Electrostatic Fields in Matter
Electrostatic Fields in Matter
Electrostatic Fields in Matter
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Take the length of the plates to be L and the distance the dielectric<strong>in</strong>trudes <strong>in</strong>to the space between the plates to be x. The totalcapacitance is thus:C = ɛ 0A L − xd L+ Kɛ 0A xd L = ɛ 0Ad+ ɛ 0A (K − 1)xd LIf x changes by dx, then the change <strong>in</strong> C will be:(27)dC = ɛ 0A (K − 1)dx (28)d LComb<strong>in</strong><strong>in</strong>g equations (26), (27) and (28) gives f<strong>in</strong>ally:F = − 1 2 V 2ɛ 0A (K − 1)(29)d LThe expression itself is not particularly important. The <strong>in</strong>terest<strong>in</strong>gpo<strong>in</strong>t is that it is possible to calculate the force <strong>in</strong> a complex situation<strong>in</strong> such a simple way.15