What is Magnetic field: Definition and 1000 Discussions
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, they are described as a map assigning a vector to each point of space or, more precisely—because of the way the magnetic field transforms under mirror reflection—as a field of pseudovectors.
In electromagnetics, the term "magnetic field" is used for two distinct but closely related vector fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter (A/m). B, magnetic flux density, is measured in tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, the two fields are related through the vacuum permeability,
B
/
μ
0
=
H
{\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} }
; but in a magnetized material, the terms differ by the material's magnetization at each point.
Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force, one of the four fundamental forces of nature.
Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.
For this problem,
The solution is,
However, why did they not use limits of integration for the integral in red? When I solved this, I used
as limits of integration.
I see that is not necessary since you get the same answer either way, but is there a deeper reason?
Many thanks!
Hi, the problem statement is above. I have some questions about how to calculate the area and the direction of the magnetic field of this problem.
As the magnetic flux, my professor have defined it as Phi= integral(B dS)=(Area)e_x B= (Area_triangle + (L^2/2) *(β + α(t)))*B e_z.
How can one know...
According to Chapter 8 of Griffiths' book Introduction to Electrodynamics, the magnetization force that acts on a magnetic dipole is
$$F_M=\nabla (m \cdot B)$$,
where ##m## is the magnetic moment and ##B## is the magnetic field.
For a paramagnetic or diamagnetic particle...
An idea came to my mind after I saw the plasma reactor and how the plasma floats through a magnetic cage that prevents the nuclear reactor from melting, to make a magnetic cage that prevents the rocket engines from melting while they are working.
Is this possible, or does it take a critical...
By following article a magnetic field can produce a least a minimum distortion in spacetime.
If we have a inertia disk spinning 50% inside of a strong closed magnetic field may we suppose that we will create an unbalanced in the angular disc moment producing a propulsion without mass variation...
Hi!
So my question is this, I have done measurements with an magnetic field meter around a transformer from 0.5 meter away (then measure some points around) and then I moved out 0.5 meters and so on until I reached a nearby building.
So my issue now is I want to visualize this to my customer...
I know that each material is made up of tiny magnets due to electrons orbiting the nucleus and also from electron spinning about its own axis. In ferromagnetic or paramagnetic rod these tiny magnets align with the applied field causing the net field in the rod to increase. But for diamagnetic...
If we have charged particles having Brownian motion, would this motion be associated with (or produce) heat or electricity? Would it produce electromagnetic radiation (and if it would produce it, what type of radiation in the electromagnetic spectrum)? Could there be Brownian motion of charged...
It is "easy" to produce experimental setups that could and should for all practical purposes be described as having a constant background magnetic field everywhere, especially in the "asymptotic region" where the detectors are located.
You can do this both in vacuum, and inside a solid sample...
I am unsure of my solutions and am looking for some guidance. a.)The real part of the wave in complex notation can be written as ##\widetilde{A} = A^{i\delta}##. Writing the Complex Wave equation, we have ##\vec E(t) = \widetilde{A}e^{(-kz-\Omega t)} \hat x##. Therefore the real part is ##\vec...
Can a train (e.g. like a maglev train) use a set of permanent magnets (not electromagnets) that somehow can be propelled and maintain at least a constant speed with them?
Is this an example of such system...
Gravity isn't a force in the strictest sense of the word, yet magnetism is exactly that: a force. As is strong, EW, etc.
Therefore, it's possible that the more massive magnetic object gets drawn to the center of a magnetic source at a faster rate than the less massive magnetic object. Discuss!
A piece of metal moving West to East in a North to South fixed magnetic field slows down...but how? Yes of course eddy currents are set up in the metal and these currents generate their own magnetic field which somehow slows down the moving metal piece...but how does this actually slow the...
Sorry if I post again about this topic (last time I promise!) but I still have some doubts regarding the concept of flux. This collection of problems I have quite standard but there are so many variations. Here is the circuit in question:
Something tells me that I could write a function that...
Statement: The magnetic field around a straight wire carrying a current can be explained Relativistically by changing the inertial frame of reference to the frame of the moving electrons - i.e., a Lorentz contraction of the positive charges in the wire will give a denser concentration of the...
The amplitude of ##\vec{B}## is given by:
$$B(x) = B_{0} - B_{0} \frac{x}{2l}$$ for ##0 \leq 0 \leq 2l##
This was my attempts at finding the flux of B:
$$\Phi(B) = (B_{0} - B_{0} \frac{x}{2l})(2l-x(t))l = B_{0}2l^2-2B_{0}x(t)l+ B_{0}\frac{x(t)^2}{2}$$
and the current: $$ i = -\frac{d...
$$B(t) = B_{0} \frac{t^2}{T^2}$$
for ##0 \leq t \leq T##
The issue here is more conceptual, because once I find the flux of B I know how to proceed to find the current. I got velocity (but it seems to me that it is the initial velocity), I could use it to find the time in function of space...
This question appeared in a university entrance exam.Basically, if magnetic flux passing through a surface of a loop changes over time ,only then e.m.f will be induced to that loop.But here only a straight line is used and there's no chance of forming any area.So by definition there's no chance...
I know that for a single cylindrical neodymium magnet, the formula
$$ \displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z-L}{\sqrt{(z-L)^{2}-R^{2}}})}} $$ shows the relationship between the magnetic field strength and the distance between the magnet. I was...
d(ɣmv)/dt = qvB
(dɣ/dt)mv + ɣm(dv/dt) = qvB
Substituting gamma in and using the chain rule, it ends up simplifying to the following:
ɣ^3*m(dv/dt) = qvB
Now, I am confused on how to solve for v.
I am trying to derive radial and axial magnetic fields of a current carrying loop from its magnetic vector potential. So far, I have succeeded in deriving the radial field but axial field derivation gives me trouble.
My derivation of radial field (eq 1) can be found here.
Can anyone point out...
To solve this problem, we need to evaluate the following integral: $$\epsilon = \int_{P}^{C} (\vec v \times \vec B) \vec dl$$
The main problem is, in fact, how do we arrive at it! I can't see why a Electric field arises at the configuration here. The magnetic field of the rotating sphere is...
If a magnetar is a neutron star, how do the neutrons composing the star generate a magnetic field? A neutron has zero charge, so it generates no magnetic field.
My solution was as follows:
$$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$
The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...
Hi, here's a theoretical problem that I am trying to find a satisfactory answer for.
Imagine a coil that is temporarily switched on an off and generates a magnetic field that permeates through space. Now imagine a charged particle passing through this field, at time that the coil is already...
If we increase the magnetic field, the radius of the particle's circular path will decrease which increases the tangential acceleration. How do I find the tangential acceleration. Do I use derivatives?
If I'm correct then the maximum change in magnetic flux occurs when the semi circle crosses the point at which it's plane is parallel with the magnetic field and minimal when it crosses the point at which the magnetic flux is maximum ( perpendicular with the field). I'm having trouble writing a...
At first I tried plugging everything in with 60Hz in the numerator but that did not work. I was told to think about sinusoidal waves and derivates but I'm not sure how that works. Any ideas? Thanks a lot
Does electron beam in empty space generate magnetic fields around them just as with current in conductor.
If yes, then is it experimentally proven that two parallel electron beam would attract each other.
Can someone explain how there can be a radial magnetic field? I thought the magnetic field was always tangent to the circle using the right hand rule where you wrap your fingers around the current and point your thumb in the direction of the current.
if a sphere rotates, it's like multiple currents going around in a circle. I can find the magnetic field of each of those currents at the center point of the circle and add them together. We can integrate with respect to y and R. y ranges from 0 to 5 cm away from the center of the loop and the...
I am confused about this, do the black arrows represent the direction of magnetic force?
The torque ##\tau = -IABsin\theta##, where I = current A is area of loop and B is magnetic field strength and I am a little confused how ##\theta## here is 45 degrees when the angle between the normal for...
I am a beginning graduate student and I've been assigned a paper which uses landau levels for 3d fermionic gas in uniform background magnetic field. I am having trouble finding a proper source which deals with solution of dirac equation in such a case. With the two papers that i have found which...
I was wondering if anyone could walk me though a better explanation on how to get the given results for these two questions. The solutions posted by my professor aren't really clear to me so if anyone is able to better explain how to get the solution it would be much appreciated!
If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...
I am building small, simple version of a railgun using 2 copper bars and a couple of neodymium magnets to increase the magnetic field. I have also been trying to mathematically describe the magnetic field created by the conducting rods themselves. I am coming across some trouble when trying to...
Hello there,
I am given a diagram of a Josephson Junction like so:
With a magnetic field ##B = \mu_oH## in the z-direction. I'm reasonably sure ##d_x,d_y,d_z## are normal lengths, not infinitesimal lengths although that is up for debate. Using the above equations I rearrange the expression...
I want to improve the magnetic field strength at the surface of a magnet configuration by utilizing diamagnetic materials to guide the magnetic field lines. I have not the proper equipment to measure the effect myself but would this work?
This is the initial configuration with four magnets side...
Suppose a molecule from our surrounding air (at ambient temperature) is being selected and is ionized. By some mechanical means, some velocity (say 100 m/s) is added to it and it has been put into a magnetic field perpendicular to its direction of motion. We all know how the molecule will behave...
Hello there, for the above problem the wavefunctions can be shown to be:
$$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$
Here ##b = \sqrt{1 +...
My understanding of why Mars lost its atmosphere was because it cooled down too much internally and that when this happened, the planet lost its magnetic field that helped protect it from solar winds (which then ended up stripping away the planets atmosphere). Is there anything that people could...
I have to prove three equations above.
For first two equations, I've been thought and made reasonable answer by using a definition of the electricfield.
However, for third, I can't use a definition of a magnetic field due to the cross product
Like J_2 X J_1 X (r_2 - r_1).
I think three of 'em...
To calculate the Hamiltonian of a charged particle immersed in an electromagnetic field, one calculates the Lagrangian with Euler's equation obtaining ##L=\frac{1}{2}mv^2-e\phi+e\vec{v}\cdot\vec{A}## where ##\phi## is the scalar potential and ##\vec{A}## the vector potential, and then we go to...
I don't understand why there is potential difference between point A and O. Is there any change in magnetic flux experienced by the ring? I think the magnetic field passing through the ring's cross sectional area is constant
Thanks
(My multipart question is from a very naive perspective, so sorry if it is rife with misunderstandings. Please answer conceptually, with as few & as simple equations as possible. I think that all of the answers to these questions should be understandable to a high schooler, though maybe the...