Solution to Exam 1
Paul Avery, Arthur Hebard
PHY2049, Fall 2003
Sep. 24, 2003
1. Two parallel conducting plates are brought to a potential difference of 4000 V and a
small object of mass 4 mg and charge 0.2
µ
C accelerates from rest at one plate. With
what speed in m/s will it reach the other plate?
Solution:
The work done by the electric field is
qV
, where
q
is the charge and
V
is
the potential difference. Thus the kinetic energy is
K
=
qV
. Solving
1
2
mv
2
=
qV
for
the velocity
v
gives
v
=
2
qV/m
, yielding
v
= 20m/s.
2. Consider a dipole with dipole moment
p
oriented at an angle
θ
with respect to a
constant electric field
E
. At what angle
θ
in degrees is the torque
τ
a maximum, and
what is the magnitude of
τ
for this orientation?
Solution:
The torque is maximum when the dipole is oriented perpendicular to the
electric field. Thus
θ
= 90
◦
and
τ
=
pE
.
3. Five capacitors, each of capacitance
C
, are connected as shown in the figure. What is
the equivalent capacitance of the arrangement?
Solution:
It’s best to do this in stages. Capacitors add in parallel, so the arrangement
can be immediately simplified to 2
C
,
C
and 2
C
in series. The equivalent capacitance
can be found from
C
eq
= 1
/
2
C
+ 1
/C
+ 1
/
2
C
, giving
C
eq
=
C/
2.
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 Spring '08
 Avery
 Physics, Charge, Mass, Electric charge, qV

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