A. maxwell’s equations are a set of 4 equations that describe the rule of electromagnetics. write down the 4 equations and try to explain in your own words the physical insights behind each of them. (b) in addition to the 4 maxwell’s equations, there is another equation that relates the variations of the current density and the charge density this equation is referred to as the continuity equation because it relates the net flow of current out of a small volume to the rate of decrease of charge. it takes the form: ∇ ∙ = − / derive the continuity equation from maxwell’s equation. (try start by taking divergence on both sides of the modified ampere’s law and substituting with gauss’s law.) (c) for the special case of electrostatics (time invariant), try to derive the poisson’s equation ∇ = − / from the maxwell’s equations.

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?