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 Aug 16 revised The Stern Gerlach Experiment Revisited added 938 characters in body Aug 14 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? $B_x$ and $B_y$ have been assumed to be zero individually in the above comment.Small non-zero values of $B_x$ and $B_y$ definitely changes the picture. What about B_z?It as not supposed to produce any acceleration in the z-direction directly through magnetic effects or indirectly through electrical forces! Aug 14 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Point to Observe:If $\vec{B}$ varies spatially only in the z direction,we may have electric forces only in the y-z plane and not in the z direction.(Initial electric field is assumed to be zero).This follows from the Curl B equation The model proposed will not produce any force in the z-direction initially.Magnetic force being normal to $\vec{B}$ will also be on the x-y plane. There will no force in the z direction --electrical or magnetic in nature. Aug 14 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Edit:For the above comment $\int \vec{E}\rho dV=\nabla(\vec{\mu_0}\cdot\vec{B})\cdot\vec{dr}$Integration should cover all the chage in the current loop. Aug 14 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Magnetic force cannot perform work but electric field can do work.Such a field may result from the spatial variation of B from the curl B equation[comment to the answer may be considered] Aug 14 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Spatial variation of $\vec{B}$ can produce an electric field:$\nabla \times \vec{B}=\mu_0 \vec{j}+\mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}$.If $\vec{E}\cdot\vec{dr}=\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}$ to produce non-zero work then,$\vec{E}=\nabla(\vec{\mu_m}\cdot\vec{B})$. How do you prove that by direct calculation?[here you have a view of the problem through the differential equations which are supposed to represent the physical conditions accurately.] Aug 13 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Let the magnetic field be in the x direction.If the observer moves along the y direction with a uniform speed v,we have $\vec{E}=\gamma(\vec{v}\times\vec{B})$. The electric field accelerates the charged changing its speed and doing work. Initially there was a acceleration normal to the direction of motion. But now we have acceleration due to change of speed also . If the net acceleration changes the radiating power should be different from the two frames.But energy is not an invariant wrt frame transformation though it is a conserved quantity. It might have different values in differentframes Aug 13 comment How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? You can think of redistribution of charges and currents elsewhere(gadgets producing the field) to produce an electric field due to variations of magnetic field at some fixed point. But a pure magnetic field which does not vary with time cannot perform any work.What would be your mechanism for accounting for such variations of $\vec{B}$ in evaluating:$\nabla (\vec{\mu_m}.\vec{B}).\vec{dr}$. What would be the mechanism of including electric field in the said evaluation of elementary work? Aug 13 asked How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Aug 12 comment The Stern Gerlach Experiment Revisited In so far as the last equation in the answer is concerned, the value of x is the same for all particles passing though the region of interaction of the magnetic field. The value of y is confined to the dimemsions of the region of interaction. Its becomes negligible due to the large vale of $\frac{C_1}{k}$. We have in effect:$\frac{C_1}{k}z+\frac{c_2}{k}=(V\pm v_m \frac{C_1}{k})t$ Aug 12 answered The Stern Gerlach Experiment Revisited Aug 11 revised The Stern Gerlach Experiment Revisited added 131 characters in body Aug 11 revised The Stern Gerlach Experiment Revisited added 10 characters in body Aug 11 revised The Stern Gerlach Experiment Revisited added 858 characters in body Aug 11 revised The Stern Gerlach Experiment Revisited added 40 characters in body Aug 11 revised The Stern Gerlach Experiment Revisited deleted 8 characters in body Aug 11 awarded Critic Aug 11 comment The Stern Gerlach Experiment Revisited We may take $\langle v_x \rangle=\langle v_y \rangle$. They correspond to internal motion.The averages masy be taken over time or space and they should be equal in consideration of the Ergodicity principle Aug 11 revised The Stern Gerlach Experiment Revisited added 50 characters in body Aug 11 comment The Stern Gerlach Experiment Revisited Do you find anything counter-intuitive with the above considerations(ie, the answer provided)?Classical prejudice seems to be working out excellently ,at least with the problem at hand---the Stern-Gerlach Experiment.