Question

A parallel plate capacitor is made of two square plates of side "l" separated by a distance "d". Each plate lies parallel to the x-z plane. (see picture below) The capacitance of the parallel plate capacitor is Cpp = One of the plates is now tilted at a SMALL angle as shown Note that the separation between the plates, d(z) now varies with "z". Consider this capacitor as an infinite number of parallel plate capacitors connected to each other in a parallel configuration. Each infinitesimal capacitor has a length 'I", width "dz" and plate separation d(z). d(z) 15. Write an expression for the distance between the plates, 'd(z)'_ as a function of "z". Express the answer using the constants "T", "d" and "" The capacitor of width "dz" at the height "z" has a capacitance of app = 16. Integrate both sides to find the total capacitance Express the answer using the constants "T", "d" and "". 17. Use the small angle approximation for tangent and the small value expansion (keep 2 terms) of In(x) to approximate the total capacitance as C pp pp2012

Answer 1

Ztant 6 infinitesimal capacitor at a distance 157 z has plate separation. d(Z) = + 7 tan - zd+zo 227777 The plate of this capacitor is a differential Strip of area eaz so its capacitance de = a to e del toldz d + ze zad (2) I 16 total capacitance total capacitance c= S tol de d + zo + 20 10 for o small en tol In(1+x) = x 2 for aan PP 0 2d² = to i to d²o d 22 for o=o. the parallel plate capacitance value epp- to A Teco - cap- to lo foeso C (0) PP = I Cpp - Cpp - 2d2