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0

Your mistake is to assume that higher current means higher velocity. The current speed is always the same for a given material. You can use the Hall effect to measure it and it is of order cm/s.


3

Maxwell's equations in vacuum are symmetric bar the problem with units that you have identified. In SI units $$ \nabla \cdot {\bf E} = 0\ \ \ \ \ \ \nabla \cdot {\bf B} =0$$ $$ \nabla \times {\bf E} = -\frac{\partial {\bf B}}{\partial t}\ \ \ \ \ \ \nabla \times {\bf B} = \mu_0 \epsilon_0 \frac{\partial {\bf E}}{\partial t}$$ If we let $\mu_0=1$, ...


1

In Gaussian units, we set $\epsilon_0 = \frac1{4\pi}$ (and so $\mu_0 = \frac{4\pi}{c^2}$) and change the units of $B$ so both electric and magnetic fields have the same dimension. In these units, Maxwell's equations are as follows: $$\begin{align} \nabla \cdot \mathbf{E} &= 4\pi \rho \\ \nabla \times \mathbf{E} &= - \frac1{c} \frac{\partial ...


7

In fact the light is not split up like in a rainbow or a prism. The colours appear due to thin film interefence - see e.g. http://en.wikipedia.org/wiki/Thin-film_interference The thickness of the petrol or oil is similar to the wavelength of visible light, which is about 380 to 750 nm or 0.38 to 0.75 $\mu$m (- or about 500 atoms think). Different colours ...


2

Yes, the frog will be repelled from the field if the field is non-uniform. Its magnetic moment is given through the susceptibility of Water $\vec \mu = V \chi \vec H$ and $\chi_\mathrm{water}\approx -9\times 10^{-6}$ Lets say the average field over the Frog is $\mu_0 H = 10\;\mathrm{T}$. This results in an induced moment of $\mu = -0.3 \mathrm{Am}^2 $ ...


-1

Do not open the cone. Think of it in the profile view : You have an isosceles triangle. Now move along the axis of the cone, say a distance $x$ and take an element $\mathrm{d}x$. Somewhat like this : This small element is similar to the rectangle you described. With length as $2\pi r(x)$ and width $\mathrm{d}x$. You also know the velocity with which the ...


0

Let me explain the nearfield phase shift of π/2 by how an antenna work. The antenna is an open electrical "circuit" where a electrical generator push and pull electrons inside the antenna rod. And the antenna rod one can imagine as a capacitor with its electrical field. How the electrical and the magnetic fields are produced, see here. During each half ...


5

You speak of fading over seconds. This is not likely to be a result of filament glow in a mains voltage domestic light as they cool very fast. There is unlikely to a sodium vapour lamp in your bathroom either. Most LED lights will turn on and off pretty fast as storage capacitors are expensive to waste. Possibly a thick filament (low voltage) halogen ...


0

Lenz's law tells you that the coil will act to try to keep the magnetic flux constant. You're removing a magnet bar with the north pole on the right, so the coil will try to produce a magnetic field to cancel that removal by making a $B$ as if the bar were sitting inside the coil. As you correctly predicted, this means the end of the coil near the bar is ...


2

If photons transmit the electromagnetic force, which is observable: the photon or the electron? Do we ever directly measure a photon, or do we only measure it's effect on electrons. For example suppose I shine a laser at a wall Let us clear up that photons ( and also electrons) are quantum mechanical elementary particles, and classical electromagnetic ...


0

Fields were first invented as a tool for "book-keeping" or keeping track of how a configuration of charges would effect a charge at a distant point, but it was soon realized that the field itself is much more "real" than simply a convenient mathematical tool. The first reason we treat the field as a separate real thing is the theoretical fact that you don't ...


0

I'm going to vote to close, for lack of a clear question statement. For the record: The first expression looks like a scrambled version of the solution via Green's function for the vector potential in the Coulomb gauge. (Among other things, there's a missing $e^{-i \omega t}$, and $\beta=\omega/c$ should not be allowed to escape the integral.) The ...


0

Both Photon and electron are real. Electron has rest mass while photon is a form of energy which gains some mass when it travels at speed of light. "For example suppose I move some electrons around in my laser, these electrons move the electrons around on the wall, and then these electrons move around some electrons in my eyes, so I see a red spot on the ...


1

Possibly you are talking about the difference between the "far field" and "near field" solutions for the simple oscillating electric dipole. Often when dealing with such a system, if we are looking at the field more than a few wavelengths away from the dipole (or more formally, $kr \gg 1$ or $r \gg \lambda/2\pi$) then the solution looks like a spherically ...


0

Using a 4" square piece of steel we had the machinist turn a flat cone 4" at the base and 1" at the top. When attached to the end of a salvaged electromagnet previously used for separating junk scrap iron, we were able to attain (IIRC- this was thirty years ago) a four-fold increase in density to about 80 kG/in². And yes, a good time was had by all.


0

Think about it: They come into contact with it consecutively - the first contact leads to them equalizing, so you will have the charge on the initial sphere as $Q' = Q_1$ with $Q' + Q_1 = Q$. Then, the second sphere contacts the inital sphere, and now it equalizes with $Q'$, leading to $Q'' = Q_2$ with $Q'' + Q_2 = Q'$. Since $Q$ is known, this is a system ...


1

AC can be made from DC, and vice versa. DC is a steady voltage, with AC the voltage fluctuates from negative to positive and back, many times per second. Most electricity generators generate AC. The reason for preferring AC is that, historically, it is easier change voltage with AC: all you need is a transformer. The generators generate a high voltage, ...


1

imakesmalltalk's answer is a good description of how the fields superpose in a solenoid to produce a final field similar to a bar magnet, but I want to discuss one or two subtle differences. The final picture in imakesmalltalk's answer is clearly showing lines of H-field (which are often referred to as magnetic field), because they appear to begin and end ...


0

Opposite. Solenoid is actually like real magnet bar Imagine one iron atom. It has electrons run in circle around that atom so it generate magnetic force. Every iron atom is like a solenoid loop by itself Then Imagine a bar magnet is clump of iron which almost all atoms align in the same direction so every atom contribute a magnetic force. That's it much ...


2

By applying Fleming's Right Hand in each turn, we get magnetic field lines that look like this :- .. .. .. But Magnetic field lines never intersect. They interact with the fieds of the surrounding turns of solenoid to form a combined magnetic field which looks like this:- .. .. .. From www.nde-ed.org :- The magnetic field circling each loop of wire ...


1

First at all the magnetic lines 'connect' the two poles. There is no flow of energy or material nor preferred direction of these lines. In this sense the north and the south pole are equal. Then, the magnet field lines are not connecting only the ends of a magnet bar (see this picture). Internally exist small dipols, which are orientated more or less. This ...


4

Magnetic field lines do not go anywhere. Field lines are useful for visualizing vector fields. These are not physical that are actually present at certain locations. And the direction you are talking about is a convention. By convention, the field lines are taken to direct away from the N-pole and towards S-pole. Internally, these field lines complete a loop ...


0

You're using Lorentz force in Gaussian Units. The constant $c$ is the speed of light in vacuum.


3

You said that the lamp gave off a yellow glow, so it is possible that it could be a sodium lamp. However, your conception about light intensity and wavelength is a bit off. If the lamp that you are speaking of gives off a monochromatic light source, it is most likely using an electrical current to excite the atoms of a single element. When excited, ...


1

Radio frequency Paul traps confine charged particles without applying any magnetic fields (As in Penning traps), but since confining charged particles only using electrostatic forces is impossible according the the Earnshaw's theorem, a quasi-static approach is taken, and the particles are trapped dynamically. Radio frequency ion traps do this by forming a ...


1

Is a "wire plate" different from a wire loop in some way? If you envision a circular wire loop of area $A$ spinning with a diameter of the loop along the $\hat{z}$ direction as the axis of rotation, with a constant magnetic field $\vec{B}$ in the $\hat{y}$ direction, and we take the normal vector to the loop of wire $\vec{n}$, where $\vec{n} = cos(\omega ...


0

It requires 2 of Maxwell's laws: the Maxwell-Faraday equation, $$ \frac{\partial\mathbf B}{\partial t}=-\nabla\times\mathbf E $$ the divergence condition $$ \nabla\cdot\mathbf B=0 $$ Then it requires 2 vector calculus identities: divergence of the curl is identically zero $$\nabla\cdot\nabla\times\mathbf A=0$$ curl of the gradient is identically zero ...


1

If you integrate acceleration w.r.t. time, you'll get the change in velocity. If you add the initial velocity to that and integrate again, you'll find the change in position. what they mean by calculate the "path" is find the function that describes its position w.r.t. time.


2

Yes. The class of materials with magnetic particles suspended in a liquid are generally known as ferrofluids and have wipe application. Buy some off eBay, get a magnet and have some fun.


2

Typically electrical measurements rely on skin contact electrodes and do not directly provide detailed information on the electrical characteristics of the heart. On the other hand, magnetic fields go through the skin and provide a direct "view" of the heart and its movement. Electrical pickups are easy. Low field magnetic sensors are difficult to implement ...


1

The right hand rule is used to find the direction of magnetic induction based on the source currents. This direction is purely conventional : the magnetic flux density does not have a physical direction by itself, you have to choose one (by the right hand rule, or by choosing a vectorial product). The direction of induced EMF is physical. The induced ...


1

If by ECG you mean electrocardiogram, then no. You just need very sensitive amplifiers optimized for small signals with plenty of filtering to get rid of unwanted signals. This is a good description of how to build one and the problems involved.


2

Googling "Why are neodymium magnets so strong" led me to the following explanation: Neodymium may the rare earth metal neodymium magnets are named for, but the magnets themselves are actually an alloy of iron, boron and neodymium. The magnet's chemical composition is typically Nd2Fe14B, a composition that forms a tetragonal crystal structure. This ...


0

let me restate the question: What holds electron together and how? That depends on theory (view) of the electron. In the beginning of 20th century, people thought electron was a small marble packed with charged particles. These would repel each other with tremendous force so some balancing forces are needed in this model. This view was always quite ...


0

The currents responsible for the Meissner effect (the cancellation of magnetic field inside the superconductor) are only surface currents, and the cancellation of magnetic fields doesn't happen on the surface, although it decays exponentially as you move deeper inside according to the equation for the London penetration depth. See for example this page which ...


5

First let me make it clear I don't on a Hendo engine and I've never seen the design for one, so what follows is based on what I've found by Googling and what seems intuitively obvious. The Hendo engine uses a technique called electrodynamic suspension. This can get very complicated very quickly when you try to do the calculations, so I'll just describe it ...


7

As explained on this page, Earnshaw's theorem says it's impossible to have perfectly stable magnetic levitation where none of the fields are changing with time. But as is also discussed there, it is possible to have levitation that appears stable to the naked eye if the the currents that create the magnetic field continually adjust to small movements of the ...


3

There is no notion of quantization of charge in classical electrodynamics. Charge is a continuous, infinitely divisible quantity there, and there's nothing at all that would indicate what carries the charge. The electron (or any other particle, for that matter) is not predicted by classical electrodynamics, and thus none of the classical notions of ...


0

For grains of sand, each grain is made of atoms, and the number of atoms in each grain can be different. There is no evidence that electrons are composed of plural particles.


1

The short answer is no, the diameter of the wire doesn't affect the bandwidth. Bandwidth can be a tricky subject. If you are talking about injecting a very high frequency sine wave at one of the wire, and seeing if it is detectable at the other end, then wires of all diameters have a surprisingly high bandwidth. But if you are talking about the ability of ...


1

The current is not directly due to the magnetic field, rather it is due to the electric field that is induced by the changing magnetic field. It is true that the electrons will experience a force from the magnetic field according to the Lorentz Force Law, but this force will always be perpendicular to the direction of motion and therefore will not produce a ...


-1

Bandwidth is a function of the frequency of the signal carrier. As the diameter of the copper increases you start to lose "conductivity" because of skin effect as the current tends to be carried in thin surface areas as the frequency increases. This does not directly impact bandwidth but it does hinder its application and forces the use of thin wires for ...


0

Fulvio Melia's Electrodynamics. My graduate course on E&M used this text as a basis for the lectures (subsequently changed to the aforementioned Jackson). This book is very short (246 pages as compared to say Griffiths at 624 pages!), but covers all the relevant topics of E&M (Electrostatics, Magnetostatics, etc) before smoothly transitioning into ...


1

Actually it was that maxwellian electromagnetism had no problems, in contrast to the newtonian classical mechanics framework. Theory of Relativity alters the Newtonian framework not the Maxwellian framework. i would say that even if Einstein hadn't invented SR, someone else would (as indeed many others notably Poincare, Lorentz et al) were alredy on the ...


0

Yes, you can certainly differentiate the Hamiltonian with respect to the momentum (or more generally with respect to anything in the Hamiltonian). For Dirac Hamiltonian (assuming $c=1$): $$H=p_i \alpha^i + m \beta,$$ we simply have $$v_i\equiv\partial_{p_i} H=\alpha^i,$$ which is the velocity (current) operator of the fermion. In quantum field theory, $v_i$ ...


3

W. K. H. Panofsky and M. Phillips, Classical electricity and magnetism, Addison Wesley, 2nd ed., 1962 Especially the first 14 chapters are very enjoyable yet carefully written study text about both basic and more advanced topics in macroscopic EM theory (including discussion of EM energy from more experimental angle than is usual and of density of force ...


4

Besides Purcell I really like Feynman Vol. II. I finally could understand magnetic materials and electromagnets. (Warning, Feynman uses his own notation for B,H and M.) The lectures are available online and for free, as the New Millenium Edition, at http://www.feynmanlectures.caltech.edu/, in a nice re-mastered edition with re-drawn ...


8

Purcell is a good non-Griffiths option. I would judge the completeness of the material between Griffiths and Jackson, but with an intuitive level of understanding close to Griffiths. I used it to study for graduate qual exams when Jackson was making me feel particularly obtuse. Some positives: Touches more ideas than Griffiths Uses some real-world ...


12

D.J. Griffith's Introduction to Electrodynamics must be mentioned. To my knowledge this text is ubiquitous in junior-level E&M courses. The writing is extremely friendly and is excellent for self-study. The author frequently tells you what he is doing and provides motivation, unlike the ubiquitous graduate-level text by Jackson. Equations often use a ...


2

Jackson's classical electrodynamics is very complete, and often seen as the reference on CED. But I also like Rohrlich's classical charged particles that, as the title suggests, puts more emphasis on the subject of particles interacting with EM fields.



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