Unformatted text preview: E ( z ) = ±-3 8 ± ± 2 ˆ z ≤ z ≤ d-3 8 ± ± 1 ˆ z d ≤ z ≤ 1 (1) a) Write the expression for the electrostatic potential V ( z ) for < z < 1 m in terms of ± 1 , ± 2 , and d . b) Does V ( z ) determined in part (a) satisfy Laplace’s Equation in the region < z < 1 m? Explain your answer. c) If the two parallel plates were each conﬁned to have a ﬁnite area A (where √ A ± d , so that fringing ﬁelds may be neglected), what would be the capacitance C of the structure in terms of ± 1 , ± 2 , and d ? Hint: You may derive C in one of two ways: (1) as the ratio Q/V of the total charge accumulated on the top plate to the total voltage drop between the plates, or (2) the combination of the capacitance of each dielectric slab in series C = ( C-1 1 + C-1 2 )-1 . 1...
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- Spring '08
- Electric charge, Fundamental physics concepts, perfectly conducting plates