Matthew Feickert
PHYS 1304: Introductory Electricity and Magnetism
Quiz 5 Key
February 19th, 2015
Problems
1. (4 points) A parallel plate capacitor made of two very smooth plates has a potential
∆V between its plates. This potential difference is maintained while a glass plate is inserted
between the two parallel plates.
(a) Will the capacitance of the capacitor increase?
(b) Will the energy stored in the capacitor increase?
(c) Will the charges stored on either plate chanage? If yes, will the absolute value of the
charge increase or decrease?
(d) Will you need to push the glass plate in, or will it be sucked in by the electric force
(ignoring friction)?
(e) Instead of the potential difference, the charge stored in the capacitor is held constant.
In this situation, will you need to push the glass plane in, or will it be sucked in by the
electric force (ignoring friction)?
2. (4 points) A parallel-plate capacitor of plate area A = 100 cm2 and plate separation
of 2d = 10 mm exists. The left half of the gap is filled with material of dielectric constant
κ1 = 4. The top of the right half is filled with material of dielectric constant κ2 = 3, and
the bottom of the right half is filled with material of dielectric constant κ3 = 6. What is the
capacitance of the capacitor?
3. (2 points) Check all the statements that are correct.
(a) Electric current is defined as the number of electrons in a unit volume.
(b) Electrons are the charge carriers in a copper wire, but it is the electric field that drives
them transmits energy.
(c) When a current flows through a resistor it converts electric energy at the rate I 2 R.
(d) A light emitting diode (LED) is an Ohmic device.
1
Solutions
1. (4 points) A parallel plate capacitor made of two very smooth plates has a potential
∆V between its plates. This potential difference is maintained while a glass plate is inserted
between the two parallel plates.
(a) Will the capacitance of the capacitor increase?
Yes .
As
C=κ
ε0 A
,
d
and κglass > 1.
(b) Will the energy stored in the capacitor increase?
Yes .
As ∆V is held constant and
1
U = CV 2 .
2
(c) Will the charges stored on either plate chanage? If yes, will the absolute value of the
charge increase or decrease?
Yes .
As ∆V is held constant and q = CV .
(d) Will you need to push the glass plate in, or will it be sucked in by the electric force
(ignoring friction)?
Push in .
As Work = U2 − U1 > 0.
(e) Instead of the potential difference, the charge stored in the capacitor is held constant.
In this situation, will you need to push the glass plane in, or will it be sucked in by the
electric force (ignoring friction)?
Sucked in .
1 q2
As U =
, so for constant q, Work = U2 − U1 < 0.
2C
Points:
• 0.5 points each for correctly answering question a and b
• 1 point each for correctly answering questions c, d, e
2
2. (4 points) A parallel-plate capacitor of plate area A = 100 cm2 and plate separation
of 2d = 10 mm exists. The left half of the gap is filled with material of dielectric constant
κ1 = 4. The top of the right half is filled with material of dielectric constant κ2 = 3, and
the bottom of the right half is filled with material of dielectric constant κ3 = 6. What is the
capacitance of the capacitor?
As
ϵA
d
ε0 A
=κ
,
d
C=
then
κ1 ε0 A
κ2 ε 0 A
, C2 =
,
4 d
2 d
As C2 and C3 are effectively in series, then
C1 =
C3 =
κ3 ε 0 A
.
2 d
1
1
1
C2 C3
=
+
=⇒ C23 =
,
C23
C2 C3
C2 + C3
and as C1 and C23 are effectively in parallel, then the total capacitance is
C123 = C1 + C23
C2 C3
= C1 +
C + C3
[ 2
(
)]
κ2 κ3
ε 0 A κ1 2
=
+
d
4
4 κ2 + κ3
(
)
ε0 A
2κ2 κ3
=
κ1 +
4d
κ2 + κ3
[
]
(8.854 × 10−12 F · m−1 ) (0.01 m2 )
2 (3) (6)
≈
4+
2 (0.01 m)
3+6
−11
≈ 3.54 × 10
F.
Points:
• 1 point for getting C1 , C2 , C3 correctly
• 1 point for correctly adding C2 and C3 in series
• 1 point for correctly adding C1 and C23 in parallel
• 1 point for the right answer
• -1 point for wrong units
3
3. (2 points) Check all the statements that are correct.
(a) Electric current is defined as the number of electrons in a unit volume. 7
Electric current is the flow of electric charge,
I=
dQ
.
dt
(b) Electrons are the charge carriers in a copper wire, but it is the electric field that drives
them transmits energy. ✓
∫
E 2 d3 r
U = ε0
(c) When a current flows through a resistor it converts electric energy at the rate I 2 R. ✓
P = IV = I 2 R,
and power is energy per unit time, which is a rate.
(d) A light emitting diode (LED) is an Ohmic device. 7
Diodes are non-Ohmic.
Points:
• 0.5 points for each correctly checked box (✓).
• 0.5 points for each incorrect box left blank (7).
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