A slab of dielectric ( ) is being drawn into a parallel-plate capacitor of plate…

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

A slab of dielectric (χe=1.5\chi_e = 1.5) is being drawn into a parallel-plate capacitor of plate width b=0.050 mb=0.050\,\mathrm{m} and gap d=0.50 mmd=0.50\,\mathrm{mm}, held at a constant potential V=1000 VV=1000\,\mathrm{V} by a battery. Someone writes: "the force is found from the change of stored energy alone: F=−∂W/∂x=−ε0χebV2/(2d)F=-\partial W/\partial x = -\varepsilon_0\chi_ebV^2/(2d), giving a force that pushes the slab back out of the gap." ((a)) Find the error in this working. ((b)) Give the correct magnitude and direction of the force.

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