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Even the Helmholz coil standard for uniform magnetic field fails at points other than the exact center. How uniform must it be? Uniformity will be perturbed by magnetic substances like water or liquid oxygen. The bottom line: You can’t get a uniform magnetic field over a non-zero volume, just like you can’t get absolute zero temperature.


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Note that these dimensions will be functions of time if the geometry of the inductor varies. The 'geometry' of a toroid could be thought of as a topology, and a few dimensions. The topology is the fact that it's a toroid, and the dimensions are the length and cross section of the ring. If the geometry varies, then the dimensions vary, by definition. If they ...


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In any given motor, a higher field means better efficiency, with a lower current needed for any given torque, so lower copper losses. It also means better power per volume/cost/weight of motor. The permanent magnets have to set up that field across the airgap. With a longer airgap, you need stronger (aka more expensive) or longer (aka heavier, more expensive ...


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Heat drives up the resistance of the windings, thus you loose torque. Excessive heat can weaken the permanent magnets, thus loss of torque. Air gaps of 10 mils are common. The issue with very tight 1 mil air gaps is when bearings wear out, the rotor has a slight wobble and if it hits the stator that is bad news. To compensate ultra-hard bearings can be used, ...


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The charges distribute evenly on both conductors but the E field is inverse linear between parallel planes. But it is inverse quadratic between parallel lines where the fringe E-field may be strongest for large angles.. The surface area of the diverging planes is much greater than gap lines. The ratio of fringe capacitance to the total will greatly be ...


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Those steps described by the textbook apply mostly to situations where there is a lot of symmetry in the problem so that you can easily calculate the voltage between the conductors knowing only the total charge on the conductors. You will have to be more creative than following the recipe described in the text. The charge distribution on these conductors ...


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What's wrong? The problem is that as the angle between the plates increases from zero, the E field and the charge distribution becomes nonuniform — a function of how far you are from the narrow gap. That's why the book is telling you to do the integration.


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Looking at the following three bits: I want to see if a design using permanent block magnets is feasible in terms of cost and construction. The volume inside the chamber is approximately 13cm x 13cm x 13cm. To reduce construction costs, I am planning to laser-cut many pieces and stack them This is an experimental prototype design, in which I care more ...


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The magnetic field in the region between the arms would be relatively uniform in direction, but non-uniform in intensity. Below, I've attached an image of the field that I made using very simple simulation software (note: this is extremely simple software meant for didactic use only. its results are not necessarily representative of reality); notice how the ...


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You'll get a field. It will produce a fairly uniform field, for some values of 'fairly' that you may not recognise. There are FEMM solvers, some free, that will show you how horribly non-uniform a field you'll get. It all depends on your specification, does uniform mean +/- 10%, or +/- <1ppm (as required in MRI)? You have a strong axis of asymmetry, with ...


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Back inn 1898 and 1900 (120 years ago), this was one of the views of E&M https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential For an more modern interpretation, consider Jefimenko's Equations https://en.wikipedia.org/wiki/Jefimenko%27s_equations The importance of these equations is many fold; one factor is the LACK OF CAUSALITY in ...


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The expression for the vector potential as an integral over the current is derived for electrostatic fields, or for fields slowly varying enough to neglect the displacement current. So your observation is correct that these expressions neglect the dependence of B upon displacement current. Edit, after dusting off my EM textbook: Although the equation for A ...


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Extending the thoughts on Maxwell, when such waves attempt to propagate INTO a sea of electroncs, the differential_equation solution is not a sin, but the erfc(T,X). And a distributed_element model is appropriate. Some years back, I actually measured the speed_of_propagation of a fast edge into and thru standard thickness (35 microns, 1.4 mils) PCB foil. The ...


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If you take the Maxwell equations, they can be combined to derive the wave equation for light. Since the orthogonal basis for the solution space of the wave equation is the complex exponentials, we can see that sine waves are intimately related to the Maxwell equations here. When wave propagation is defined by the Maxwell equations / the wave equation, ...


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According to this patent application: A nonreciprocal bandpass filter is one that only allows electromagnetic waves (signals) to flow in one direction. It seems to be a way to eliminate circulators or other expensive devices in order to reduce the effect of reflections on a driving circuit.


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The thin insulation can also be verified by stripping it -- by using a small flame to burn it (I use a good-quality lighter, like BIC). Then, steel wool can be used to remove the remaining residue, making a very clean surface to accept your solder. This is in my experience the best way to remove the tough coating, especially for the thinnest magnet wire. ...


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Chamfered and beveled corners are used when the size of the interconnect is large relative to the wavelength of the signal, meaning that it begins to apply at microwave speeds at the PCB/microstrip scale. IC interconnect is very small, such that it is small enough to not experience these effects strongly enough to need chamfered corners. Furthermore, very ...


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You are encountering a concept called frequency response. This is the electrical analogue to hitting a bell with a hammer. The hammer strike injects a wide range of frequencies into the system, which filters these frequencies according to its resonance. This is formalized with the impulse function, which uniformly contains all frequencies; when you inject ...


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My question is little bit hypothetical. What will be the output of the series RLC circuit if we apply AC \$\color{red}{\text{current}}\$ of mixed frequency where one of its frequency is f_r? $$\boxed{\text{The question is about a} \color{red}{\text{ current }} \text{source}}$$ Whatever current you apply to the input of the series RLC you will also get on ...


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The difference between the two refractive index values determines the range of angles that can undergo total internal reflection, and thus the numerical aperture (range of angles that can propagate inside the fiber) of the fiber. If you make the difference large, you get a high NA fiber, which is sometimes used for things like relaying LED light from a ...


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The magnetic field inside a long solenoid of homogenous material (all air, all ferro rod etc...) is homogenous: the field strength (density of field lines) is the same near/at the center of the core as it is near the edge of the core where the windings are. If the core of the solenoid is not homogenous, and composed of a hollow cylinder, as in your case, ...


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I'm adding this in an answer just so i can show the graphic - the results seem to agree with how Andy explains it in his answer and subsequent comments (Charles answer as well). I did this model in the free 2-d FEMM software. I started with the .fem file from this neat page and watched this video to learn how to use the simple program. The clear rectangle ...


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The magnetic field would be concentrated in the areas occupied by the mass of the ferromagnetic core. The empty centre of the core would be largely devoid of magnetic lines of flux. This usually means that there will be a higher level of flux density in the material mass of the core compared to a solid core. However, at the ends of the core (where air ...


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Iron provides the easiest path for magnetic flux. The flux will be concentrated in that path the extent that is doesn't need to go too far in the air to get to that path. The magnetic field will try to move whatever iron is nearby to become a part of that path. Without the iron, the magnetic field would tend to go through the center and around the outside to ...


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