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First the laser beam should be highly focused and with a high numerical aperture. Due to the electromagnetic forces of the light beam, the particle experiences a change of momentum, such creating the gradient force and the scattering force on the surface of the particle. Combining different variables such as power of the laser, the numerical aperture, the ...


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If question 1. is a question about equilibrium, the general answer is: we must first of all specify which constraints define the possible equilibrium states – for example constant temperature, or magnetization, and so on. (You understand that this specification is important because otherwise any state can be an equilibrium state: we just need to fix the ...


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Short answer: think energy, not entropy. Long answer: Think of the field lines evidenced by small iron particles in presence of a bar magnet. They form curved shapes, slowly reverse direction and end up connecting the magnet's North with its South pole, right? Now think of the same kind of magnetic field lines being generated by one of the magnetic domains ...


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Yes, at some point in space their fields will sum to zero, for four charges this can happen in two locations. For example, if you have the charges evenly spaced in a plane ordered as (+,-,+,-) then you will have two quadrupoles midway between the charges at heights above the plane $\pm z_0$. If you have them ordered as (+,+,-,-) then the quadrupoles will be ...


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Why won't a locked dipole react to AC transient? If an AC polarity goes one way, the dipole will point to that direction. The dipole should reverse its direction if the AC polarity changes. You're picturing AC centered around zero, not an AC transient on top of a DC-bias. In use you shouldn't get AC transients so large and powerful they can actually ...


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The equilibrium of a state is the constra-balance of two factor: internal energy and entropy. Puting these two factors in math form becomes the Helmholtz free energy: $$ F = U - TS \tag{1}. $$ The equilibrium of a state is to reach minimum of free energy. (1) As long as the internal energy, $U$, is concerned, the energy is a all-aligned magnet has lower ...


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Qualitatively, how does the magnetic field around an ideal dipole compare with the magnetic field around a circular current loop? As one moves away from a circular current loop, in any direction, the magnetic field more and more closely approximates that of an ideal magnetic dipole.


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Yes you are absolutely right in stating that the external torque $τ_{ext}$ will have a sign opposite to that of the torque exerted by the electric field. However note that the expresion $$τ = 2aqEsin\theta = pEsin\theta$$ is only indicative of the magnitude of the torque applied by the field on the dipole. Consider the conventional diagram accompanying such ...


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