Download ELECTROMAGNETIC FIELD THEORY

ELECTROMAGNETIC FIELD THEORY
FALL 2002
NAME: _________________________________________
Problem 1:
____________________________________ (30 pts)
Problem 2:
____________________________________ (20 pts)
Problem 3:
____________________________________ (20 pts)
Problem 4:
____________________________________ (20 pts)
Problem 5:
____________________________________ (20 pts)
Problem 6:
____________________________________ (10 pts)
Problem 7:
____________________________________ (24 pts)
Problem 8:
____________________________________ (16 pts)
Total:
____________________________________ (160 pts)
Grade:
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1.
The electric potential for the wedge capacitor shown below is only a function
of . Given that electric potential on the plates of the wedge capacitor is
V( = 0) = 0 and V ( = ) = Vo, find the electric field between the capacitor
plates. You can treat the plates as infinitely large in area and an infinitesimal
insulator along the z-axis prevents the plates from shorting out the voltage supply.
(Hint: Start with Laplace’s Equation)
z
V=0
Vo
y

x
1.
Continued
2.
A +3.0 uC and -4.0 uC charge are located 2.0 cm and 3.0 cm respectively above a
grounded metal plate as shown below. What is the electric potential at point P
which is 1.0 cm above the plate? (Hint: Method of Images)
3 cm
2 cm
P
1 cm
3.
Find the electric potential at a distance z above the center of a flat circular disk of
radius R as shown below.
P
z
R
4.

An electric field is represented by E  a y î  a x ĵ where a = 100 volts/m2.
A.
Find the charge density at any point.
B.
Find the electric potential function V, taking V=0 at the origin.
5.
A hollow spherical shell carries charge density ρ 
shown below.
a
b
A.
What is the electric field in the region a  r  b ?
k
in the region a  r  b as
r2
B.
What is the electric field in the region r < a?
6
6.
Evaluate the integral:
 (3x
4
2
 2x  1) δ 3x  6 dx
7.
Matching
Find the charge distribution that will produce the given electric field strength or
electric potential. Each object is centered at the origin and any given potentials are
measured with respect to zero potential at infinity. (If you have a question about
this problem, please ask it!!)
A.
Point Charge at the Origin
B.
Electric Dipole at the Origin
C.
Charged Metal Sphere
D.
Charged Hollow Metal Cylinder
E.
Uniformly Charged Cylinder
F.
Electric Quadrupole at the Origin
G.
Charged Metal Plate
H.
Uniformly Charged Sphere
_____ V 
1
r2
 r for r  a

_____ E  
 1 for r  a
 r 2
 E 0 for z  0

_____ E  
0 otherwise
 0 for r  a

_____ E  
1 for a  r
 r
 V0 for r  a

_____ V  
 V0 a for a  r
 r
1
_____ E   2
r
8.

Prove that the vector A  3 x 2 y  z î  2xz ĵ  4zx k̂ can not represent an
electrostatic field.