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TUTORIAL 2
1.
(SADIKU, p. 74, practice exercise 3.6)
Determine the divergence of the following vector fields.
Also, evaluate them at the
specified points:
(a)
A
=
yz
a
x
+
4
xy
a
y
+
y
a
z
at (1, –2, 3);
(b)
B
=
ρ
z
sin
φ
a
+
3
z
2
cos
a
at (5,
π
/2, 1);
(c)
C
=
2
r
cos
θ
cos
a
r
+
r
1/ 2
a
at (1,
π
/6,
π
/3).
2.
Gauss’s Law says that if we have a point charge
outside
some closed surface S, then there is
no flux of
E
from S.
Prove this assuming only Coulomb’s Law.
3.
Consider a charged conductor bounded by a closed surface S as shown in (a).
(a)
(b)
In Lectures, we applied Gauss’s Law to show that any charge on the conductor resides on
the surface S.
Now consider the surface indicated in (b).
i)
Where does the charge reside?
Consider that the conductor is now uncharged and contains a hollow cavity as shown in (c).
(c)
(d)
ii) If the cavity contains charge
Q
cav
, what is the charge on the inner surface of the conductor?
iii) If the conductor is then charged and contains charge
Q
con
, what are the charges on the inner
and outer surface, respectively?
We now place a second, initially uncharged, conductor in the cavity, as shown in (d) with
other charges as previously.
iv) What is the charge on the surface of the inner conductor?
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View Full Document The inner conductor is now charged and contains charge
Q
inner
.
v) What happens to the charge on the outer surface of the outer conductor?
vi) The charge on the outer conductor is now doubled.
What happens to the charge on the inner
conductor?
What does this mean with regards to electrostatic screening?
vii) We now ground the outer conductor.
How does this change the screening properties?
4.
In Lectures, we calculated
E
for a uniformly charged sphere of charge density
ρ
v
and
radius
a
.
Calculate the field
E
for a conducting sphere of the same radius and carrying the
same total charge.
5.
A sphere of radius 10 cm has
v
r
=
001
3
.
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This note was uploaded on 04/17/2008 for the course ELEC 3305 taught by Professor  during the Spring '07 term at University of West AlabamaLivingston.
 Spring '07
 
 Electromagnet

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