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Quiz #3 Form #321
Physics 2212 GH Spring 2015
Name:
Recitation Section:
• Print your name, quiz form number (3 digits at the top of this form), and student number (9 digit Georgia Tech ID
number) in the section of the answer card labeled “Student Identification.”
• Bubble the Quiz Form Number in columns 1–3, skip column 4, then bubble your Student Number in columns 5–13.
• Free-response questions are numbered I–III. For each, make no marks and leave no space on your card. Show all your
work clearly, including all steps and logic. Box your answer.
• Multiple-choice questions are numbered 1–10. For each, select the answer most nearly correct, circle this answer on
your quiz, and bubble it on your answer card. Do not put any extra marks on the card.
• Turn in your quiz and answer card as you leave. Your score will be posted when your quiz has been graded. Quiz
grades become final when the next quiz is given.
• You may use a calculator that cannot store letters, but no other aids or electronic devices.
Fundamental Charge e = 1.602 × 10−19 C
Mass of an Electron me = 9.109 × 10−31 kg
9
2
2
Coulomb constant K = 8.988 × 10 N·m /C
Vacuum Permittivity ϵ0 = 8.854 × 10−12 C2 /N·m2
Unless otherwise directed, friction and drag should be neglected.
Any integrals in free-response problems must be evaluated. Questions about magnitudes will state so explicitly.
I. (18 points) Capacitors C1 = 9.0 µF and C2 = 12.0 µF are each charged with an E = 14 V battery as in (i).
They are then disconnected from the battery without changing the charge on the capacitor plates. The two
capacitors are then connected in parallel as in (ii), with the positive plate of C1 connected to the negative
plate of C2 and vice versa. Afterward, what is the charge on each capacitor?
Form #321 Page 1 of 8
II. (16 points) The network shown comprises five capacitors of identical capacitance C = 8.0 µF. An insulating
material of dielectric constant κ = 5.0 is inserted in the rightmost capacitor and fills it entirely. The network is charged by
a battery of emf E = 15 V. Once electrostatic equilibrium is
reached the battery is disconnected. How much electric potential energy is stored in the network, with respect to zero when
all capacitors are uncharged?
1. (5 points) In the above network, what is the ratio of the charges |Q2 | / |Q5 | between the capacitor labeled 2
and the capacitor labeled 5?
(a)
(b)
(c)
(d)
(e)
1
6/5
1/5
5/6
5
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III. (16 points) You are given a block of aluminum (i) of length ℓ, height h and square cross-section, and a copper
rod (ii) one-third of that length (ℓ/3) and with diameter d = h.
Using an Ohmmeter, you measure an electrical resistance Ri =
1.6 kΩ between the right and the left faces of the aluminum
block. Knowing that the electrical conductivity of copper is
approximatively σCu = 2σAl , what resistance Rii would you
measure between the right and the left faces of the copper
rod?
2. (5 points) You now connect the block and the rod as shown. The right and left faces of this object are
connected to a power-supply of emf E. What is the ratio of current densities JAl /JCu between the aluminum
part and the copper part of the object?
(a)
(b)
(c)
(d)
(e)
π
3π/4
π/3
π/4
1
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3. (5 points) The empty parallel-plate capacitor in (i) is charged such that an electric field of magnitude E0
exists between the electrodes separated by a distance d. An insulator of dielectric constant κ and width d/2
is carefully inserted inside the charged capacitor resulting in (ii). What is the magnitude E of the electric
field between the electrodes of the capacitor (ii)?
(a)
(b)
(c)
(d)
(e)
E
E
E
E
E
= E0 everywhere between the plates.
= E0 outside the insulator, E = E0 /κ inside the insulator.
= E0 outside the insulator, E = κE0 inside the insulator.
= E0 /κ everywhere between the plates.
= E0 outside the insulator, E = 0 inside the insulator.
4. (5 points) In the above problem, what is the difference of potential |∆V | between the electrodes of the
capacitor (ii)?
(a)
(b)
(c)
(d)
(e)
|∆V | = E0 d (1 + κ) /κ
|∆V | = E0 d (1 − κ) /2κ
|∆V | = E0 d (1 + κ) /2κ
|∆V | = E0 d
|∆V | = 0
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5. (5 points) A parallel-plate capacitor has plate area A and plate separation d. It is charged by connecting it
to a battery with emf E, then it is disconnected from the battery. If it is possible to double the electric field
magnitude between the plates by changing their geometry, how could that be done?
(a)
(b)
(c)
(d)
(e)
By halving the plate area to A/2.
By halving the plate separation to d/2.
It is not possible.
By doubling the plate separation to 2d.
By doubling the plate area to 2A.
6. (5 points) A parallel-plate capacitor has plate area A and plate separation d. It is charged by connecting
it to a battery with emf E. If it is possible to double the electric field magnitude between the plates by
changing their geometry, how could that be done?
(a)
(b)
(c)
(d)
(e)
By halving the plate separation to d/2.
It is not possible.
By halving the plate area to A/2.
By doubling the plate separation to 2d.
By doubling the plate area to 2A.
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7. (5 points) An electric potential V varies with position x, as shown. If it can be determined, what is the
direction, if any, of the electric field at location ii?
(a) Electric field direction cannot be determined
from a graph of potential.
(b) In the +x direction.
(c) In the −x direction.
(d) In no direction because V = 0 at location ii.
(e) In no direction because E = 0 at location ii.
8. (5 points) An electric potential V varies with position x, as shown. At which location does the electric field
have its greatest magnitude?
(a)
(b)
(c)
(d)
(e)
location
location
location
location
location
ii.
iv.
iii.
i.
v.
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⃗ varies only with position x as shown. If the electric potential is zero at x = 0 m,
9. (5 points) An electric field E
what is the greatest electric potential in the range x = 0 m to x = 12 m?
(a)
(b)
(c)
(d)
(e)
80 V
0V
20 V
40 V
60 V
10. (5 points) Two segments of wire have equal diameters but different conductivities σ1 and σ2 . A current I
passes through the wire. What is the sign of the charge, if any, that lies on the boundary between the wire
segments?
(a)
(b)
(c)
(d)
(e)
It is positive regardless of the relationship between σ1 and σ2 .
No charge lies on the boundary between the wire segments.
It is negative if σ1 > σ2 , but positive if σ1 < σ2 .
It is negative regardless of the relationship between σ1 and σ2 .
It is positive if σ1 > σ2 , but negative if σ1 < σ2 .
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YOUR form number is 321
Recitation Sections
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