Could you explain how any magnetic B line "begins" anywhere? I can see how a MAGNET can be thought of as a "beginning" point, or more accurately the "source of" a magnet field, by how could any magnetic field "begin" in a "vacuum"?
You're at a considerable disadvantage here because you never even tried to answer
Reality Check's question about the magnetic field surrounding a single current-carrying rod. It looks like this:
[qimg]http://www.cesura17.net/~will/Ephemera/Nerdliness/MR/figure0.png[/qimg]
Now consider the contributions made to
B4 at the origin by each of the four rods. For the east rod, its contribution is some particular intensity m in the southward direction. For the west rod, its contribution is that same intensity m in the northward direction, so the net contribution of the east and west rods to
B4 at the origin is 0. Similarly, the net contribution of the north and south rods is 0. Hence
B4 is zero at the origin; that's why Dungey calls it a neutral point.
Now consider the value of
B4 at some point of the form <dx,-dx> where dx is very small but positive. For the east rod, its contribution is some intensity mE (which is very close to m but slightly greater) in a direction that's very close to southward but slightly east. For the west rod, its contribution is some intensity mW (which is very close to m but slightly less) in a direction that's very close to northward but slightly west. The east and west rods almost cancel each other's fields at <dx,-dx>, but their net effect is a very small resultant in the general direction of southeast. Similarly, the north and south rods almost cancel each other's fields at <dx,-dx> but their net effect is a very small resultant in the general direction of southeast. Adding those two very small resultants together, you get a very small magnetic field directed southeast.
For larger values of dx, the direction continues to be southeast but the intensity grows larger (up to a point, after which the intensity begins to decrease and continues to decrease all the way out to infinity). For smaller positive values of dx approaching zero, the direction of the magnetic field at <dx,-dx> continues to be southeast but its intensity approaches the zero value we calculated for the origin.
If you don't believe me, you can calculate the partial derivatives of
B4 with respect to x and y at points of the form <dx,-dx> with 0<dx.
It's a good thing we all agree that magnetic B lines do not disconnect or reconnect, magnet FLUX induces an E field that results in an electrical discharge that we call a "solar flare".
That's absurd. Even if we ignore the fact that a
B field's magnetic field lines can disconnect or reconnect at neutral points, a steady magnetic flux does not induce an
E field.
Come to think of it, everything you have ever written about magnetic flux is wrong.