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# Capacitors

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1. Two parallel plates of area 100cm^2 are given charges of equal magnitudes 8.9X10^-7 but opposite signs. The electric field within the dielectric material filling the space between the plates is 1.4X10^6 V/m. (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface.

2. You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 10000V. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 15cm tall with an inner radius of 3.6cm and an outer radius of 3.8cm. What are the (a) capacitance and (b) breakdown potential of this capacitor?

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The expert examines two problems on capacitors. A step by step solution provided.

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Solution

1.
A = 100 cm2 + + + + + + + + + + + + + + Q = 8.9x10-7 C
- - - - - - - - - - - - - - - - - - -
Eo Em E=Eo-Em
Dielectric E = 1.4x106 V/m

+ + + + + + + + + + + + + +
- - - - - - - - - - - - - - - - - - - Q = - 8.9x10-7 C

a) Electric field between the plates of the capacitor = E = σ/Єm .....(1)
where σ = charge density on each plate = Q/A = 8.9x10-7/100x10-4 = 8.9 x 10-5 C/m2

and Єm permittivity of the medium = KЄo (K = ...

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