Electromagnetism Physics Problems: Get Expert Help with Plainmath

How does an electromagnet work?

An isolated conducting Sphere of radius R has a charge Q. What is the total stored energy? What is the radius r within which half the stored energy is contained?

Why is it not possible to induce current from the Earth's magnetic field? I thought Maxwell said that electric fields and magnetic fields were the same thing.

Temporal distribution of a single photon pulse in an interferometer experiment in vacuum via the Gaussian function $\mathrm{\psi <!--\; \psi \; -->}$ :
$\mathrm{\psi <!--\; \psi \; -->}(t)=\frac{1}{(2\mathrm{\pi <!--\; \pi \; -->}{\mathrm{\sigma <!--\; \sigma \; -->}}^2{)}^{1/4}}{\text{e}}^{-<!--\; -\; -->\frac{t^2}{4{\mathrm{\sigma <!--\; \sigma \; -->}}^2}}{\text{e}}^{\text{i}{\mathrm{\omega <!--\; \omega \; -->}}_{0}t}.$
It is normalised
$\int <!--\; \int \; -->|\mathrm{\psi <!--\; \psi \; -->}(t){|}^2\text{d}t=1,$
and the fourier transform is the wave function in the frequency domain,
$\stackrel{~<!--\; ~\; -->}{\mathrm{\psi <!--\; \psi \; -->}}(\mathrm{\omega <!--\; \omega \; -->})=\frac{1}{\sqrt{2\mathrm{\pi <!--\; \pi \; -->}}}\int <!--\; \int \; -->\mathrm{\psi <!--\; \psi \; -->}(t){\text{e}}^{-<!--\; -\; -->\text{i}\mathrm{\omega <!--\; \omega \; -->}t}\text{d}t=(\frac{2{\mathrm{\sigma <!--\; \sigma \; -->}}^2}{\mathrm{\pi <!--\; \pi \; -->}}{)}^{\frac{1}{4}}{\text{e}}^{-<!--\; -\; -->{\mathrm{\sigma <!--\; \sigma \; -->}}^2(\mathrm{\omega <!--\; \omega \; -->}-<!--\; -\; -->{\mathrm{\omega <!--\; \omega \; -->}}_0{)}^2},$
such that $|\stackrel{~<!--\; ~\; -->}{\mathrm{\psi <!--\; \psi \; -->}}(\mathrm{\omega <!--\; \omega \; -->}){|}^2$ represents the frequency distribution of the photon.
However, since a single photon pulse is still a electromagnetic pulse, is there any link between $\mathrm{\psi <!--\; \psi \; -->}(t)$ and the electric field $E(t)$ of this pulse? Like that
$E(t)\sim <!--\; \sim \; -->\text{Re}[\mathrm{\psi <!--\; \psi \; -->}(t)]\sim <!--\; \sim \; -->{\text{e}}^{-<!--\; -\; -->\frac{t^2}{4{\mathrm{\sigma <!--\; \sigma \; -->}}^2}}\cos <!--\; \; -->({\mathrm{\omega <!--\; \omega \; -->}}_{0}t)?$

Light can be slowed down to a walking pace and even stopped in a medium of hot rubidium vapour. If an electromagnet was placed in this medium and turned on would the popagation of the magnetic field be slowed down or stopped?

If we have a solenoid electromagnet with an iron core, the magnetic field produced is proportional to the permeability of the iron and the current through the coil. As we increase the current through the coil and the magnetic field increases in strength, wouldn't the permeability of the iron also increase? But this would only happen until the iron core saturates and its permeability reaches a maximum. Is there any way to calculate beforehand at what current the permeability would reach its maximum?

Hypothetically, if I were to move at the speed of light, would I see an oscillating electromagnetic wave or photons oscillating or what?

How can magnetic force be reduced?

You have a bar magnet whose poles are not marked. How can you find which pole is north and which is south by using only a piece of string?

a) Faradays formulate two basic laws of electromagnetic induction based on Faradays experiments.
Explain Faradays experiment and at the end depending on the experiment, state Faradays laws.
b) Explain how one can increase the emf induced in the coil by change in magnetic field.
c) State Lenz law.

I want to derive Gauss's law for magnetism,
$\mathrm{\nabla <!--\; \nabla \; -->}\cdot <!--\; \cdot \; -->\stackrel{\to <!--\; \to \; -->}{B}=0.$
The derivation in Griffiths Introduction to elecrodynamics uses
$\mathrm{\nabla <!--\; \nabla \; -->}\cdot <!--\; \cdot \; -->\stackrel{\to <!--\; \to \; -->}{B}=\frac{{\mathrm{\mu <!--\; \mu \; -->}}_0}{4\mathrm{\pi <!--\; \pi \; -->}}\int <!--\; \int \; -->\mathrm{\nabla <!--\; \nabla \; -->}\cdot <!--\; \cdot \; -->(\stackrel{\to <!--\; \to \; -->}{J}\times <!--\; \times \; -->\frac{\stackrel{\to <!--\; \to \; -->}{r}}{r^3}),$
but to use this, I would need $\stackrel{\to <!--\; \to \; -->}{J}\times <!--\; \times \; -->\frac{\stackrel{\to <!--\; \to \; -->}{r}}{r^3}$ and $\mathrm{\nabla <!--\; \nabla \; -->}\cdot <!--\; \cdot \; -->(\stackrel{\to <!--\; \to \; -->}{J}\times <!--\; \times \; -->\frac{\stackrel{\to <!--\; \to \; -->}{r}}{r^3})$ to be continuous.
Since $\stackrel{\to <!--\; \to \; -->}{J}=\mathrm{\rho <!--\; \rho \; -->}\stackrel{\to <!--\; \to \; -->}{v}$ , then if $\mathrm{\rho <!--\; \rho \; -->}$ (charge density) has a continuous derivative, I'm done; but, I'm not sure why can I affirm this because clearly, I can construct charge distributions with jump discontinuities.

If electromagnetic fields and waves are the same, then doesn't that mean that you can induce current from waves? Therefore transferring electricity over long distances?

It is well established that the photon is the propagator for the electromagnetic force. How are the set of photons used in the H-field behaving differently than those in the E-field? Is it different when dealing with an electromagnet versus an intrinsic magnet? In what way do the photons need to be emitted by a bar magnet to result in a magnetic interaction? How about a charged object to interact with a charged object?

Magnetic force storage or amplification question
all forms of energy can be stored or amplified for example : capacitor , hydraulics ,laser , pulley , etc..
what is the equivalent to that for magnetic force ? can magnets be connected in series or parallel ?

New "gravity force" analogous to magnetic force?
I was watching Eugene Khutoryansky's physics video about Einstein's Gravito-Electromagnetism, Gravity of moving mass in General Relativity . In that, he discussed why maxwell's electromagnetism laws hold for special relativity also. He took the following situation:
Adam is in a spaceship or the reference frame of two charged particles such that their gravitational force cancels their electromagnetic repulsion. Adam would see no magnetic force since charges are at rest according to his frame. Now Sarah is watching Adam from a ground reference and sees the charges moving and hence they must exert an attractive magnetic force pushing particles towards each other. But now Eugene, said that a force (gravity) analogous to the magnetic force produced by moving charge, is produced by moving mass, which will be repulsive, and will balance the attractive magnetic force.
Now I became confused here, what is this "new gravity force"? I never heard about it before, at least in high school. Is it a mathematical trick or tweaking? Or is there really is a repulsive gravitational force that is exerted by moving masses? So this is my doubt here, can someone please explain this further?

Let's consider rotating charged ring. Theoretically mass of this ring has no limit as rotation speed increases. So what about magnetic moment of the ring? Is it limited by the value of speed of light?

If the magnitude of the magnetic induction is less than that in a vaccum within a solid, so, this material called
a) Ferrimagnetic
b) Ferromagnetic
c) Diamagnetic
d) Paramagnetic