Final Exam20492010

Final Exam20492010 - Final
Exam
 
 Name:
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Unformatted text preview: Final
Exam
 
 Name:
 Problem
1
 
 
 6
charges
(+q)
are
held
in
a
hexagonal
 arrangement
by
some
plastic.
Each
side
of
 the
hexagon
has
length
a.

 
 (a)
Calculate
the
net
force
(magnitude
and
 direction)
on
the
charge
+Q
at
the
center
of
 hexagon
 
 (b)
Calculate
the
force
(magnitude
and
 direction)
on
the
charge
+Q
if
the
charge
 indicated
by
a
red
circle
is
removed.
 Problem
2


 Consider
a
uniformly
charged
sphere
of
radius
R.

The
charge
density
is
given
by
 ρ/m3.

 
 Calculate
electric
field
(magnitude
and
direction)
for
 (a)
r>R
 (b)
r<R
 
 Calculate
voltage
(assuming
V=0
at
r=infinity)
for
 (a)
r>R
 (b)
r<R
 Problem
3


 Calculate
the
capacitance
of
a
spherical
capacitor,
which
is
composed
of
two
spheres
 (one
inside
another),
with
inner
radius
a
and
outer
radius
b.



 Problem
4


 Parallel
capacitors
are
half
filled
by
dielectric
materials
as
shown
below.

(a)
 calculate
the
capacitances
in
terms
of
ε0,
A,
d.
(b)
Which
capacitor
has
higher
 capacitance?

 
 
 
 
 
 
 
 
 
 
 
 
 
 Problem
5
 At
t=0,
the
switch
is
closed.



 (a)
Calculate
the
current
sourced
by
the
 battery
at
t=0
 (b)
Calculate
the
current
sourced
by
the
 battery
at
t=infinity
 (c)
what
is
the
voltage
across
the
capacitor
at
 t=infinity
 (d)
After
a
long
time,
the
switch
is
released.

 Calculate
the
current
through
the
capacitor
as
 a
function
of
time
after
the
switch
is
released.
 Problem
6

 Consider
a
cylindrical
wire
with
radius
R
with
current
I
flowing
through
it.

Calculate
 magnetic
field
for

 (a)
r>R
 (b)
r<R
 assuming
that
current
is
uniformly
distributed
 Problem
7
 Consider
a
coaxial
cable
as
depicted
below.

Calculate
the
inductance
per
unit
length
 for
the
cable
if
the
inside
wire
has
the
diameter
of
a
and
the
outside
wire
has
a
 diameter
of
b.
 Problem
8
 Find
the
complex
impedance
for
the
parallel
RLC
circuit
as
 shown.
Assume
that
we
have
a
voltage
source
for
which
we
 can
adjust
the
angular
frequency
ω.

V(t)=Vmaxcos(ωt).
 
 (a)
Find
the
total
complex
impedance
of
the
circuit
 (b)
Calculate
I(ω).
 (c)
Find
an
expression
for
the
phase
φ.
 
 (d)
Given
R=500
ohms,
L=
1
henry,
C=1.0µF
and
ω=100
 rad/sec.
Will
the
current
lag
or
lead
voltage
and
by
how
 much?
 ...
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