Dear All,
I'm confused after reading of some chapter in a book, in which equations related to TEM mode have been derived. I want to prove mathematically, that Electric and Magnetic fields are ortogonal to each other. Thus, I use well known Maxwell equation:
$$\nabla \times \overrightarrow{E} +...
In my latest 10th grade physics lesson, we were learning about the refraction of light. I decided to share what I knew about why light slows down in a vacuum, which is, in short, because the electric field of the electromagnetic wave exerts a force on the charged electrons of a medium, which in...
Above is an example figure.
2. When a ring in a changing magnetic field is not complete (i.e. open circuit with a small gap), how to analyze the emf of the ring?
According to the general form of Faraday's law, ## \oint \vec{E} \cdot d \vec{s} = -\frac{d \Phi}{dt} ##, I deduce that although it...
Hi.
In order to explain the motion of an (accelerating) electromotor, we need the Lorentz force which itself is not one of Maxwell's equations.
Conversely, if we use the same electromotor inversely to generate electricity, Faraday's law (which is a Maxwell's equation) and the resistance of the...
I was wondering if the [Feynman-Heaviside formula](http://www.feynmanlectures.caltech.edu/II_21.html) for the electric field of a moving charge could be used to write down the force/reaction force between charges ##q_1## and ##q_2## in a Machian purely relational way.
The retarded electric...
Hi,
I just finished studying Maxwell's equations. Based on my understanding, when you solve maxwell's equation, you get the wave equation and it simplies to
in a charge and current-free region.
I understand that these two equations are similar to an equation of a wave in space. What I am...
Homework Statement
Are longitudinal magnetic waves possible? Give reasons for your answer.
Homework Equations
Working with Maxwell's equations, Lorentz force, electrostatic and electromagnetic waves in plasma.
The Attempt at a Solution
No idea whatsoever. I believe it is possible based on...
Homework Statement
For a medium of conductivity ##\sigma##:
$$ \nabla^2 \vec{B} = \sigma \mu \mu_0 \frac{\partial \vec{B}}{\partial t} + \mu \mu_0 \epsilon \epsilon_0 \frac{\partial^2 \vec{B}}{\partial^2 t} $$
A long solenoid with ##r=b## has n turns per unit length of superconducting wire anc...
I started studying the book "A Student's Guide to Maxwell's Equations" by Daniel Fleisch some time back. It is an excellent book, giving a very good idea about the main laws of electromagnetism.
I will soon finish the book. Now I need some book(s) which has problems on all the laws in classical...
Homework Statement
A current I flows along a wire toward a point charge, causing the charge to increase with time. Consider a spherical surface S centred at the charge, with a tiny hole where the wire is – see figure below. The circumference C of this hole is the boundary of the surface S...
I'm having trouble figuring out how to solve Maxwell's equations for the electric field of an AC wire.
I assume the Voltage waveform in the wire is 120sin(60t). This circuit only has a 14ohm heater in it, according to Ohm's law I=V/R. The current is equation to I(t)=120sin(60t)/14
It is...
My professor told that poission equation has a unique solution even for mixed boundary conditions( i.e. Dirichlet bc for some part and Neumann for the remaining part). But how is this possible? As different boundary conditions for the same problem will give different solutions.
Homework Statement
A static charge distribution has a radial electric field of magnitude
##E = \alpha \frac{e^{-\lambda r}}{r} ##
where λ and α are positive constants. Calculate the total charge of the distribution.
Homework Equations
Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot d\vec{S}##...
The 4-Squares-Identity of Leonhard Euler
(https://en.wikipedia.org/wiki/Euler%27s_four-square_identity) :
has the numeric structure of Maxwell’s equations in 4-space:
Is somebody aware of litterature about this?
Why does an increased electrical permittivity reduce the phase velocity of light in a medium? Furthermore, what interactions do we see on an atomic level?
I am aware of the equation that defines the speed of light in terms of the electrical permittivity and magnetic permeability, but I do not...
Consider a waveguide with axis parallel to axis ##z##. Using cartesian coordinates the fields inside the waveguide can be written as
Where ##\alpha## is the wavenumber and ##k=\frac{\omega}{c}## .
The maxwell equations ##\nabla \times E=-\frac{\partial B}{\partial t}## and ##\nabla \times...
My professor said that the first two maxwell equation's are about static fields
Another fast question:
Do a single charge that is moVing generate a magnetic field?
I saw a demonstration that explains the magnetic field as an electric field using only special relativity, there is a free charge...
Homework Statement
A thin and straight metallic rod of length L is rotating about its middle point with angular velocity ##\omega## in a uniform magnetic field B. The axis of rotation is perpendicular to the length of the rod and parallel to the magnetic field. The strength of the induced...
As I understand it, the classical source-free electric, ##\mathbf{E}## and magnetic, ##\mathbf{B}## wave equations are solved by solutions for the electric and magnetic fields of the following form: $$\mathbf{E}=\mathbf{E}_{0}e^{i (\mathbf{k}\cdot\mathbf{x}-\omega t)}$$...
I am studying to about maxwell's equations on the electric and magnetic field.
First of all, just do the example and exercise: https://www.princeton.edu/ssp/josep...ide-to-maxwells-equations-D.-FleischLEISC.pdf [Broken]
I have this dipole antenna...
Howdy,
So, I'm curious, is there a general relationship between current input into an electromagnetic and the magnetic field that it generates in space? The trivial example is wrapping a wire around a rod, then sending a current through it which causes a magnetic field.
My set up is a simple...
For example, if I have a magnetic field perpendicular to some surface and I change this magnetic field with constant speed, how do I calculate the Electric field at any point on this surface, since ∫E⋅ds=k, where k is some constant, could be done with many different vector fields.
Hello.
I would like to ask one simple question. Do we need to distinguish E-field (Electric field) in Gauss's law from those in Maxwell-Faraday equation and Ampere's circuit law? I firstly thought that E-field in Gauss's law is only for electrostatics so I need to distinguish it from E-field in...
I've always heard that maxwell's equations contains essentially all of eletromagnetic theory. However, there's one thing I'm having trouble doing for myself: deriving the magnestatics equations from the maxwell's equations. Of course: it's clear that if you put ∂[t]E=∂[t]B=0 (partial derivative...
I need some help in defining what are the assumptions needed to derive a constant speed of light from Maxwell equations.
Is it correct to say that this result applies to a sinusoidal wave as an assumption? In my understanding that is (more or less) equivalent to planar waves in vacuum: is it...
Homework Statement
Initially there is a spherical charge distribution of with a radius ##R_0## and uniform charge density ##ρ_0##. Suppose the distribution expands spherically symmetrically such that its radius at time t is ##R_0 + V t##, where V is the velocity. Assuming the density remain...
Homework Statement
When the capacitor driven by DC voltage ##V_0##,it has the electric field distribution ##f(x,y,z)##
When ##V=V_0e^{iwt}##,how to show the EM travel in the space forever like the light?
Homework Equations
##-{\nabla}^2E-u{\epsilon}\frac{{\partial}^2{E}}{{\partial}t^2}=0...
Hey everyone
Just a picture of my configuration.
The assumption here is $$\epsilon_a,\epsilon_b,\epsilon_c$$ are different from one another. Really the interest of this problem is to find the scalar potential $$\phi$$, such that $$\nabla^2 \phi = 0$$.
So now my question, about jump...