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I have had an idea but I do not know whether or not my analysis is flawed? Rather than starting by looking at a motor I want to start with a consideration of a generator. A conducting coil $WXYZ$ with a small gap in it is in the plane of the screen rotating as shown in the diagram with side $XY$ coming out of the screen and side $WZ$ going into the ...


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Definitions First, let's start by defining some parameters: $\mu_{o}$ is the permeability of free space $\varepsilon_{o}$ is the permittivity of free space $\mathbf{E}$ is the 3-vector electric field $\mathbf{B}$ is the 3-vector magnetic field $\mathbf{S}$ is the 3-vector Poynting flux (also called the Poynting vector) $\mathbf{j}$ is the 3-vector ...


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The toroidal multipole moments are actually no independent family of multipole moments (see http://arxiv.org/pdf/1507.00755.pdf). Hence, the statements made by Dubovik in his 1990 paper and in his other papers are effictively wrong. The toroidal moments are just a higher order in the Taylor expansion of the electric parity multipole moments.


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In a perfect transformer, if we run a current through either the primary or secondary coils, we are guaranteed in the quasistatic case that $\Phi_1=\Phi_2$ for each individual turn of the coils. Now suppose we ran a current $I_1$ through the primary coil, and waited long enough so that $I_1$ was steady and $I_2$ (current induced on second coil) was zero. we ...


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To answer your question it takes a little bit longer as usual. Let us start with permanent magnets. Where the magnetic field of permanent magnets come from? The process of its production is the next: Some material is milled to powder, then it will be pressed into its form under the influence of a strong magnetic field and sintered. Why this we do? The best ...


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Here is how I think about this intuitively (I assume you know the mathematical formulation, but that doesn't necessarily help with the intuition; so forgive the deliberately imprecise language I am about to use). When you have a very low magnetic field, you draw field lines far apart. As the field increases, the field lines come closer together. Now if you ...


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You've taken a wrong turn with the cross product business. A cross product is a vector operation - it maps two vectors to a third vector. However, you seem to be imagining that your three equations for $F_x$, $F_y$, and $F_z$ have a cross product in them, but they can't, because those equations contain only scalars. The Lorentz equation as written like this ...


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In the simple mechanical wave on a string , the energy transmitted is given by: As a sinusoidal wave moves down a string, the energy associated with one wavelength on the string is transported down the string at the propagation velocity v. From the basic wave relationship, the distance traveled in one period is vT = λ, so the energy is transported one ...


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I believe this is a valid gauge condition. You can use the hint given by AccidentalFourierTransform in a comment and for arbitrary $A^\mu$ find such $\Omega$ that $(A_\mu+\Omega_{,\mu})(A^\mu+\Omega^{,\mu})=0$, as the latter equation can be resolved with respect to $\Omega_{,0}$, so a Cauchy problem can be posed. Of course, the usual mathematical issues of ...


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We know that light is an electromagnetic wave and it does interact with charges. It contains magnetic field and electric field oscillating perpendicularly but when we apply an electric or magnetic field in any direction to the wave the applied electric field or magnetic field vector doesn't alter the magnetic or electric field in the electro magnetic ...


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An applied electric or magnetic field don't alter the field of an electromagnetic field because, as you said, the superposition principle holds. This principle is a principle of linearity, and comes from the linearity of electromagnetic equations : there is no interaction between photons at low energies. You can see it from a field theory point of view, as ...


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Please answer the point where the magnet is a solenoid(core-less), and what is the action/reaction force on the wire. This is a two wire current carrying situation which in effect is a two streams of moving charges interaction. So the action and reaction are the forces on particles in stream 1 due to stream 2 and the forces on particles in stream 2 ...


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As safkan & Brionius have said, as a first guess the resulting orbit is just as stable as a normal Newtonian one. There is a catch however. The problem with this planetary system is exactly the same as with the Rutherford atom. As the electron travels around the nucleus it is being accelerated towards the centre. As a result it emits electromagnetic ...


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The overall problem with magnetic or electrically charged objects "orbiting" each other is that those forces decay by the square of distance. So if you can get an object into a perfectly circular orbit at exactly the right speed, it works; but if the orbiting "moon" every strays out of that, the unstable orbit collapses quickly and the "moon" falls into the ...


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I believe I have an answer that is a little unconventional. First, recognize that magnetic forces are a little odd. Ferromagnetic and paramagnetism are actually quantum mechanical and can be derived from spin properties (see for example States of Matter, Goodstein). In practice, they are measured macroscopically. Since you don't have a description of ...


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The underlying problem of your trap design is that two dipoles can't make a quadrupole! You are probably aware of the multipole expansion of electric (or magnetic) fields. This is where the terms "dipole" and "quadrupole" come from. As a physics student, one often encounters the exterior multipole expansion: When there are charges inside some volume, and ...


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The glass bob reaches faster. when the two bobs are freely falling the metallic ball which is conducting, produces a current on its surface called eddy currents which opposes the direction of the acceleration i.e. opposite to gravitational acceleration. and hence reduces the speed of the metallic ball which falls under the earth's magnetic field this effect ...


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Any charge placed in the vicinity of another charge will always respond to the electric field created around it. In this case the charge A is experiencing a force due to the charge B by responding to B's electric field and vise versa. So the force on A is time varying. in the same manner the charge B will experience a force due charge A by responding the ...


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I think a step back to a bigger picture can be helpful if you want a physical picture. Forces cause changes in momentum and an object reacts to absolutely every single force it feels. Simply put, when a force acts on an object that object doesn't just change its momentum, it exchanges its momentum with something else. For a contact force, the two objects ...



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