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4

First of all, there is no real or observable lines. Even the magnetic and electric fields are nice and abstract fields which describe observable forces. The term "line" you read is an old unit of magnetic flux. One line is the flux of a uniform magnetic field of one gauss across a surface of one square centimeter perpendicular to the field, $$1\ line = 1 ...


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A field is a field: not a force. A force describes the effect of the field on a specific "object" (see below) coupling to the field. In the current state of research, quantum fields (such as the photon field for electromagnetism, see Virtual photon description of B and E fields) are fundamental structures that cannot be decomposed or explained in simpler ...


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It may be that the mild steel is not sufficiently permeable (relative permeability is around 100) and is not shielding enough of the magnetic field. You could try soft iron, mu-metal or permalloy as alternatives, which are more permeable (relative permeabilities of more than 10,000). Some of these are available in tapes and foils that make it easier to ...


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Might be an elementary answer to your question. But if you look at the Biot and Savart Law, you will see that the magnetic field generated depends on the cross product between the position vector and the "current loop" vector. This vector of course points in a direction that is perpendicular to both vectors. The symmetry is not broken, there are already 2 ...


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Field lines are a good concept for imagining things, but it does not reach too far. Imagine for example the field of two distinct sources -- the field lines would cross if you just draw them both. But this does not represent the sum field. Field lines are drawn by convention so, that their density is approximately proportional to the field strength. This is ...


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The difference is only how you define $\theta$ and the zero of potential energy. The $\cos \theta$ expression takes the zero of potential energy to be when $\theta = \frac \pi 2$ whereas you derivation with $\sin \theta$ in it takes the zero of potential to be when $\theta = 0$.


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I do not see how a loop of wire with many turns is different from a solenoid The solenoid is shaped like a cylinder with length $L$. Image credit while the loop of wire with $n$ turns is essentially still in a plane and so is shaped like a circle of radius $R$ Image credit Note that for a solenoid, with $L$ 'large enough', the magnetic field is ...


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A force field is called conservative if its work between any points $A$ and $B$ does not depend on the path. This implies that the work over any closed path (circulation) is zero. This also implies that the force cannot depend explicitly on time. Consider for instance a time decaying force on a straight line. Choose a long closed path. The magnitude of the ...


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You just use vector addition and Newton's Second Law. For example, if you have $$\overrightarrow{F}_E=qE\hat{x},\space\space\space\overrightarrow{F}_B=qvB\hat{y}$$ then your total force $F_{tot}=F_E+F_B$ is just $$\overrightarrow{F}_{tot}=qE\hat{x}+qvB\hat{y}$$ Since $\hat{x}$ and $\hat{y}$ are totally linearly independent, these terms cannot be combined. ...


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This sort of calculation, especially when the speed of the electrons from an observer's point of view is close to $c$, has to be done using special relativity, in that sense that the transformation between reference frames is determined by Lorentz rather than Galileo transformations. As you mentioned, you can put your reference frame origin at one of the ...


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If it is a magnet which is drawn through a solenoid then the curve of emf against time is unlikely to be sine curve. The emf will however start at zero when the magnet is a long way away from the solenoid. The induced emf will then start increasing because the rate of change of flux linked with the solenoid is increasing because the magnetic field due to the ...


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The convention is that the direction of the magnetic dipole is determined from the direction of the current using the right hand rule. For example, looking down on a loop with a clockwise current means that the magnetic moment is downwards.


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To quantize just means to impose this commutation relation: $$ [x_i , p_j ] = i \hbar \delta_{ij}.$$ By the way, remember that a function of position $f(x)$ may not commute with the momentum operator $p$. $A_i = A_i(x)$. Do $A_i$ and $p_j$ necessarily commute?


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So, We have freedom to set up the problem. So I said the magnetic field on the x axis is the earths magnetic field. The current in the wire will also induce a magnetic field. I said this current is aligned with the y axis. I assumed the current was travelling upwards using the right hand rule (point your thumb up along the current of your right hand) ...


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Do you know a straight line is a circle with infinite radius. Similarly at centre you get a circle with infinite radius. When wire is bent in form of circle, magnetic field is no more concentric circles. Electric field at centre of ring is much stronger than outside. This causes field to form ovals.


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Must admit this got me really worried, and I wondered if the problem was maybe in the use of $\bf{\tau} = \bf{r \times F}$ and identifying the force with the (negative) gradient of some potential. Then, I really got worried because it seemed to me that the same problem would occur if you were to make similar calculations with determining the torque on an ...


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No alignment of magnetic domains in a medium is needed for a magnetic field to propagate in that medium. Magnetic fields can propagate through a vacuum despite the fact that there are no magnetic moments or domains at all in a vacuum, right? Similarly, no dielectric moments are required for electric fields to propagate in a medium, and electric fields can ...


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Of course in theory nothing stops you from doing the same thing on a bigger scale. Consider however that the effect is rather feeble and you need really strong field for heavier objects, which is expensive and quite cumbersome. The relevant equation is given here. If you are mainly looking for a fascinating project, I would consider magnetic levitation, ...


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The convention chosen for the cross product defines the direction of the magnetic field. You are interested in the observable effects of the magnetic field, like the force on a particle in motion. The force should be given by $$\mathbf F = q\mathbf v\times\mathbf B \tag{1}$$ where $q$ is the charge, $\mathbf v$ is the velocity, and $\mathbf B$ is the ...


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The company explanation is wrong, really except for the first sentence. The correct hand waving explanation would be much longer. Materials are composed of atoms which contain electrons, and electrons have intrinsic magnetic moments and specific orbitals around atoms that are not affected by temperature. The molecular bonds are affected at high ...


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The lines are indeed visualisations to represent a vector field. At each point in space there is a magnetic field strength and a direction for that field. The left hand diagram is such a representation for the magnetic field around a current carrying conductor with the current coming out of the screen. If it was correctly drawn then the length of each of ...



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