2.2
EEE 241Spring 2016
HW 1 Due January 19
Given A = ax2ay+3az and B = ax+ay2az, find the expression for a unit vector C
that is perpendicular to both A and B.
We can find the vector that is perpendicular to both these vectors by
EEE 241Spring 2016
Final Exam Solutions
1.
A conducting sphere is located at the origin of the coordinate system. This sphere
has a uniform charge density such that the total charge is Q. The radius of the
sphere is a. Concentric with the sphere is a sphe
EEE 241Spring 2016
HW 4Due February 9
310 Assuming that the electric field intensity is E = 100xax (V/m), find the total
electric charge contained inside (a) a cubical volume 100 mm on a side
centered symmetrically at t
EEE 241
Solution to Assignment #9
P.628
Consider the magnetic circuit in Figure 645. A current of 3(A) flows through 200 turns of wire
on the center leg. Asssuming the core to have a constant crosssectional area of 103 (m2 ) and a
relative permeability
1.
EEE 241Spring 2016
HW 6 Due February 23
Work problem 334 from the textbook.
The coordinate system is cylindrical coordinates, and we can take the surface
charge on the inner coaxial cylinder as
Q
.
s =
2 ri L
Then, betwee
EEE 241
Solution to Assignment #3
P.311
[
(
)]
A spherical distribution of charge = 0 1 R2 /b2 exists in the region 0 R b. This charge
distribution is concentrically surrounded by a conducting shell with inner radius Ri (> b) and outer
radius Ro . Determ
P.41
The upper and lower conducting plates of a large parallelplate capacitor are separated by a distance d and maintained at potentials V0 and 0, respectively. A dielectric slab of dielectric constant 6.0 and uniform thickness 0.8d is placed over
EEE241 Fundamentals of Electromagnetics Spring 2007
Solutions to Homework 3
P3.5: Two point charges, Q1 and Q2 are located at (1,2,0) and (2,0,0) respectively. Find the relation between Q1 and Q2 such that the total force on a test charge at the p
EEE 241 Solution to Assignment #8
P.628
Consider the magnetic circuit in Figure 645. A current of 3(A) ows through 200 turns of wire on the center leg. Asssuming the core to have a constant crosssectional area of 103 (m2 ) and a relative permeabi
EEE 241 Solution to Assignment #1
P.21
Given three vectors as follows, A = ax + ay 2 az 3, C = ax 5 az 2, nd (a) aA (c) A B (e) the component of A in the direction of C (g) A (B C) and (A B) C Solution: (a) aA =
A A
B = y 4 + az , a
Solution of Wave Equations for Potentials due to a point charge at the origin: =
2
2 =
2
1
2
, =
2
2 = 0
2
1. V is radial:
, , = ()
2. This equation is valid everywhere except at the origin
1
(, )
2
2
2 = 0
2
Any twicedifferentiable functi
Direct consequence of the principle of conservation of charge:
The current flowing across a closed surface S
is equal to the rate of change of the charge
in the volume V bounded by the surface
If the volume is stationary
=
=
=
swap of integral and
deriv
=
E is conservative
l = 0
=
1
l = 0
A steady current J cannot be
maintained in the same direction in a
closed circuit by an electrostatic field E.
nonconservative device
Electric battery
1
1
v =
2
l =
l
nonconservative part
2
inside
the source
2
Several types of electric current:
Conduction currents  electrons in a metal or semiconductor
Electrolytic currents  ions in an electrolytic solution
Convection currents  electrons or ions in vacuum
Amount of charge passing through s:
=
= =
The c
Laplaces Equation:
if the z dimension of the system is much larger
than the r one,
2
2
1
1 2
2
+ 2
+ 2 =0
2
0: , , = ,
1
1 2
+ 2
=0
2
assume separability:
, = ()()
()
1 2 ()
+
=0
()
()
2
for this to hold for all values of and , each te
General approach for the solution of problems governed by partial differential equations
with prescribed boundary conditions (boundaryvalue problems)
Useful for systems of conductors at fixed potentials and with no isolated
charges (Laplaces problems)
System: one point charge Q above a grounded conducting plane
2 2
2
Formal approach: = 2 + 2 + 2 = 0
2
Conditions for the solution:
1. At all points on the ground conducting
plane, the potential is zero:
(0, , 0)
Grounded plane
conductor
, 0, = 0
2. At
Used to compute the potential distribution
Useful for systems with conducing bodies held at fixed potential
boundary value problems
Elliptic differential equations: relatively easy to solve numerically
gridding is crucial
Derived from postulates of electr
Electrostatic forces move a body by the distance and the system loses energy:
=
+
= ( )
(N)
=
=
=
=
;
=
+
;
=

+
+ + +
+
+
+
+ + +
;
Torque component along the axis of rotation




if the body is constrained to rotate about an axis, the
Dielectrics contain bound charges affecting the external electric field
External electric fields cause small displacements in positive and
negative bound charges within the dielectric material
The displacements create or modify existing dipoles that ar
Wen a current crosses an interface between two media, the
current density vector J may change both in direction and
magnitude
continuity equation for steady currents
Governing equations for steady current density
Differential form
Integral form
=0
= 0
=
An atom has a set of energy levels
Some (but not all) are occupied by electrons
energy
energy gap
increasing density
Gas
Solid
Graphics inspired by www.geo.umass.edu/probe/electronic%20structure.ppt
no interaction
outer levels interact
levels overlap
and