文档介绍：EXERCISES 301
-1 A large farm field is in the shape of a parallelogram. Two adjacent
sides are defined by the vectors:
~ ~ ~ ~ ~
AA ¼ð3000 ftÞEE þð4000 ftÞNN and BB ¼ð10;000 ftÞEE
~ ~
where the directions are EE ¼ east and NN ¼ north. Use the vector
cross product to determine how many acres of land are contained in
the field. Note that 1 acre ¼ 44,000 ft2 .
-1 a. A coaxial transmission line consists of an inner conductor of
radius a and an outer conductor of radius b. Between these con-
ductors is a dielectric having a relative dielectric constant of eR.
Derive an expression for the capacitance per unit length of this
line.
b. A certain model of this transmission line has an inner conductor
diameter of 1 cm and an outer conductor inside diameter of
cm, with a relative dielectric constant between the conductors of
. What is the capacitance per unit length of this transmission
line?
-2 The energy stored in an electric field is given by
ð
e0eR 2
UE ¼ jEj dV
2 V
and for a capacitor it is also given by
1 2
UE ¼ 2 CV
Show that both of these expressions give the same result for UE for a
unit length of coaxial line L, where C is the capacitance/unit length
examined in -1.
-1 A static electric potential function exists in a region described by a
ðx; y; zÞ coordinate system. The function is
F ¼ 3x3 þ 5ðy 2 À yÞþ17z þ 6 volts
Calculate the amount of energy required to move an electron from
the origin to the point (4; 5; 2).
-2 What is the gradient of the potential function
F ¼ 3x3 þ 5ðy 2 À yÞþ17z þ 6 volts
at the point (4; 5; 2)?
302 IC FIELDS AND WAVES
-1 Two straight parallel conductors are a distance D apart and carry
currents þI and ÀI, respectively, ‘‘into and out of the paper.’’ Find
an expression for and graph the magnitude of the total H field in the
plane of the paper as a function of position between and outside of
the l