Current density Definition and 189 Threads

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...

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...

(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...

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...

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 =...

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...

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...

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...

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!

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}...

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...

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...

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...

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...

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...

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...

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...

*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...

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...

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...

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...

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)...

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...

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...

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'...

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...

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

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...

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...

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...

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.

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...

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...

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

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...

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...

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)...

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

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...

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...

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...

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...

I beg you to understand my poor Eng.. If there is any poor grammar or spelling..please correct me.. While studying MHD with "An Introduction to Magnetohydrodynamics" written by Davidson, I encountered the term 'current density'.. As you know well, empirically, \mathbf{J} = \sigma...

Let's say you have a square plate with a voltage applied across two opposite corners, connected by the hypotenuse. Presumably, the electric current density distribution throughout the plate would be such that it would follow the path of minimal resistance, i.e. through the hypotenuse. If...

Homework Statement The figure represents a section of a circular conductor of nonuniform diameter carrying a current of 5.00 A. The radius of cross-section A1 is 0.400 cm. http://img97.imageshack.us/img97/7220/img01mn.th.jpg Homework Equations (a) What is the magnitude of the...

Homework Statement A section of a circular conductor of non uniform diameter carrying a current of 5.00 A. The radius of the cross-section A1 is 0.400cm.(a) What is the magnitude of the current density across A1?(b) The radius at A2 is larger than the radius at A1. Is the current at A2 larger...

Normally, when we encounter un normalizable wave functions, they are considered to be representing streams of particles.Like in the case of of transmission thru a step potential,We find out the probability flux of reflected wave and transmitted wave and hence find transmission coeff. Can...

Homework Statement The figure shows wire section 1 of diameter 4R and wire section 2 of diameter 2R, connected by a tapered section. The wire is copper and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wire's width. The electric...

In the time between posting this and now, I have found my mistake. So, problem solved. Homework Statement Earth's lower atmosphere contains negative and positive ions, created by radioactive elements in the soil and cosmic rays from space. In a certain region, the atmospheric electric field...

Homework Statement Write down an expression for the current density per unit length flowing at the surface of a magnetised material.The Attempt at a Solution Any ideas?