Page 160 - Engineering Electromagnetics, 8th Edition

142 ENGINEERING ELECTROMAGNETICS

5.32 Two equal but opposite-sign point charges of 3 µC are held x meters apart by
a spring that provides a repulsive force given by F sp = 12(0.5 − x)N.
Without any force of attraction, the spring would be fully extended to 0.5 m.
(a) Determine the charge separation. (b) What is the dipole moment?
5.33 Two perfect dielectrics have relative permittivities r1 = 2 and r2 = 8. The
planar interface between them is the surface x − y + 2z = 5. The origin lies
in region 1. If E 1 = 100a x + 200a y − 50a z V/m, find E 2 .
5.34 Region 1 (x ≥ 0) is a dielectric with r1 = 2, while region 2(x < 0) has
r2 = 5. Let E 1 = 20a x − 10a y + 50a z V/m. (a) Find D 2 .(b) Find the energy
density in both regions.
5.35 Let the cylindrical surfaces ρ = 4cmand ρ = 9cm enclose two wedges of
perfect dielectrics, r1 = 2 for 0 <φ <π/2 and r2 = 5 for π/2 <φ < 2π.
If E 1 = (2000/ρ)a ρ V/m, find (a) E 2 ;(b) the total electrostatic energy stored
ina1m length of each region.