2049H Exam1 - 2049H
Exam
#1
 
 
 
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Exam
#1
 
 
 
 Name:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Problem
1
[44
pts]
 
 Uniformly
Charged
Solid
Sphere
(note
it
is
not
metallic)
has
radius
R
and
volume
 charge
density
ρ.


 
 Calculate
electric
field
(its
dependence
on
 r)
 (a) for
outside
the
sphere
[8
pts]
 (b) for
inside
the
sphere
[8
pts]
 
 Calculate
potential
(its
dependence
on
r)
 (c)
for
outside
the
sphere
[12
pts]
 (d) for
inside
the
sphere
[12
pts]
 
 (e) Does
potential
vary
inside
the
 sphere?

[4
pts]
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Problem
2
[44
pts]
 Parallel
plate
capacitor
is
charged
to
area
charge
 density
as
depicted.

You
can
assume
that
the
area
of
 the
capacitor
is
A
and
the
distance
between
capacitor
 is
d.
 
 (a) What
is
the
electric
field
between
the
plates?
 [4
pts]
 (b) What
is
the
voltage
difference
between
plates?

 Which
plate
has
the
positive
voltage?
[4
pts]
 (c) What
is
the
force
between
the
plates?
[proceed
 carefully.

Ask
what
is
the
electric
field
by
one
 plate
first
before
doing
the
superposition]
[12
 pts]
 (d) How
much
work
does
it
take
to
move
the
plate
 on
the
left
further
away
from
the
other
plate
 by
distance
d?
[12
pts]
 (e) What
is
the
energy
stored
in
the
original
 configuration?

You
can
assume
that
you
need
to
move
the
plate
from
 distance
0
to
d.

Answer
in
terms
of
Q
(σ×A),
and
C
(capacitance)
[12
pts]
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Problem
3
[True
or
False
Questions]
[12pts]
 Dielecric
strength
(maximum
electric
field)
of
air
is
3×106
V/m.



 
 (a) Given
a
parallel
plate
capacitor,
maximum
charge
per
unit
area
you
can
store
 depends
on
the
separation
between
two
plates.
[3
pts]
 
 
 
 (b) If
you
have
large
spherical
metallic
shell
and
small
spherical
shell,
you
can
 store
more
charge
on
larger
shell.
[3
pts]
 
 
 
 
 (c) If
you
have
two
capacitors
(with
equal
capacitance)
in
series,
the
total
 capacitance
is
larger
than
that
of
each
capacitor.
[3
pts]
 
 
 
 
 
 (d) Energy
of
500
eV
is
equivalent
to
an
electron
being
accelerated
through
a
 potential
difference
of
500
volts.

It
does
not
matter
how
the
potential
is
 being
applied.
[3
pts]
 
 
 
 ...
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