Mineral oil (

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric fields in matter · Electric fields in matter

The Boundary-Value Problem, Ch Energy and force in dielectrics

Problem

Mineral oil (εr=2.3\varepsilon_r=2.3, so χe=1.3\chi_e=1.3; ρm=860 kg m−3\rho_m=860\,\mathrm{kg\,m^{-3}}) sits in the gap of a vertical parallel-plate capacitor of separation d=1.5 mmd=1.5\,\mathrm{mm}, held at V=3000 VV=3000\,\mathrm{V}. Someone argues: "the field lines simply end at the oil's free surface between the plates, and the electric force acts right there, pulling the liquid up like a stretched membrane." ((a)) Using chapter 6's dipole picture, explain why this cannot be the mechanism, given that the field between two flat plates is uniform. ((b)) State where, in that same picture, the net upward force on the oil originates. ((c)) Estimate the height hh to which the oil rises above the reservoir level, neglecting surface tension. Take g=9.8 m s−2g=9.8\,\mathrm{m\,s^{-2}}.

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