnitude of the current density? Homework Equations J = nev n = electron density e = electron charge v = drift velocity The...

Homework Statement a) A charge q is released a distance d above a grounded infinite conducting plane. It's non relativistic velocity is v. Find the induced surface current density on the plane. b) Show that the above current density produces a vanishing magnetic force on the charge. Homework...

Homework Statement Prove that a current density J(r, t) such that ∇ × J = 0 implies the magnetic field B = 0.Homework Equations Maxwell's equations, vector calculus The Attempt at a Solution I've played around with Maxwell's equations and with the properties of vector calculus but I can't...

eq.1 eq2. eq.3 eq.4Hello, I have a question about eq.4 If we find the closed surface flux integral of J, would it be current?

Homework Statement Not sure if this is the correct place to post so move if needed. In a cylindrical conductor of radius R, the current density is givne by j_0 e^{- \alpha r} \hat{k}. Where ##\alpha## and ##j_0## are some constants and ##\hat{k}## is the unit vector along the z-axis. ...

Homework Statement A long, straight wire, radius R, carries total current I. The current is distributed in the wire so that the current density is proportional to s, the distance from the center of the wire. (a) Write an expression for the current density J in the wire, as a function of s...

Homework Statement Determine the conductivity of the insulator in a spherical capacitor filled with weakly conductive dielectric. Specific conductivity of the dielectric is λ, the dielectric permittivity ε. Ansver in book is ##\Lambda = \frac{4\pi\lambda}{\epsilon} \frac{R_1R_2}{R_1-R_2}##...

Hello, I would like to calculate the current distribution in a coaxial cable where the skin effect is significant. I asked this question on stackexchange and I provided pictures and more details there...

Derive the probability current density for a particle in an electromagnetic field. (I previously posted this on StackExchange. Please pardon, but I have been spending a lot of time on this and if anyone knows exactly what the subtle trick involved is, I would really appreciate it.)...

Suppose we have an elliptical loop of wire in the x-y plane with constant cross-section. And let's also assume that the cross-section is very small, so we have a thin wire. $$\vec{r}=\begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} a\cos \theta \\ b \sin \theta \end{bmatrix}$$ A tangent...

Hi, I'm trying to figure out how the current density for a poloidal current in toroidal solenoid is written. I found you may define a torus by an upper conical ring ##(a<r<b,\theta=\theta_1,\phi)##, a lower conical ring ##(a<r<b,\theta=\theta_2,\phi)##, an inner spherical ring...

Hi, I'm trying to write the current density for such circular loop in spherical coordinates. For a circular loop of radius a that lies in the XY plane at the origin, the current density it's simply: \mathbf{J}= \frac{I}{2\pi\sin\theta}\delta(\theta-\frac{\pi}{2})\frac{\delta(r-a)}{a}\hat{\phi}...

Hello everyone, I have a physics problem that I have been struggling with for a long time. Many many hours of searching around for theoretical or practical answers have not given me anything definitive. The question is in the context of electrical engineering, more specifically peaks in...

What is current density

we know i = dq/qt = enLA/dt = en(Vd)(A) standard derivation i en(Vd)(A) where e is charge on electron n is electrons per unit vol. Vd is drift velocity of electrons A is area of cross section of conductor SO my doubt is if we have a conical conductor or some kind of conductor whose CSA is not...

Surface current density, K is defined as: K = σv where σ is surface charge density and v is velocity. Given a uniformly charged spherical shell with radius R, spinning at constant angular velocity ω, find the current. So, I start with this formula: dI = K dl dI = σ Rω dl and I placed the...

Homework Statement Homework Equations Ienclosed = ∫ JdA ∫B*ds = m0*I The Attempt at a Solution This is my take of finding [/B]when r is greater than R--so, the magnetic field is m0*I/2pir, since B(2pir) = m0*I This is because the amperian circle covers the whole wire. Can somebody verify...

Hi All, I'm working on a research project that requires putting an electrode array with 4 elements into a flexible tube filled with conductive liquid. The electrode array is a series of balls, with the first being positive and the last being negative. The idea is to measure the change in...

Hello, I am having trouble getting the correct solution to the following problem, even though I think my steps all are correct! What did I do wrong? 1. Homework Statement Homework Equations Current = current density * area Current = charge/time So, time = charge / current The Attempt at a...

Greetings all, I know that Faraday's and Ampere's law are related by M.E., but can I say the following? By Faraday’s Law, a time varying magnetic field induces an electromotive force, which produces an electric current density in a media. Up until EMF, that's Faraday's, but is the rest of...

Homework Statement Two plane parallel electrodes are separated by a plate of thickness s whose conductivity \sigma varies linearly from \sigma_0 near the positive plate to \sigma_0 + a near the negative plate. Calculate the space charge density \rho_f when the current density is J_f ...

Homework Statement The Biot-Savart law for a current density j in a volume V is: d\vec{B} = \frac{\mu_0\vec{j}\times\vec{r}}{4\pi r^3} dV Derive the formula for the magnetic field created by a single point-like particle carrying charge q moving with velocity \vec{v}. Explain and justify all...

Just trying to derive the units for current density but i keep getting A*m rather than A/m^2. J = I/A A length derivation would help.

Homework Statement (a)The current density across a cylindrical region of radius R varies according to the equation: J=J0(1-r/R), where r is the distance from the axis of the cylinder. The current density is the maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R...

Is there a current density operator or something equivalent? If so, how does it relate to other operators like momentum and angular momentum? Basically, the classical picture of a magnetic moment is a little loop of current, I would like to understand the quantum analog.

could someone explain to me why the the time derivative of current density J would be zero? more specifically.. $$\mu_0\frac{∂\vec{J}}{∂t}=0$$ trying to derive maxwell's wave equation for E-field and i guess one of the assumptions i have to make is the above. but if I'm making a wave...

Hello all. As far as I know, the equations to obtain current density is: J=∑(qi ni vi) , where qi is the charge of each class of charge carrier in the material, ni is the volumen density of that class of charge carrier, and vi is the average drift speed of those charge carriers. Current...

Why does the current across the cross section of an element, with perpendicular area vector ##d \vec{A}##, have a normal integral symbol in its definition: ##i = \int \vec{J} \cdot d \vec{A}## Why is it not a closed surface integral? ##i = \oint \vec{J} \cdot d \vec{A}## Usually we take the...

Hi, I just read a paper on graphene's basic properties and it says that since current density J is given as J=q*n*v where q is the elementary charge, n is the electron density and v is the Fermi velocity of electrons and for graphene n=6*10^12 cm^-2 and v=10^8 cm/s, the current density...

I can see the purpose of J for currents taking place in a volume like, say.. plasma physics but for current in a wire, it's all surface current, so why use J?

I have been thinking about the Maxwell equations lately and was wondering about their "natural" differential form formulation to get some nice geometric interpretation. This post mainly concerns the inhomogenous microscopic Maxwell equations on some spacetime ##(M,g)##, as the homogenous ones...

Hello. I'm floundering. What is the right way to formulate a problem of calculating the current density distribution across the wire's cross-setion, taking into account eddy currents? If the Maxwell's equations are not the way to go, what is? What should be the boundary conditions or any...

that is my solution: I=J.A=J.∏r^2 Since r =a => J=0 => I=0 ≠ Io I think this is wrong but i can't answer why this solution was wrong. Help me Please

Homework Statement So I was able to find a problem that was kind of similar to a homework problem that I am working on. Unfortunately, I'm not quite sure what is going on partially within the problem. In the problem they state that \phi=\phi*, but it does not state why. I was wondering...

This is more electrical engineering than chemistry I would think. If the current density required is 200mA per cm^2, and the electrode is a hollow copper tube that is submersed in an electrolyte in which the inside of the tube is not touching any solution, should the current be calculated...

1. Problem statement The current density from the axis in the wire of radius R is given by J = cr3/2 A) draw the current density as a function of r graph B) determine the constant c in terms of Itotal C) determine the current as a function of r. D) draw the graph of the current as a function...

Although I understand the derivation of boundary condition in case of steady electric current but I did not understand, that the electric field which is in direction of J current density which is generated from permanent potential to have a current in a conductors that is applied between two...

Current Density = (I/A) I = (Q/t) = (nVq)/t where n is the number of charges, V is the volume, q is the average charge and t is time. nVq/t = n(Ax)q/t = nAvq where v is velocity. Current Density = (I/A) (nAvq)/A = nvq My question is on the step where it goes Q/t = nVq/t Why does...

Homework Statement Find an expression for the magnetic field inside a wire carrying a current density J = Cr2 where C is a constant to be determined in the problem. The total current in the wire is I and the radius of the wire is R. Your answer should be a function of r, R and I, but should not...

Hi, I'm trying to use stock's theorem with the following magnetic field - B=1/r\hat{\theta} on Cylindrical coordinate. From one side I get - \nabla X B=0 = \mu \int\int J \cdot dA, means that the current density is zero. From the other side I get - \oint B \cdot dl = 2 \pi r \cdot...

Why is there a uniform current density in a conductor at DC. It’s my understanding that generally in a conductor, a sphere for instance, in a static situation, all charge is at the surface of the conductor because it the charges repel each other. So in a cylindrical conductive wire even though...

The electric intensity E, current density j and specific resistance k are related to each other by the relation please explain

Homework Statement Find the current density as a function of distance ##r## from the axis of a radially symmetrical parallel stream of electrons if the magnetic induction inside the stream varies as ##B=br^a##, where ##b## and ##a## are positive constants. Homework Equations The...

Homework Statement In the drude model of electrical conduction, the current density (J) is not directly proportional to : a. The average time interval between sucessive collisions b. the number of charge carriers per unit volume c. The square of the electron charge d. The electric field...

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...

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...

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...