MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Spring 2010
8.02 Exam Two Spring 2010 Solutions
Question 1: (5 points) Circle the correct answer.
Consider a simple parallel-plate capacitor whose plates are given equal and opposite
charges and are separated by a distance d. The capacitor is connected to a battery.
Suppose the plates are pushed together until they are separated by a distance D = d/2.
How does the final electrostatic energy stored in the capacitor compare to the initial
energy?
a)
Final is half the initial.
b)
Final is one fourth the initial.
c)
Final is twice than initial.
d)
Final is four times the initial.
e)
They are the same.
Answer c.
Because the capacitor is connected to the battery, the potential difference
across the plates is constant. Therefore the ratio of the final stored energy to the initial
stored energy is proportional ratio of the final capacitance to the initial capacitance,
2
2
1
1
/
/
/
2
2
f
i
f
C
i
C
f
i
U
U
C
V
C
V
C
C
=
Δ
Δ
=
. For a parallel plate capacitor, the capacitance is
inversely
proportional
to
the
distance
separating
the
plates,
0
0
(
/
)
A
Q
Q
A
C
V
Ed
d
d
ε
σ
σ
ε
=
=
=
=
Δ
.
Therefore
the
ratio
of
the
capacitance
is
/
/
/(
/ 2)
2
f
i
i
f
C
C
d
d
d
d
=
=
=
. So
/
2
f
i
U
U
=
.

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