Download ELECTROMAGNETIC FIELD THEORY

ELECTROMAGNETIC FIELD THEORY
EXAM 2
FALL 2002
NAME: _________________________________________
Problem 1:
____________________________________ (25 pts)
Problem 2:
____________________________________ (30 pts)
Problem 3:
____________________________________ (20 pts)
Problem 4:
____________________________________ (20 pts)
Problem 5:
____________________________________ (10 pts)
Problem 6:
____________________________________ (30 pts)
Problem 7:
____________________________________ (20 pts)
Problem 8:
____________________________________ (25 pts)
Problem 9:
____________________________________ (20 pts)
Total:
____________________________________ (200 pts)
Grade:
____________________________________
1.
Three wires carry constant currents of 10, 20, and 15 amperes in the
directions shown below.
15 A
y=0.6 m
y=0.2 m
20 A
y=0
10 A
A.
What is the magnetic field (magnitude & direction) at y = 0.2 m.
x
1B.
What is the force per unit length (magnitude & direction) seen by the wire
at y = 0.2 m?
2.
A thick spherical shell (inner radius a, and outer radius b) is made of dielectric
material with a “frozen-in” polarization
 k
P r   r̂
r
where k is a constant and r is the radius from the center as shown below. There is
no free charge.
b
a
A.
What is the electric and displacement fields in the spherical shell (a < r < b)?
2B.
What is the electric field and displacement fields outside the shell (r > b)?
C.
What is the bound charge density inside the shell (a < r < b)?
3.
Using Biot-Savart, find the magnetic field at a distance z along the z-axis for the
current loop of radius R with current I shown below.
R
z
P
I
4.
A deuterium particle with mass m = 3.34x10-27 kg and electric charge 1.6x10-19C
is produced and accelerated in a cyclotron with a radius of 0.75 m and a magnetic
field of 20,000 Gauss. Calculate the energy of the particle at the exit in MeV.
(Note: A cyclotron is an example of a charged particle moving in a perpendicular
magnetic field.)
5.
A group of wires each carry 10 Amperes either into or out of the page as shown
 
below. Calculate the circulation of the H-vector (i.e.  H  d l ) for each of the
curves requested.
S1
S2
A.
Curve S1 is a square with sides of length a.
B.
Curve S2 is a triangle with base of length b and height of length h.
6.
A toroid having a rectangular cross-section (a = 2.0 cm by b = 3.0cm) and inner
radius R = 4.0 cm consists of 500 turns of wire that carries a current I  I 0 1  e 3t 
with I0 = 25 A. A rectangular loop consisting of 20 turns of wire links the toroid
as shown below.
a
R
r
b
A.
What is the magnitude of the magnetic field at a distance r from the center of the
Toroid?
6B.
Determine the magnitude of the emf induced in the rectangular loop by the
changing current in the toroid.
7.

A wire of radius R has a current density of J  c r k̂ where c is a constant.
z
R
A.
What is the magnetic field at a radial distance r inside the wire (r < R)?
7B.
What is the magnetic field at a radial distance r outside the wire (r > R)?
8.
A capacitor is a sandwich of two different dielectric materials between two metal
plates. Each layer is 1 mm thick and has an area of 0.5 m2. The top plate carries
6 C of free charge and the bottom plates carries -6 C of free charge.
z
k = 1.5
k = 3.5
A.
Find the electric field in each dielectric.
8.B.
Calculate the Polarization vector inside each dielectric?
8C.
Calculate the bound surface charge density at the interface between the two
dielectrics.
9.
Provide a short answer for each of the following questions.
A.
What is the source of the magnetic fields?
B.
What is the source of circulation for electric fields?
C.

What does Gauss’ Law of Magnetism (   B  0 ) tell us about the shape of
magnetic field lines?
D.

If you were given the magnetic vector potential, A , how would you field the
magnetic field?