Effect of the Earth'S Magnetic and Electric Fields on Ion Paths in the Upper Atmosphere

Abstract

It is shown that the lines of force of the earth's magnetic field can be treated as if rotating with the earth in so far as the calculation of ion paths are concerned only if there exist positive charges over the poles accompanied by negative charges over the equator. The earth would have a total charge of -72 coulombs although observers on the earth would be aware of no electric field. Assuming that the earth is an uncharged, conducting, uniformly magnetized sphere, rotating about its magnetic axis with angular velocity $\Omega$, it is shown that ion paths progress to the west, the velocity of progression increasing with altitude so as to approach the limiting value $-\Omega \times r$ which measures the progression that would exist if the earth's field were solely magnetic relative to observers who do not partake of the rotation. The earth would have an apparent charge of +72 coulombs although actually uncharged. It is shown that a uniformly distributed charge $q$ on the earth merely changes the value of the limiting westward velocity found above, increasing the westward progression if $q$ is positive, and decreasing it if $q$ is negative.