Download problem set #5 – s

ECE221H1S:ELECTRIC AND MAGNETIC FIELDS
PROBLEM SET #5 – SELECTED SOLUTIONS
DIELECTRICS, POLARIZATION, ELECTRIC FLUX DENSITY, DIELECTRIC STRENGTH,
AND BOUNDARY CONDITIONS FOR ELECTROSTATIC FIELDS
Workbook (Knight):
Chapter 30:
22:
23:
24:
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Textbook (Ulaby):
4.48:
4.49:
4.51: Solution to be discussed in tutorials
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Supplementary Problems:
1. A material has a dielectric constant of εr = 3 and has an atomic density of 1028 atoms per
cubic meter. If only two electrons in the outer orbital shell will distort with an applied Efield, and both electrons follow the same orbital path as a pair, find the spacing between
the center of the nucleus and the average location of the electrons when the applied Efield is 10,000 V/m.
2. Water (H2O) is a polar molecule, with a dipole moment of 6.15 × 10-30 C⋅m and a dielectric
constant of 80. If the density of water is 33.4 × 1027 molecules per cubic meter, find the
percentage of water molecules that align themselves with an applied E-field of magnitude:
(a) 10 V/m
(b) 10 kV/m
3. If the earth is considered to be a metal sphere (radius ≈ 6371 km), how much charge Q
must be deposited on its surface in order for an arc to be established in the air. If the
earth’s surface was charged to this value by removing all the electrons from a volume of
soil, how large would this volume be? Assume that the electron density of soil is
approximately 7 × 1023 cm−3.
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Supplementary Problems (cont’d):
4. A perfectly conducting sphere of radius ܽ and placed at the origin is
half-embedded in a liquid dielectric medium of permittivity ߝଵ as
shown to the right. The region above the liquid is a gas of
permittivity ߝଶ . If the total free charge on the sphere is ܳ, determine
the electric field intensity everywhere.
ߝଶ
ܽ
ߝଵ
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