Hot answers tagged

5

If you're thinking about stable orbiting systems the big difference between gravity and the magnetic force is that magnetic monopoles do not exist. The simplest source of a magnetic field is the magnetic dipole. By contrast gravitational monopoles exist but gravitational dipoles do not. The Sun and the Earth are both (approximately) gravitational monopoles, ...


4

Dynamo Effect : The dynamo effect is a geophysical theory that explains the origin of the Earth's main magnetic field in terms of a self-exciting (or self-sustaining) dynamo. In this dynamo mechanism, fluid motion in the Earth's outer core moves conducting material (liquid iron) across an already existing, weak magnetic field and generates an ...


4

Lorentz Transformations Suppose we call the lab frame the K-frame and a frame moving at velocity, $\mathbf{v}$, relative to the K-frame called the K'-frame. Then we can express the electromagnetic fields in the K'-frame in terms of the K-frame fields as: $$ \begin{align} \mathbf{E}' & = \gamma \left( \mathbf{E} + \boldsymbol{\beta} \times \mathbf{B} ...


3

The direction of a magnetic field is arbitrary. Some time ago it was noticed that magnetic materials aligned themselves in an geographic North to South line. The part of the magnetic material which point roughly towards the geographic North pole was called the north-seeking pole of the magnet which then became the the north pole of the magnet. Faraday ...


2

The observer moving with the CM will measure that the force of repulsion the electrons is given by $F=\frac{e^2}{4 \pi \epsilon_0 d^2}$ ($d$ is their separation), he can only make measurements in his reference frame (that is moving with speed $v$), and will not be able to be determine this speed.


2

The principle of relativity says that there is no experiment that can determine absolute motion. So all observers, regardless of relative motion, need to agree on the outcome of any experiment. Because to the relativity of observers' measuring devices, they may not numerically agree on the measurements. By applying the laws of relativity they will be able ...


2

A few comments before doing the calculation: In the CM frame, there is only an attractive force, while in the given frame, there is both an attractive and a repulsive force. This is no more mysterious than the fact that a vertical object in my frame can look tilted to somebody with rotated axes. Going from the CM frame to your frame mixes the electric ...


2

Let the magnetic field be in the $\hat z$ direction. If you calculate the expectation values of $S_x$ and $S_y$, you find that they have time dependence like $\cos(\omega t),\sin(\omega t)$ while the expectation value of $S_z$ is constant. Explicitly, the Hamiltonian is $H = -\omega \sigma_z$. Using the Heisenberg equation of motion, \begin{align} \dot ...


2

Magnetic fields are affected by all materials, but only very weakly unless the material is ferromagnetic (like iron and nickel and permanent magnetic materials) or a strong diamagnet (like a superconductor). We do understand the nature of magnetism very well, unfortunately, a real explanation requires quantum mechanics. There is no classical theory of ...


2

The answer to your question is, to a minute degree, is yes, since the total energy of something measures its source strength / coupling to gravity. So, if an system has energy $\Delta E$ added to it, it will weigh more - its gravitational mass will increase by $\Delta E/c^2$. Practically, the effect is almost unmeasurable; a magnet's stored magnetic energy ...


1

For $\partial_iB_i = 0$ $$ \partial_iB_i = \epsilon_{ijk}\partial_iF_{jk} = 0 $$ The Levi-Civita symbol permutes so that $\epsilon_{ijk} = \epsilon_{jki}$ $= \epsilon_{kij}$ we can write $$ \epsilon_{ijk}\partial_iF_{jk} + \epsilon_{jki}\partial_jF_{ki} + \epsilon_{kij}\partial_kF_{ij} = 0, $$ since each of these vanish, and we collect the permuted ...


1

Case 1 ( Magnetic field is constant)No, while it can change velocity DIRECTION, it cant change the magnitude of velocity. That is, since force due to magnetic field is always perpendicular to direction of propogation, we infer that the speed of a moving charged particle always remains constant in a magnetic field.Case 2 (Varying magnetic field)Situation is ...


1

The magma has temperature between 700 and 1300 Celsius degrees. The Curie temperature of iron is at 770 degrees Celsius. Above that temperature, iron loses magnetism. Note that right above 770 °C, iron is still solid because the melting point is around 1500 °C. So magma almost never can be magnetic because it's just too hot for that. Incidentally, if it ...


1

In general your relation is $$ \vec{B}(\omega) = (1 + \chi_m(\omega))\vec{B}_0(\omega) $$ or in the time domain $$ \vec{B}(t) =\vec{B}_0(t) + \int\limits_{-\infty}^\infty \chi_m(t,t') \vec{B}_0(t') \;\rm{d}t' $$ Only in the case of instantanous material response, i.e. $\chi_m(t,t') = \chi_{m,0} \cdot \delta(t-t') $, your equation is correct. This already ...


1

As per the comments, I assume that your question is: Can an electromagnetic wave induce emission of photons? and the answer is yes: this is what stimulated emission is all about. I encourage you to read the Wikipedia article and come back if you have more questions, but long story short, photons can induce the emission of more photons, and this is how ...


1

I think your confusion is coming from the fact that you are actually using theta for two different things here. Let's use phi for the angle between the velocity of the rod and the magnetic field, and use theta as it is depicted in the diagram. Then your expression should be written as $$qvBsin\phi$$ This comes from the fact that $qvBsin\phi$ is derived from ...


1

This is a typical electromagnet. Let's refer to your figure and say that $g$ is the width of the gap and $A_c$ the section of the core. If $g << \sqrt A_c$,the magnetic field $\vec B$ inside the core will be approximately the same as the magnetic field $\vec B_0$ in the air gap (this is because in this case the magnetic field lines will stay ...


1

Repulsion is the surest test for Magnetism. For finding polarity of magnetism, this may help you: http://m.wikihow.com/Determine-Polarity-of-Magnets


1

MRI signal is always complex and it is related with signal demodulation. The detected signal is multiplied by a sinusoid or cosinusoid with frequency equals to $\omega_0 +\delta \omega$, respectively leading to the real and imaginary channels. You can find the complete algebra at $Haacke,\ Magnetic\ resonance\ imaging$ chapter 7.3.3 Phase is really useful ...


1

Kindly follow the following link.https://en.wikipedia.org/wiki/Jean-Baptiste_Biot and plese go to the heading "Work". It says that the law was discovered experimentally in in the year 1820 i.e. 45 years before the Maxwell equations were published. The general formulation to the Biot-Savart law was given by P. Laplace. The expression of the Biot-Savart Law ...


1

Since the electron is negatively charged, the index finger should point up. The force is to the right, so the thumb points to the right. And then the middle finger comes out of the page. You said you have your thumb pointing to the left because the electron is negatively charged. But in that case you should consider the current to be to the bottom of the ...


1

Then the velocity is towards the right so my index finger is pointed to the right. To apply the right-hand rule, you need to know the charge of the particle. If the charge is -1, like an electron, then the current, $qV$, is in the opposite direction as the velocity and that changes the force from up to down.


1

You are probably not using the hand rule correctly i've posted a picture.


1

Both questions have the same answer: The coordinate system is chosen such that $\theta = 0$ points to the top. So if $\theta_0 = 0$, then the circle is fully immersed in the magnetic field. The limits of integration will be just $0$ to $2\pi$. In the other extreme case, where the circle barely touches the magnetic field, one has $\theta_0 = \pi - \epsilon$ ...


1

The formula for the solenoid or toroid assumes that the length of the solenoid is much greater than its radius, and that the pitch (distance between turns) is much smaller than the radius. These assumption do not hold for a single current loop.


1

I like the above two answers, I think it's more what you're looking for, but I'll still add my two cents.. You could combine Maxwell's equations (while neglecting the timescales for charges to move to conductor surfaces ($\frac{\partial \mathbf{E}}{\partial t}$)) to get the induction equation $\frac{\partial \mathbf{B}}{\partial t} + \nabla \times ...


1

Consider a rectangular Amperian loop instead of a circular one, oriented so the normal is perpendicular to the current. The current enclosed is equal to the current $I$ times the length of the loop. $$\mu L K = \int B\cdot dl$$ B is perpendicular to the loop along the vertical axis, so the only current left after the dot product is along the top and ...



Only top voted, non community-wiki answers of a minimum length are eligible