The discussion centers around the mathematical manipulation of integrals involving the cross product in the context of calculating the force on a wire segment in a uniform magnetic field. Participants explore whether the integral of the cross product can be simplified under certain conditions, specifically when the magnetic field is constant in magnitude and direction.
Participants express varying levels of agreement regarding the manipulation of the integral, with some supporting the idea that the simplification is valid under the stated conditions, while others seek a formal proof and clarify that the analogy used does not serve as a proof.
The discussion does not resolve whether the proposed simplification is universally applicable, as participants have not reached a consensus on the proof or validity of the approach.
Yes, we can.Jonathan K said:I am curious if, from this, we can say:
can you offer a proof?blue_leaf77 said:Yes, we can.
In essence, it is the same as doing this:Jonathan K said:can you offer a proof?
This is how I arrived at my original idea, just wasn't sure if was applicable to integration.Nathanael said:In essence, it is the same as doing this:
L1×B + L2×B + ... = (L1 + L2 + ... )×B
Which is the distrubative property of cross product.
(That's not a proof of course; I just want to make sure the idea is clear.)