Page 64 - Engineering Electromagnetics, 8th Edition

46 ENGINEERING ELECTROMAGNETICS

2.17 A uniform line charge of 16 nC/m is located along the line defined by y =
−2, z = 5. If = 0 :(a) find E at P(1, 2, 3). (b) find E at that point in the
z = 0 plane where the direction of E is given by (1/3)a y − (2/3)a z .
2.18 (a) Find E in the plane z = 0 that is produced by a uniform line charge, ρ L ,
extending along the z axis over the range −L < z < L in a cylindrical
coordinate system. (b) If the finite line charge is approximated by an infinite
line charge (L →∞), by what percentage is E ρ in error if ρ = 0.5L?(c)
Repeat (b) with ρ = 0.1L.

2.19 A uniform line charge of 2 µC/m is located on the z axis. Find E in
rectangular coordinates at P(1, 2, 3) if the charge exists from (a) −∞ <
z < ∞;(b) −4 ≤ z ≤ 4.
2.20 A line charge of uniform charge density ρ 0 C/m and of length is oriented
along the z axis at − /2 < z < /2. (a) Find the electric field strength, E,in
magnitude and direction at any position along the x axis. (b)With the given
line charge in position, find the force acting on an identical line charge that is
oriented along the x axis at /2 < x < 3 /2.
2.21 Two identical uniform line charges, with ρ l = 75 nC/m, are located in free
space at x = 0, y =±0.4m. What force per unit length does each line
charge exert on the other?
2
2.22 Two identical uniform sheet charges with ρ s = 100 nC/m are located in free
space at z =±2.0 cm. What force per unit area does each sheet exert on the
other?
2
2.23 Given the surface charge density, ρ s = 2 µC/m ,existing in the region ρ<
0.2m, z = 0, find E at (a) P A (ρ = 0, z = 0.5); (b) P B (ρ = 0, z =−0.5).
Show that (c) the field along the z axis reduces to that of an infinite sheet
charge at small values of z;(d) the z axis field reduces to that of a point
charge at large values of z.
2.24 (a) Find the electric field on the z axis produced by an annular ring of
uniform surface charge density ρ s in free space. The ring occupies the region
z = 0, a ≤ ρ ≤ b,0 ≤ φ ≤ 2π in cylindrical coordinates. (b) From your part
(a) result, obtain the field of an infinite uniform sheet charge by taking
appropriate limits.
2.25 Find E at the origin if the following charge distributions are present in free
space: point charge, 12 nC, at P(2, 0, 6); uniform line charge density, 3 nC/m,
2
at x =−2, y = 3; uniform surface charge density, 0.2 nC/m at x = 2.
2.26 A radially dependent surface charge is distributed on an infinite flat sheet in
the x-y plane and is characterized in cylindrical coordinates by surface
density ρ s = ρ 0 /ρ, where ρ 0 is a constant. Determine the electric field
strength, E,everywhere on the z axis.