A capacitor has parallel plates of area 12 cm2separated by 2.5 mm . The space be

Question

A capacitor has parallel plates of area 12 cm2separated by 2.5 mm . The space between the plates is filled with polystyrene (K=2.6, Em=2.0×107V/m).

Part A

Find the permittivity of polystyrene.

Express your answer using two significant figures.

Part B

Find the maximum permissible voltage across the capacitor to avoid dielectric breakdown.

Express your answer using two significant figures.

Part C

When the voltage equals the value found in part B, find the surface charge density on each plate.

Express your answer using two significant figures.

Part D

Find the induced surface-charge density on the surface of the dielectric.

Express your answer using two significant figures.

Explanation / Answer

A)

= ko = 2.6*8.85 x 10^-12 = 2.301 x 10^-11 C^2/n*M^2

B)

V = Emxd = (2 x 10^7)(0.0025) = 5 x 10^4 m/s

C)

E = / = V/d,

= V/d = (2.301 x 10^-11 x 5 x10^4) / 0.0025 = 0.4602 x 10^-3 C/m^2

D)

- =

= oV/d = (8.85 x 10^-12 x 5 x10^4) / (0.0025) = 1.77 x 10^-4 C/m^2

(from part 3) - 1.77 x 10^-4 = 0.4602 x 10^-3 - 1.77 x 10^-4 = 0.2832 x 10^-3 C/m^2

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