Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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A piezoelectric crystal is characterized by a constant, 12 × 10-13 (V/m)/ (N/m2). The diameter of crystal is 8 mm, thickness is 2 mm and leakageresistance is 108 Ω.[1]. Determine the sensitivity of crystal for measurement of displacement inV/m?[2]. Also what will be the output voltage for an input force of 10 N?[3]. If above crystal is connected to an amplifier with input capacitance of 4× 10-10 F and resistance of 108 Ω. The connecting cable has a capacitance of2 × 10-10 F. Determine the time constant for measurement of displacement.[Dielectric constant = 1.250 × 10-8 F/m and Young’s modulus of 1.2 × 10-11 N/m2].
( Please answer all parts)
Consider a dielectric medium whose electric polarization is P(r, t). Demonstrate that the
associated scalar potential is equivalent to that generated by a (bound) charge distribution
whose change density takes the form
Pb = -V.P.
In addition, show that the conservation of electric charge requires the existence of a (polar-
ization) current density
jp
=
OP
Ət
Problem (1): If you have an infinite conductor wire with radius R carrying a
current I, answer the following:
a) Find its auxiliary field inside and outside the conductor?
b) Find the volume current density inside and outside the conductor?
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