SredniVashtar
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- TL;DR Summary
- Looking for examples of neat ways to visualize the magnetic field B, the vector potential A and their time derivatives of currents in curled paths in a quasi-static context. (Real conductor simulations welcome, as well).
I am looking for some neat way to visualize various fields in the space around the usual electronic components: a straight wire, a single turn circular coil, a multi-turn finite solenoid, and an infinitely long cylindrical solenoid.
I can get the expression, either in their analytical exact form (the infinitely long rectilinear wire and infinitely long solenoid are treated in all textbooks) or some approximation of the integrals involved. I have found publications with the A and B fields of single circular filamentary currents, and also of a finite solenoid (NASA Technical Note D-465, https://ntrs.nasa.gov/citations/19980227402).
But before embarking in the time consuming task of plotting a 3D entity in 3D space, I'd like to see some neat examples of the representation of these fields. By experience, my biggest problem with visualizing vector fields is with scaling: field lines can gets too crammed in one part and nonexistent in other parts, and when I try to plot arrow fields, I get either absurdly long arrows where the field is strong and points or empty space where it is weak.
How to plot - or even draw - these fields (the static A and B fields) in a way that gives an intuitive view of their direction (ok, circles around straight wires, deformed circles around the single loop, elongated football shapes around the finite solenoid, for the B field) and also magnitude?
I am looking for a didactic representation, more than a faithful numerical representation. If you look at the NASA technical node, the graphs are actually useful (smart people at NASA) but they are not exactly intuitive...
Also, do you agree that in the quasi-static approximation (the dynamic case is a sequence of static snapshots), the dA/dt (which - sign apart is the induced electric field) and dB/dt (which - sign apart - is the curl of E) fields should have the same 'shape' of the A and B fields? Can be in the same direction if the field is increasing or in the opposite direction when it is decreasing, but if the field is going in circles, then its time-derivative does too, right?
I can get the expression, either in their analytical exact form (the infinitely long rectilinear wire and infinitely long solenoid are treated in all textbooks) or some approximation of the integrals involved. I have found publications with the A and B fields of single circular filamentary currents, and also of a finite solenoid (NASA Technical Note D-465, https://ntrs.nasa.gov/citations/19980227402).
But before embarking in the time consuming task of plotting a 3D entity in 3D space, I'd like to see some neat examples of the representation of these fields. By experience, my biggest problem with visualizing vector fields is with scaling: field lines can gets too crammed in one part and nonexistent in other parts, and when I try to plot arrow fields, I get either absurdly long arrows where the field is strong and points or empty space where it is weak.
How to plot - or even draw - these fields (the static A and B fields) in a way that gives an intuitive view of their direction (ok, circles around straight wires, deformed circles around the single loop, elongated football shapes around the finite solenoid, for the B field) and also magnitude?
I am looking for a didactic representation, more than a faithful numerical representation. If you look at the NASA technical node, the graphs are actually useful (smart people at NASA) but they are not exactly intuitive...
Also, do you agree that in the quasi-static approximation (the dynamic case is a sequence of static snapshots), the dA/dt (which - sign apart is the induced electric field) and dB/dt (which - sign apart - is the curl of E) fields should have the same 'shape' of the A and B fields? Can be in the same direction if the field is increasing or in the opposite direction when it is decreasing, but if the field is going in circles, then its time-derivative does too, right?