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14

Maxwell's equation can be given in the form $$\text dF = 0$$ $$\text d\star F + J = 0$$ where $F$ is a 2-form and $J$ an $n-1$-form (a current density) which in principle can be generalised to any manifold (for physical reasons one might want to consider pseudo-Riemannian manifolds with signature $(+,-,\cdots,-)$). In the four dimensional theory one usually ...


8

Yes a magnet can damage a compass. The compass needle is a ferromagnetic material. The degree to which a ferromagnetic material can "withstand an external magnetic field without becoming demagnetized" is referred to as its coercivity. Another magnet near the compass needle imposes a magnetic field upon the compass needle. It is a matter of the ...


7

You can generalize Maxwell's equations to an arbitrary number of dimensions by using either the tensor or differential form version, as the vector formalism does not help too much (For instance, in two dimensions, the magnetic field is a (pseudo) scalar field, not a vector field). The equations are then : $\partial_\alpha F^{\alpha\beta} = \mu_0 J^\beta$ ...


4

You are mixing up two different things. The refractive index is usually defined in terms of the velocity of light: $$ n = \frac{c}{v} $$ where $v$ is the velocity in the medium. However the velocity is related to the frequency and wavelength by: $$ v = \lambda f $$ so: $$ n = \frac{\lambda_0 f_0}{\lambda f} $$ The frequency of the light, $f$, doesn't ...


4

You usually cannot push your hand through the table, because it's a single solid. The atoms are held together by covalent bonds, which are electromagnetic in nature. Sand on the other hand is grainy - the $SiO_2$ grains do not interact with each other and are only held "in place" because of gravity. You can run your hand through sand similar to driving a ...


3

Classical you work the intensity of a wave out by integrating the energy arriving over a known area in the course of one cycle, and then divide by the period and the area. The form you exhibit is correct for harmonic waves in SI units if the $E$ is the maximum amplitude of the electric field. But for a general normally-incident plane-wave you are looking ...


2

Copper is a diamagnetic material. Individual copper atoms have one unpaired electron in the valence shell, and thus might be considered paramagnetic, but when many copper atoms are combined into the bulk metal, their valence electrons are sent into a cloud that forms metallic bonds among the copper atoms, and the metal is diamagnetic. All the answers given ...


2

If you drive an electromagnet with AC, part of the power will be dissipated in the form of eddy currents - both in the core of the magnet, and in the object you are trying to attract. These eddy currents dissipate power and generate magnetic fields that resist the flux change. If you use DC, there are no eddy currents and all the power is available to ...


2

Yes. The quantum-mechanical origin of the magnetization is largely irrelevant: all you need to know is the material's magnetization field $\mathbf M(\mathbf r)$, which is defined to be the (locally averaged) total magnetic dipole moment per unit volume at and near position $\mathbf r$. The magnetization then determines the magnet's magnetic field outside it ...


1

Attempting an answer: Eddy currents are induced where there is a change in the field. The way you have drawn the situation, there is no place where the field changes while the white rectangle moves: $\frac{dB}{dt}=0$ everywhere in the conductor. So while there is a current flowing around the loop, there is no eddy current induced (that I can see). The ...


1

The Faraday motor consists of a pool of mercury at the bottom of which a permanent magnet is affixed. A stiff straight wire is dropped into the pool of mercury above the permanent magnet. When electric current runs through the wire, a magnetic field is created around the wire. The magnetic field follows the right hand rule. It is circular and curls in ...


1

The Bohr model is not an accurate model, electrons do not move in circles with a statistical distribution of circles. Even if they did, just because two charges have the same velocity does not mean the other one sees the other as static. The force one charge $q_1$ feels do to another charge $q_2$ depends on the position and velocity right now of the charge ...


1

It seems like the key problem is that you are conducting your integration over the wrong surface. The problem is, you have an infinitely extending sheet of charge on the surface $\rho=1.2$. Based on this, as you seem to have done, we work in cylindrical coordinates and consider a plane of constant $z$. Taking your expression: and converting it into ...


1

Losses in ferromagnetic materials There are two mechanisms which produce losses in ferromagnetic materials. One of them is hysteresis, the other is eddy currents. Hysteresis Hysteresis losses occur while the magnetic dipoles rotate, meaning while you change the direction of magnetization. You can look at it through single dipoles or through Weiss domains. ...


1

What you are trying to do would "break the laws of physics" if it worked. You can't, so it doesn't. As the system rotates there will be losses. Air drag and friction and more. These losses absorb energy and cause things to slow down. For a system to rotate indefinitely it must get energy from somewhere. If there is no input energy it must make its own. A ...


1

what will happen to the speed when the load on the motor is fixed and the torque increases? You need to define what you mean by "load" very precisely here to make sense of this question. If by load you mean a constant torque $\tau_L$ opposing the motor's rotation, then if the motor's torque $\tau_M$ output increases we have a nett unbalanced torque on ...


1

A few hints: The field at the middle wire is "indeterminate" since there is a singularity due to the current in the middle wire. If you sketch the field as a function of $x$ you would get something like this: (this is the plot of $\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+1}$ courtesy of Wolfram Alpha) The zeros in the field are easily seen as occurring ...


1

(a) You're about right on the calculation for the two points on $(-a, 0)$ and $(0, a)$ but the $2a-s$ thing looks weird. Is $s = x + a$ or something? On $(0, a)$ it should be $1/x + 1/(x + a) + 1/(x - a) = 0$ or $$(x + a)(x - a) + x (x - a) + x (x + a) = 0$$ simplifying to $3 x^2 = a^2$ and giving $x = \pm a \sqrt{1/3}$, which appears to be what you got by ...


1

Only in a perfect diamagnetic. In a real conductor the induced magnetic field is limited by the resistance of the material, so it will always be smaller than the inducing field.


1

Clarification from another source: Source: Physics For Scientists And Engineers, Paul A. Tipler and Gene Mosca, Sixth Edition, W. H. Freeman and Company, New York, 2008, p. 971, Fig. 28-20. I maintain that the loop will act the same as the bar. In other words, if you cut a thin slit down the center of the bar and less than the length of the bar (you ...


1

Why is it that two carbon atoms fired at each other will bounce off and not stick together? It is because as the atoms move close together their orbital electrons begin to repel more than their nuclei attract each other's electrons. The result is greater potential energy as they approach and this leads to the tendency to move apart much like compressing a ...



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