An air-filled capacitor consists of two plates. One of which is horizontal and t

Question

An air-filled capacitor consists of two plates. One of which is horizontal and

the other is slightly tilted as shown in the diagram below (the drawing is not to

scale). If a=0.20m, b=0.20m, c=0.010m, and d=0.002m what is the

capacitance of the system? Hint: you will need to calculate the capacitance of

a strip of length dx and then sum up all contributions.

An air-filled capacitor consists of two plates. One of which is horizontal and the other is slightly tilted as shown in the diagram below (the drawing is not to scale). If a=0.20m, b=0.20m, c=0.010m, and d=0.002m what is the capacitance of the system? Hint: you will need to calculate the capacitance of a strip of length dx and then sum up all contributions.

Explanation / Answer

the capacitance of a strip of length dx:

C = e0 A/y = e0 b dx/y

y = c + (d/a) x

==> C = e0 b dx/y = e0 b dx/(c + (d/a) x)

==> C = int{e0 b dx/(c + (d/a) x)} ; from x=0 to x=a

==> C = e0 b (a/d) int{(d/a) dx/(c + (d/a) x)} ; from x=0 to x=a

==> C = e0 b (a/d) Ln(c + (d/a) x) ; from x=0 to x=a

==> C = 8.85e-12*0.20*0.20/0.002 * Ln(0.01 + 0.002/0.20 * x) ; from x=0 to x=a

==> C = 177e-12 {Ln(0.01 + 0.002/0.20 * 0.20) - Ln(0.01 + 0.002/0.20 * 0)}

==> C = 177e-12 * ((-4.4228) - (-4.60517))

==> C = 32 pF

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