A wafer of titanium dioxide k 173 hasin area of 140 cm2 and

A wafer of titanium dioxide (k = 173) has.in area of 1.40 cm^2 and a thickness of 0.110 mm. Aluminum Is evaporated on the parafel facts to form a iwv.r.-\' [..ite&.p.v.i v (a) Calculate tho capacitance. (b) When the capacitor Is chaiQed with a 12. 0 V battery, what K the magntude of chaise delivered to each plate? (c) For the situation in part (b), what are the tree and induced surface charge densities? (d) What is the magnitude of the electric filed?

Solution

C = epsilon₀ kA / d

= 8.85 * 10^-12 * 173 * 1.4 * 10^-4 / (0.110 * 10^-3)

= 1.95 * 10^-9 F = 1.95 nF

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Q = C V = 1.95 * 10^-9 * 12

= 2.34 * 10^-8 C = 23.4 nC

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surface charge density = Q / A = 2.34 * 10^-8 / 1.4 * 10^-4

= 1.67 * 10^-4 C/m²

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E = surface charge density / (k epsilon₀)

= (1.67 * 10^-4) / (8.85 * 10^-12 * 173)

= 1.09 * 10⁵ V/m