2/28/2024 0 Comments Flux densityIt could also be linked to the power flow and thereby to the energy flux of Poynting’s vector. It is shown how the force density could describe the forces in a synchronous machine, including both the angular torque of the load and the radial forces between the rotor and the stator. Both force densities are derived from the Lorentz force using the tnb-frame of Frenet–Serret formulas and shown to be equivalent to the divergence of the Maxwell stress tensor. The magnetic pressure gradient force acts from regions of high flux density to regions of low flux density. The magnetic tension force acts to straighten bent field lines, based on the curvature of the flux density. This approach has been applied in physics but never to forces in engineering problems. The force density is written as two vector components: the magnetic tension force and the magnetic pressure gradient force. It’s really useful in understanding in theorems like Gauss’ Law.This paper shows how to model the force density in electrical machines based on the field lines of the magnetic flux density. "Diverge" means to move away from, which may help you remember that divergence is the rate of flux expansion (positive div) or contraction (negative div).ĭivergence isn’t too bad once you get an intuitive understanding of flux.Divergence and flux are closely related – if a volume encloses a positive divergence (a source of flux), it will have positive flux.Divergence is a single number, like density.The gradient gives us the partial derivatives $(\frac)$, and the dot product with our vector $(F_x, F_y, F_z)$ gives the divergence formula above. The symbol for divergence is the upside down triangle for gradient (called del) with a dot.(Assuming $F_x$ is the field in the x-direction.) Total flux change = (field change in X direction) + (field change in Y direction) + (field change in Z direction) If there is some change in the field, we get something like 1 -2 +5 (flux increases in X and Z direction, decreases in Y) which gives us the divergence at that point. If there are no changes, then we’ll get 0 + 0 + 0, which means no net flux. To get the net flux, we see how much the X component of flux changes in the X direction, add that to the Y component’s change in the Y direction, and the Z component’s change in the Z direction. Imagine a cube at the point we want to measure, with sides of length dx, dy and dz. We need to add up the total flux passing through the x, y and z dimensions. Now that we have an intuitive explanation, how do we turn that sucker into an equation? The usual calculus way: take a tiny unit of volume and measure the flux going through it. A div of zero means there’s no net flux change in side the region. The bigger the flux density (positive or negative), the stronger the flux source or sink. Imagine a tiny cube-flux can be coming in on some sides, leaving on others, and we combine all effects to figure out if the total flux is entering or leaving. So, divergence is just the net flux per unit volume, or “flux density”, just like regular density is mass per unit volume (of course, we don’t know about “negative” density). This is a positive divergence, and the point is a source of flux, like a hose. ![]()
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