Asimple model of propagation of radio waves in the earth’s atmosphere or ionosphere consists of a flat earth at z = 0 and a nonuniform medium with = (z) for z > 0. consider the maxwell equations under the assumption that the fields are independent of y and can be written as functions of z times e i(kx−ωt) . (a) show that the wave equation governing the propagation for z > 0 is d 2f dz2 + q 2 (z)f(z) = 0 where q 2 (z) = ω 2 c 2 (z) − k 2 and f = ey for horizontal polarization, and where q 2 (z) = ω 2 c 2 (z) + 1 2(z) d 2 dz2 − 3 4 2(z) d dz 2 − k 2 and f = √ ez for vertical polarization

when insulating materials rub against each other, they may become electrically charged . electrons , which are negatively charged, may be 'rubbed off' one material and on to the other. the material that gains electrons becomes negatively charged. the material that loses electrons is left with a positive charge.

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.