Maxwells equations Definition and 29 Threads

Geometric algebra (a subset of Clifford algebra) can be consistently used for all branches of physics, that are based on Euclidean space+time or Minkowski spacetime. It uses the following concepts for Minkowski spacetime: Geometric product (Dot product + Wedge product) Multivectors ( = scalar +...

> Note: I am using SageMath to do the manipulations, I will attach it with the post I modeled the problem as a cylinder of height ##\Delta z## and anisotropic conductivity: the conductivity along the axis is different from the one along the radius. Using ##J = \sigma E##, where ##\sigma## is a...

On examining Maxwell's third equation which is about time varying magnetic fields (Faraday's electromagnetic induction) we find that time varying magnetic fields produce loops of electric fields in space irrespective of whether a coil is present or not, if any coil is present then these loops of...

Homework Statement I have a material placed between parallel plates depleted of free electrons and contain negative ions. What would happen to the charge stored across the plates? Would it still be similar to placing a capacitor with a di-electric constant between them? Homework Equations Q=CV...

Homework Statement Determine the B-field inside the middle of a circular loop of current. Homework Equations Attempt at using Ampere's law: ##\oint \vec{B} \cdot d \vec{l} = \mu_0 i## The Attempt at a Solution ##\oint B \cdot R d \theta = \mu_0 i \Rightarrow BR(2 \pi) = \mu_0 i \Rightarrow B...

Homework Statement The circuit in Fig. 32-31 consists of switch S, a 12.0 V ideal battery, a 20.0 M resistor, and an air-filled capacitor. The capacitor has parallel circular plates of radius 5.00 cm, separated by 3.00mm. At time t=0, switch S is closed to begin charging the capacitor. The...

Hey guys, Can you please refer some good books to refer to in studying relativistic Electrodynamics (introductory parts), covering the Maxwell's equations in tensor form the L-W potentials and other aspects. FYI am just a beginner in relativistic Electrodynamics. Thanks for the help.

I'm sure the inductor model, i.e. vL(t) = iL'(t)*L follows without directly from Faraday's eq. But even there, with Faraday's equation we think of the changing magnetic field as inducing the voltage in the loop, where in the model it seems the other way around, that is, the voltage increases...

Homework Statement Suppose we have a infinite cylinder of radius=R and with uniform volume charge density ρ. Use Maxwell's Equations or relationships from them to find E, B, V, and A everywhere. Pretty easy. But how do you approach the problem when you bring an angular vel into the mix...

When finding solutions to Maxwells equations we always cosider the case of a plane wave. But are plane waves real/physical solutions we can consider in real life? My guess is not because it is required to propagate infinitely. So why do we use plane waves to solve Maxwell's equations?

I came across this expression for the wave equation: \nabla^2E + \mu\sigma\frac{\partial{E}}{\partial{t}} - \frac{n^2}{c^2}\frac{\partial{E}}{\partial{t^2}} = 0 My question is what kind of medium is it for/where did it come from?

Zahid Iftikhar asked why charges get separated in a changing magnetic field over in the EE forum. I pointed him to Maxwell's equations and also pointed out we took them to be observational and axiomatic. Yet it occurred to me there might be an reason in quantum probability. So is there a...

I am getting really confused with the millions of different versions/forms of Maxwell's equations. I know there is differential form and integral form, but sometimes there is a B for magnetic field...other times there is an H. Sometimes there is dependence on \rho or J (current density) and...

My textbooks says in a region where there is no charge or current Maxwell's equations read divergence of E=0 Curl of E=-dB/dt all d are partial Divergence of B=0 Curl of B=ue(dE/dt) I get the math of showing that there are waves, but I don't get some of these conditions. 1st don't you...

1. Hey, I have to find Maxwells equations using the variational principle and the electromagnetic action: S=-\intop d^{4}x\frac{1}{4}F_{\mu\nu}F^{\mu\nu} by using \frac{\delta s}{\delta A_{\mu(x)}}=0 therefore \partial_{\mu}F^{\mu\nu}=0 3. I have had a go at the...

Are there any articles on solutions for simple self consistent systems in EM, as in when the field equations are coupled with the motion of the particles, I would like to explicitly see the energy conservation in those systems.

As i understand it, the Maxwell equations in potential form (in the Lorenz gauge) are basically 4 independent wave equations for the 3 components of A and the 1 component of Phi, with J and ρ acting as source terms: Now from the usual formulation of the Maxwell equations and from experience...

Hi, I've been trying to solve problem 2.1 a in Peskin and schroeder, an introduction to QFT. The problem is to derive Maxwells equations for free space, which I have almost managed to do, using the Euler- lagrange euqation And the definition of the field tensor as F_{μv} = d_μ A_v - d_v A_μ...

I just purchased a book on the introduction of special relativity and I seem to be stuck on a simple mathematical step. For some reason I just can't see this! This is what it says: Gotta love getting stuck on something when the book says its "Easy to see." Confidence -1.

Hi Maxwells Equations for a time-invariant system are separable, hence we can write a solution as E(r, t) = E(r)E(t). They also mention that if the system is radially invariant, then that implies that the solution splits into a product of radial and angular functions (with 2π periodic angular...

Hi In my book it says that if the dielectric function ε is time invariant, we can write a solution to Maxwells equations of the form E(r, t) = E(r)exp(jωt). I agree that the ME are separable, but I don't see how they know that the time-dependence is harmonic? What is so special about exp(jωt)...

Hi Are there other reasons why monochromatic solutions to Maxwells equations of the form E(z, t) = E(z)exp(-iωt) are good other than its plane wave solutions forming a complete set?Niles.

Homework Statement I am trying to solve prob 4.107 in Schaums' Vector analysis book. Show that solution to Maxwells equations - \DeltaxH=1/c dE/dt, \DeltaxE= -1/c dH/dt, \Delta.H=0, \Delta.E= 4pi\rho where \rho is a function of x,y,z and c is the velocity of light, assumed constant...

Homework Statement Show that the Fields E= Eo exp{i (k.r-ωt)} and B= Bo exp{i(k.r-ωt) are solutions of Maxwell's Equations in source free vaccum.Starting with maxwells equations in vaccum. And there by Derive the relations between the Magnitudes & Phases of Eo, Bo, ω, k...

Using the following identity curl(curl(B))=Grad(Div(B)-Grad^2(B) with maxwells equations in differential form in the absences of sources show that magnetic field obeys the wave equation Grad^2(B)- (1/(C^2))(d^2(B)/dt^2) [b]2. The main probelm is I'm not sure what form of B i should use, i...

Homework Statement Give a qualitative description of maxwell's equation s in non polarizable, non magnetizable media. Homework Equations \oint_{S} E \cdot dA = 4\pi\int_{V}\rho d\tau \oint_{S} B \cdot dA = 0 \oint_{P} E \cdot dl = -\frac{1}{c} \frac{d}{dt} \int_{S} B \cdot dA...

Hello. This is a first post for me. Do Maxwell's equations alone allow for propagating waves in charge/current (\phi,s[/B]J)? I was rather struck dumb by this question out of the blue. I've never seen it addressed, denyed or confirmed. Schematically the electric and magnetic fields are...

Well the question is in the title. Does Malus' Law (http://en.wikipedia.org/wiki/Malus%27s_law ) follow automatically from Maxwell's equations, or is it really an extra thing put in by hand? In particular I'm interested if there is a purely classical electromagnetic explanation (i.e. without...

A 40cmX30cm rectangular loop rotates at 130 r/s in a magnetic field of .06 in the direction normal to the axis of rotation. If the loop has 50 turns, determine the induced voltage in the loop. Heres what I did. I used B dot ds. I had my ds being the sides of the rectangle and coswt in the...