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Physics - Dielectric Materials - Important Solved Problems(Sum): Dielectric Materials

**SOLVED PROBLEMS**

**1.Find the capacitance of a layer of Al _{2}O_{3}that
is 0.5 m thick and 2000 mm^{2} of square area ( _{r} = 8.854 ×
10^{–12} Fm^{–1})**

**Solution:**

*Given data:*

**
****2.A layer of porcelain is 80 mm long, 20 mm
wide and 0.7 µm thick. Calculate its capacitance with **_{r}** = 6**

**Solution:**

*Given data:*

**
****3.If an ionic crystal is subjected to an
electric field of 1000 Vm ^{–1} and the resulting polarization 4.3 × 10^{–8}
cm^{2}. Calculate the relative permittivity of NaCl. Solution:**

*Given data:*

**
****4.Calculate the electronic Polarization of
argon atom. Given at **_{r}** =
1.0024 at NTP and N = 2.7 × 10 ^{25} atom m^{–3} .**

**Solution
:**

Relative permitivity _{=}
1.0024 at NTP

Permitivity of free space _{=} 8.854 × 10^{–12}
Fm^{–1}

^{}

**5.A
solid contains 5 × 10 ^{28} atoms/m^{3} each with a
polarisability of 2×10^{–40} F m^{2}. Assuming that the
internal field is given by Lorentz formula. Calculate the ratio of internal
field to the external field. _{0} = 8.854 × 10^{–12} Fm^{–1}.**

*6.
Calculate the polarization produced in dielectric medium of dielectric
constant 6 when it is subjected to an electric field of 100 Vm–1. (e _{0} = 8.854 × 10–12 Fm–1)*

P = 4.425 × 10^{–9} Vm^{–2} F

**7.** **Calculate the electronic polarizability of
neon. The radius of neon atom is 0.158 nm. (
= 8.854 × 10 ^{–12} Fm^{–1})**

**
****8.The dielectric constant of a helium gas at
NTP is 1.0000684. Calculate the electron polarizability of helium atoms if the
gas contains 2.7 × 10 ^{26} atoms/m^{3} and hence calculate the
radius of helium atom ( = 8.854 × 10^{–12} Fm^{–1})**

**Solution:**

1. The electronic
polarisability is 0.18x 10 ^{40} fm^{2}. Find the relative
dielectric constant at 0C and 1 atmospheric pressure. **(Ans: 1.000055)**

A
capacitor has capacitance of 0.019 F when uses wax paper _{r} 1.85
between the electrodes of Aluminum foil. The wax paper is to be replaced by
plastic film _{r} 2.15 of same dimensions. Taking other factors being
equal, obtain the change (increase/decrease) in capacitance.

**(Ans:
Increase of 0.0117 F)**

A
capacitor uses Aluminum oxide as the dielectric with relative permeability = 8.
An effective surface area of 360 cm^{2} gives a capacitance of 6 F .
Calculate the field strength and the total dipole moment induced in oxide layer
if a potential difference of 15 volts exist across the capacitor.

**(Ans:
(i) 3.535 × 10 ^{7} V/m (ii) 33.4 x 10 C – m)**

The
radium of the Helium atom is about 0..55 AU. Calculate the polarisability of
Helium and its relative permeability. The number of Helium atoms in a volume of
1 m is 2.7 × 10^{25} atoms. **(Ans:
(i) 0.185 × 10 ^{–40}**

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