Page 294 - Engineering Electromagnetics, 8th Edition

276 ENGINEERING ELECTROMAGNETICS

the rectangle 0 < x < 1, 0 < z < d,in the plane y = 0, and from this result
again find the inductance per unit length.
8.40 A coaxial cable has conductor radii a and b, where a < b. Material of
permeability µ r = 1exists in the region a <ρ < c, whereas the region
c <ρ < b is air filled. Find an expression for the inductance per unit length.
8.41 A rectangular coil is composed of 150 turns of a filamentary conductor. Find
the mutual inductance in free space between this coil and an infinite straight
filament on the z axis if the four corners of the coil are located at: (a) (0, 1, 0),
(0, 3, 0), (0, 3, 1), and (0, 1, 1); (b) (1, 1, 0), (1, 3, 0), (1, 3, 1), and (1, 1, 1).
8.42 Find the mutual inductance between two filaments forming circular rings of
radii a and a, where a a. The field should be determined by
approximate methods. The rings are coplanar and concentric.
8.43 (a) Use energy relationships to show that the internal inductance of a
nonmagnetic cylindrical wire of radius a carrying a uniformly distributed
current I is µ 0 /(8π) H/m. (b) Find the internal inductance if the portion of
the conductor for which ρ< c < a is removed.
8.44 Show that the external inductance per unit length of a two-wire transmission
line carrying equal and opposite currents is approximately (µ/π) ln(d/a)
H/m, where a is the radius of each wire and d is the center-to-center wire
spacing. On what basis is the approximation valid?