I'm curious about the general solution to
\int_{-\infty}^{+\infty} \exp[P(x)] dx
Where P(x) is a polynomial in x with real coefficients and whose leading (highest) order is even and its leading order coefficient is negative. Intuitively these integrals ought to converge, but I'm having...
Thanks for the welcome!
A solenoid electromagnet is usually a hollow cylinder wrapped with wire. Someone who wants to make a magnetic field in the middle of that cylinder needs to run current through the wire around it. The magnet strength isn't uniform inside the tube though, because near the...
Along the center of a very long solenoid tube the field strength is constant. At the ends of the tube, however, the field decays and drops off.
Is there a simple way (mathematical solution or simple trick) to make the field perfectly constant (or to a fraction of a percent tolerance)...