An early model of the atom, proposed by rutherford after his discovery of the atomic nucleus, had a positive point charge +ze (the nucleus) at the center of a sphere of radius r with uniformly distributed negative charge - ze. z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. show that the electric field inside this atom is e_in = (ze/4πε//r^3))

Suppose that an electromagnetic wave which is linearly polarized along the x−axis is propagating in vacuum along the z−axis. the wave is incident on a conductor which is placed at z > 0 region of the space. the conductor has conductivity σ, magnetic permeability µ and electric permittivity ε. (a) find the characteristic time for the free charge density which dissipates at the conductor. (b) write the maxwell equations and derive the wave equation for a plane wave propagating in a conductor. (c) find the attenuation distance at which the incident amplitude reduces to e ^−1 of its initial value. (d) find the electric and magnetic fields inside the conductor. 8 (e) find the power loss per area of the incident electromagnetic wave at the surface of conductor.

A14 kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earths velocity. earth mass is 6.0 * 10^24 kg. show your work assuming the rock earth system is closed.

Using proper grammar, spelling, and punctuation, write at least one 5 sentence paragraph describing 3 ways we use the elements of the electromagnetic spectrum (ems) in our everyday lives.