A metal rod having a mass m and length l has resistance R. The rod hangs from two vertical metallic wires of length l in a uniform vertical magnetic field B of a horseshoe magnet (see figure). The wires have negligible resistance. An AC voltage source is connected between the wires which provides a voltage U(t) = U0 cos ωt, where U0 and ω are constants.   a) Show that for small angular displacements φ the motion of the rod can be described by the equation U(t) = αφ ̈ + βφ ̇ + γφ, and express the constants α, β, γ in terms of quantities m, l, B, R and the gravitational acceleration g. b) At a certain frequency ω = ω0 the amplitude of the oscillations of the rod becomes large and the equation above does not describe the motion anymore. Estimate the frequency ω0.

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Dielectric Breakdown

A dielectric is a material with low electrical conductivity and so is classified as an insulator. Dielectric materials are used to block the flow of electricity through them, allowing them to behave as an insulators. They can also be used to store electric charge or improve capacitance.Dielectrics have no free electrons for conduction because electrons are tightly bound to the nucleus. Because dielectrics contain a small number of electrons for electrical conductivity, they have a dipole. The two primary roles of dielectrics in electrical devices are insulation and electrical energy storage. An electric field polarizes the dielectric, and the polarization of the molecules allows dielectric materials to store charge.