Current density Definition and 189 Threads

Help with curls and current density!1 Homework Statement In cylindrical coordinates, J = 105*(cos(2r)2)*az in a certain region. Obtain H from this current density and then take the curl of H and compare with J. Answer H = 105*(r/4+sin4r/8+cos4r/32r-1/32r)aphi Homework Equations J =...

Can we make a mathematical (equation) relationship between Current Density and Charge Q.

The current density vanishes for a bound state. I would like to know the proof and its physical significance. I appreciate the responses in advance!

Does current density being constant in time and the charge density NOT being constant in time imply that the charge density has to be a linear function of time? i.e of the form p(r,t) = p(r,0) + \dot{p}(r,0)t } Can this be derived using the continuity equation alone?

Homework Statement If the current density is time independent and divergence free, show that the Maxwell Equations separate into independent equations for \vec{E} and \vec{B}. Homework Equations Maxwell's equations The Attempt at a Solution The only Maxwell equation with \vec{j}...

Express the current density of a spherical shell of radius a, rotating with angular velocity omega, with surface charge density sigma Delta function will be denoted d(x). Spherical coordinates will be used I have concluded that for a given chunk (if we restrict to the 0<theta<pi/2...

Hi, I'm trying to wrap my head around the derivation of the current density of a filamentary loop. On the face of it, the result seems obvious since it involves Dirac delta functions, but it's the rest of the formulation I don't quite follow. The derivation begins by considering a loop of...

In a problem it states that: A 10.71 V battery is connected to a resistive strip that consists of three sections with the same cross-sectional areas but different conductivities. In the solution to the problem it stipulates that the current density of the three sections are equal. Where in...

Homework Statement A piece of copper wire joins a piece of aluminum wire whose diameter is five times that of the copper. The same current flows in both wires. The density of conduction electrons in copper is 1.1 \times 1029 m-3 in aluminum it is 2.1\times1029 m-3. what is the drift speed...

A copper wire is carrying a current of 1 mA. How many electrons pass a point in the wire in one minute? If the radius of the wire is 1 mm, calculate the magnitude of the current density. Given that the number of conduction electrons in copper is 8.47 × 10^28 m-3, what is the drift speed of the...

Homework Statement Current density is given in cylindrical coordinates as \vec{J} = -10^6z^{1.5} \hat{z} Am^{-2} \ \mbox{in the region} \ 0 \leq r \leq 20\mu m , \mbox{and for} \ r \geq 20 \mu m, \ \vec{J} = 0 If the volume charge density at z=0.15 m is -2000C/m^3, find the charge velocity...

K sorry for the bad drawing using paint...but anyways...so the question is :A long wire is in a conducting sheath and viewed from the top.The wire and the conducting sheath each carry opposite currents I into and out of the page with current density as J.The outer sheath has a radius of 2R and...

I read some derivations of current density from the quantum equations of motion (like Scrödinger's and Klein-Gordon's). They derive an equation with the same form as continuity equation: div(A)+dB/dt=0 Then they conclude that A=current density and B=density. However there are non-zero...

A long, straight conducting wire of radius R has a nonuniform current density J=J_{}0*r/R , where J_{}0 is a constant. The wire carries total current I .Find an expression for J_{}0 in terms of I and R .

a) The current density across a cylindrical conductor of radius R varies according tot he equation j = jo(1-r/R) where r is the distance from the axis. Thus the current density is a maximum jo at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current in terms...

Homework Statement This isn't quite a question per se. But in my review I am supposed to know how to derive a condition \psi (\infty,t) = \psi^*(-\infty,t) = 0 In addition I'm supposed to show that -\frac{d}{dt} \int_{V\infty} \rho(r,t) dV = \oint_{S\infty} J(r,t)\cdot dS' =0 where...

Hi folks! Can someone tell me how to solve the following... I'd really appreciate it. Homework Statement Show that the below two expressions for probability current density are equivalent. j(r,t) = h'/2im(\Psi^{*}\Delta\Psi- (\Delta\Psi^{*})\Psi] j(r,t) = real part of [\Psi^{*}...

We have an infinitely long solenoid of radius R along the z-axis. The solenoid is electrically neutral. The surface current density K is dependent in time, K(t)=Kocos(wt) Find the magnetic field B(s,t) produced for s<R (inside solenoid), s>R (outside solenoid), and the associated electric...

Near Earth, the density of protons in the solar wind (a stream of particles from the Sun) is 8.90 cm-3 and their speed is about 490 km/s. (a) Find the current density of these protons.(b) If Earth's magnetic field did not deflect the protons, what total current would Earth receive?For part a I...

Near Earth, the density of protons in the solar wind (a stream of particles from the Sun) is 8.90 cm-3 and their speed is about 490 km/s. a. Find the current density of these protons. b. If Earth's magnetic field did not deflect the protons, what total current would Earth receive?

You need to design a 0.9 A fuse that "blows" if the current exceeds 0.9 A. The fuse material in your stockroom melts at a current density of 540 A/cm2. What diameter wire of this material will do the job? 540x10^-2=5.40 A/m^2 5.40= .9/x Solving for x gives the answer: .166666666666667...

Hi this is the first time I've posted something don't know how long it usually take for replies but any help would be muchly apprecitated. This question asks: A long solid cylinder, radius R, carries uniform charge density p. the cylinder is rotating around the cetral axis with constant...

http://higgs.phys.washington.edu/phy121b/HW/light%20speed%20changes.pdf Above is what I need to do. So essentially, I have to show that in the new reference frame, that the new magnetic force will counter the old electric force. So then I have to use the equation of attraction due to a wire...

Can someone explain to me what the magnetization current density (given by the curl of the magnetization M) and surface magnetization current density (given by the vector product between M and a surface normal vector) are? I have a book on electromagnetism but it doesn't really give a good...

This one is from Griffiths' book on ED. For a configuration of charges and currents confined within a volume V, show that, \int_V \vec J d\tau = \frac{d\vec p}{dt} where \vec p is the total dipole moment. Well, I tried it! \frac{d\vec p}{dt} = \frac{d}{dt}\int_V \rho \vec r d\tau...

Question: Vector field and (n-1)-form representation of current density Electric current density can be represented by both a vector field and by a 2-form. Integrating them on a given surface must lead the same result. My question is, what is the relation between this vector field and the...

I know this is a retarted question, I should probably know this, but to the question. Say I have a wire of length L with a small diamter d. It has a current density J. Now say we have another wire of the same length that is hollow. They are both made of the same material. Is the current density...

The current density inside a long, solid, cylindrical wire of radius a = 10 cm is in the direction of the axis and varies linearly with the radial distance r cm from the axis according to J = J0 r / a with J0 =0.5 A/cm2 . Find the magnetic field in μT at r = 0.045 m Ok I know from amperes law...

K, the "idealized surface current density" Hey, I don't quite understand that guy, K. I have an exam on Sunday in E&M, I'm studying from Jackson. I haven't found any definition of 'K'. If anyone could give me a rigurous definition and an integral form, if there's any, I'd appreciate it...

Jackson("Classical Electrodynamics", Ch.6) uses the theorem of curl of curl to separate current density into transverse and parallel, \vec J = \vec{J_p}+\vec{J_t} to say, \begin{align*}\vec{J}(\vec{x}) &= \int\vec{J}(\vec{x'})\delta(\vec{x}-\vec{x'})d^{3}x'\\ &=...

Could anyone help me solve the following problem? Calculate the ratio of the conduction current density to the displacement current density of the electric field E = E_0 \cos(\omega t) in copper, to a frequence of f = 1 kHz. (Given: \epsilon_{Cu} = \epsilon_0, \rho_{Cu} = 2 \times 10^{-8}...

The electron drift speed in a gold wire is 3.0 * 10^-4. 1. What is the current density in the wire? 2. What is the current if the wire diameter is 0.50 mm? I am unsure of which equation to use. Q = I delta t ?? Can someone help me out?

Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (K+) channel carries a current of 1.8 pA. How many potassium ions pass through if the ion channel opens for 1.0 ms? What is the current density in the ion channel? I am completely lost for this one...

The electron drift speed in a gold wire is 3.0 * 10^-4. 1. What is the current density in the wire? 2. What is the current if the wire diameter is 0.50 mm? I am unsure of which equation to use. Q = I delta t ?? Can someone help me out?

Given a cylinder of length L, radius a and conductivity sigma, how does one find the induced currenty density (J) as a function of p when a magnetic field B is applied? Where p is the distance from the axis of the cylinder and B is applied along the axis of the cylinder, B = Bosin(wt)...

Ok, I am need of some serious help here. ,I don't want an answer just some guidance. In the attachment you'll see a diagram of a step potential. The particle is traveling from the left. There is nothing incident from the right. We need to find the probability current density in region 2 in...

Hi everybody, I study solid-state electronics, more precisely electron Fowler-Nordheim tunneling across the gate oxide of a Silicon-Oxide-Silicon capacitor. I need help on the physics of electron tunneling across a triangular barrier. It will be part of my PhD dissertation. I have been...

Let E=Eo (err...free space, not sure how to represent the symbols) V=90z^(4/3) in the region z=0(Potential) a) Find expressions for E,D and pv (volume charge density) as functions of z My work: E=-div V=0+0)120z^(1/3)az=120z^(1/3)az V/m D=Eo E=1.062z^(1/3)az nC/m^2 pv=div D=.354/z^(2/3)...

Bonjour, Relativistic current density components are the vector "J" with the scalar "j*c*rho". My questions are: Since it's a scalar and not a vector, what is the meaning of "c" times "rho"? Merci