Q. 2 (a): A certain homogeneous slab of lossless dielectric material is characterized by an electric susceptibility of 0.12 and carries a uniform flux density within it of 1.6 nC/m. Find the electric field intensity, the polarization, the average dipole moment if there are 2e19 dipoles per cubic meter and the voltage between two equipotential 2.54 cm apart.
Sol: here, electric flux density (D) = 1.6 nC/m
susceptibility (X) = 0.12
a) Electric field intensity (E):
D = EE = Er Eo E = (X + 1) Eo E
=> E = D/(X + 1)Eo = 161.3 V/m
b) Polarization (P):
P = X Eo E = 171.4 pC/mm
c) Average dipole moment = 8.57e-30 cm
d) Voltage between two equipotential 1cm apart = 4.10 V
Q. 2 (b): Calculate the inductance of a toroid formed by surfaces p = 3cm, p = 5cm, z = 0, z = 1.5 cm, wrapped with 5000 turns of wire. The core has a magnetic material with ur = 6 (Do not use approximation in evaluating the flux).
Sol:
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