Transformer oil has relative permittivity (so ) and mass density

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

Transformer oil has relative permittivity εr=2.2\varepsilon_r = 2.2 (so χe=1.2\chi_e = 1.2) and mass density ρm=880 kg m−3\rho_m = 880\,\mathrm{kg\,m^{-3}}. It is poured into the gap of a large vertical parallel-plate capacitor with plate separation d=0.50 mmd = 0.50\,\mathrm{mm}, held at a constant potential difference V=800 VV = 800\,\mathrm{V} by a battery. The oil is free to rise between the plates from the reservoir below. Treat the oil as an ideal linear dielectric and ignore surface tension (capillarity). ((a)) Check that the field between the plates is safely below air's breakdown field of about 3 MV m−13\,\mathrm{MV\,m^{-1}}. ((b)) Estimate the height hh to which the oil rises above the level in the open reservoir. Take g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}}.

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