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Instructor(s): Kumar/Stewart
PHYSICS DEPARTMENT
Exam 1
PHY 2054
Name (print, last first):
September 27, 2011
Signature:
On my honor, I have neither given nor received unauthorized aid on this examination.
YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.
(1) Code your test number on your answer sheet (use lines 76–80 on the answer sheet for the 5-digit number).
Code your name on your answer sheet. DARKEN CIRCLES COMPLETELY. Code your UFID number on your
answer sheet.
(2) Print your name on this sheet and sign it also.
(3) Do all scratch work anywhere on this exam that you like. Circle your answers on the test form. At the end of the
test, this exam printout is to be turned in. No credit will be given without both answer sheet and printout.
(4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not
make any stray marks or some answers may be counted as incorrect.
(5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing. If you
believe that no listed answer is correct, leave the form blank.
(6) Hand in the answer sheet separately.
Useful Constants:
9
2
2
ke = 8.99 × 10 Nm /C
²0 = 8.85 × 10−12 C2 /(Nm2 )
V=volt
N=newton
−19
−31
electron charge = −1.6 × 10 C electron mass = 9.11 × 10 kg
J=joule
m=Meter
−3
−6
−9
−12
“milli”=10
“micro”=10
n=“nano”=10
“pico”=10
C=coulomb g = 9.8 m/s2
1. Positive charges are arranged at the vertices of an equilateral triangle as shown
(all three angles are 60◦ , all three sides are 1 m in length. At vertex A is 1 C of
charge, at vertex B, 3 C, at vertex C, 1 C. Calculate the total of the Coulomb
forces on the charge at A from the charges at B and C. What is the ratio of
the magnitude of the total force on the charge at A from both charges at B
and C in the y-direction to the magnitude of the total force on charge A in the
x direction, |Fy |/|Fx | ?
B
60o
A
C
1m
(1) 1.04
(2) 0.74
(3) 0.96
(4) 0.87
(5) 1.00
2. Positive charges are arranged at the vertices of an equilateral triangle as shown
(all three angles are 60◦ , all three sides are 1 m in length. At vertex A is 1 C of
charge, at vertex B, 3 C, at vertex C, 2 C. Calculate the total of the Coulomb
forces on the charge at A from the charges at B and C. What is the ratio of
the magnitude of the total force on the charge at A from both charges at B
and C in the y-direction to the magnitude of the total force on charge A in the
x direction, |Fy |/|Fx | ?
B
60o
A
C
1m
(1) 0.74
(2) 1.04
(3) 0.96
(4) 0.87
(5) 1.00
3. Positive charges are arranged at the vertices of an equilateral triangle as shown
(all three angles are 60◦ , all three sides are 1 m in length. At vertex A is 1 C of
charge, at vertex B, 2 C, at vertex C, 1 C. Calculate the total of the Coulomb
forces on the charge at A from the charges at B and C. What is the ratio of
the magnitude of the total force on the charge at A from both charges at B
and C in the y-direction to the magnitude of the total force on charge A in the
x direction, |Fy |/|Fx | ?
B
60o
A
C
1m
(1) 0.87
(2) 0.74
(3) 0.96
(4) 1.04
(5) 1.00
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4. An electron, q = 1.6 × 10−19 C, is accelerated in a uniform electric field of 100 N/C. What is the acceleration of the
electron, in units of 1013 m/s2 ?
(1) 1.8
(2) 0.6
(3) 0.9
(4) 1.2
(5) 1.5
5. An electron, q = 1.6 × 10−19 C, is accelerated in a uniform electric field of 33 N/C. What is the acceleration of the
electron, in units of 1013 m/s2 ?
(1) 0.6
(2) 1.8
(3) 0.9
(4) 1.2
(5) 1.5
6. An electron, q = 1.6 × 10−19 C, is accelerated in a uniform electric field of 50 N/C. What is the acceleration of the
electron, in units of 1013 m/s2 ?
(1) 0.9
(2) 0.6
(3) 1.8
(4) 1.2
(5) 1.5
7. A charge of +5 C is located at the origin, and a charge of −20 C is located at x = 2 m, i.e., 2 m away from the origin
on the x-axis. Ignoring infinity, where along the x-axis in units of meters is the Coulomb force equal to zero?
(1) −2
(2) +1
(3) −1
(4) −3
(5) −0.67
8. A charge of +5 C is located at the origin, and a charge of −45 C is located at x = 2 m, i.e., 2 m away from the origin
on the x-axis. Ignoring infinity, where along the x-axis in units of meters is the Coulomb force equal to zero?
(1) −1
(2) +1
(3) −2
(4) −3
(5) −0.67
9. A charge of +5 C is located at the origin, and a charge of −80 C is located at x = 2 m, i.e., 2 m away from the origin
on the x-axis. Ignoring infinity, where along the x-axis in units of meters is the Coulomb force equal to zero?
(1) −0.67
(2) +1
(3) −2
(4) −3
10. A uniform electric field, E=100 N/C, is directed along the +x direction. If a
1 m2 area plate is placed along the x-axis perpendicular to the electric field
(see figure), what is the total flux (E·A) in units of Nm2 /C? Dashed lines are
E=100 N/C uniform electric field in the +x direction. The thick, solid black
line is a 1 m2 area seen edge-on that is perpendicular to the x- axis and to the
E field lines.
(1) 100
(2) 0
(3) 50
√
(4) ( 3/2) * 100
(5) −1
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
- - - - - - - - - - - - - - - - - - - - - > x-axis
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
--------------------->
(5) 75
11. A spherical volume of radius R contains +1 C in charge located at r = 0. What is the electric field vector magnitude
at the surface of the sphere?
(1) (1 C)/(4πR2 ²o )
(2) (1 C)/(πR²0 )
(3) (1 C)/( 4πR²o )
(4) (1 C)/( πR2 ²0 )
(5) (1 C)/ (R2 ²0 )
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12. A cube of side L sits at the origin as shown. 1 C of charge is inside the cube
at its center. What is the total electric flux through the surface of the cube?
(1)
(2)
(3)
(4)
(5)
Y
1 C/²0
(6 L2 ) * (1 C)/ ²0
(6 L2 ) * cos45◦ * (1 C)/ ²0
(6 L2 ) * sin45◦ * (1 C)/ ²0
0
X
L
Z
13. An electric car has a battery voltage of 200 V. After 130 km of driving, the battery needs 2 × 108 J of electrical energy
restored to fully recharge the battery. How many Coulombs have to be put into the positive terminal of the car battery
(which remains at 200 V during the recharging process) by the battery charger? (units of Coulombs)
(1) 106
(2) 103
(3) 104
(4) 105
(5) 107
14. The electric potential at the center of the square due to the +1 nC (nanoCoulomb,
or 10−9 C), +2 nC, +3 nC, and −1 nC charges at the corners of the square is
31.8 V. What is the length of the edge of the square, in m?
(1)
(2)
(3)
(4)
(5)
+1 nC
+2 nC
−1 nC
+3 nC
?
2
3
2.5
1.5
1
C
15. See sketch. Points B and C each have −3q charges, while point D has an
unknown charge. Points B and C are each a distance d from point A, while
point D is a distance of 4d away. If the electric field at point A is zero, find
the charge at point D in terms of q.
60o
A
D
60o
B
(1) 48q
(2) 36q
(3) 24q
(4) 12q
(5) 0q
16. Two point charges, each with charge Q, are held a distance r apart. Under these conditions, the force between the two
point charges is F . Now 1/2 of the charge Q from one of the point charges is taken away and placed on the other point
charge, without the distance r being changed. In terms of the original force F , what is the new force between the two
point charges?
(1) (3/4)F
(2) still F
(3) (1/2)F
(4) (2/3)F
17. The capacitances of the four capacitors shown are given in terms of a certain
quantity C. In ratio to C, what is the equivalent capacitance between points
A and D? (First imagine that a battery is connected between those two points;
then reduce the circuit to an equivalent capacitance.)
(5) (3/2)F
C
A
4C
2C
B
D
6C
(1) 0.85
(2) 0.41
(3) 13
(4) 0.63
(5) None of these
18. In the above problem, now consider a battery connected between points A and B. What fraction of the charge is stored
on the 4C capacitor? Express your answer as a ratio to the charge stored on the C capacitor.
(1) None of these
(2) 6
(3) 0.52
(4) 4.0
(5) 0.73
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19. In the circuit shown all capacitors are 6.0µF and the power supply is 5 V. The
charge (in µC) on the capacitor labeled q is:
(1)
(2)
(3)
(4)
(5)
−
12
18
38.5
29
None of these
+
V
q
C2
20. Find the energy stored (in Joules) in the system. The values are V = 10V ,
C1 = 2F , C2 = 4F , C3 = 9F , C4 = 1F , and C5 = 3F .
V
C1
C5
C4
C3
(1) 182
(2) 171
(3) 213
(4) 196
21. In the electric circuit shown, capacitors 1-4 have the same capacitance of 2.0µF
each, and the amount of charge stored in capacitor 2 is 3.0µC. What is the
total energy stored in the four capacitors [in µJ]?
(5) 245
2
1
3
4
(1) 27
(2) 48
(3) 32
(4) 2.25
(5) None of these
22. In the electric circuit shown, capacitors 1-4 have the same capacitance of 2.0µF
each, and the amount of charge stored in capacitor 2 is 4.0µC. What is the
total energy stored in the four capacitors [in µJ]?
2
1
3
4
(1) 48
(2) 27
(3) 32
(4) 2.25
(5) None of these
23. In the electric circuit shown, capacitors 1-4 have the same capacitance of 3.0µF
each, and the amount of charge stored in capacitor 2 is 4.0µC. What is the
total energy stored in the four capacitors [in µJ]?
2
1
3
4
(1) 32
(2) 48
(3) 27
(4) 2.25
(5) None of these
24. A copper cable with resistivity ρ = 1.7 × 10−8 Ω-m is designed to carry a current of 400 Amps with a power loss of
2.0 W/m. What is the required radius of this cable (in cm)?
(1) 2.08
(2) 1.04
(3) 0.52
(4) 1.56
(5) 0.66
25. A copper cable with resistivity ρ = 1.7 × 10−8 Ω-m is designed to carry a current of 200 Amps with a power loss of
2.0 W/m. What is the required radius of this cable (in cm)?
(1) 1.04
(2) 2.08
(3) 0.52
(4) 1.56
(5) 0.66
26. A copper cable with resistivity ρ = 1.7 × 10−8 Ω-m is designed to carry a current of 100 Amps with a power loss of
2.0 W/m. What is the required radius of this cable (in cm)?
(1) 0.52
(2) 1.04
(3) 2.08
(4) 1.56
(5) 0.66
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27. A 140 pF capacitor is charged to a potential difference of 60 V, and the charging battery is disconnected. The capacitor
is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first
capacitor drops to 48 V, what is the capacitance of this second capacitor?
(1) 35 pF
(2) 20 pF
(3) 10 pF
(4) 15 pF
(5) none of these
28. A 140 pF capacitor is charged to a potential difference of 60 V, and the charging battery is disconnected. The capacitor
is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first
capacitor drops to 52.5 V, what is the capacitance of this second capacitor?
(1) 20 pF
(2) 35 pF
(3) 10 pF
(4) 15 pF
(5) none of these
29. A 140 pF capacitor is charged to a potential difference of 60 V, and the charging battery is disconnected. The capacitor
is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first
capacitor drops to 56 V, what is the capacitance of this second capacitor?
(1) 10 pF
(2) 20 pF
(3) 35 pF
(4) 15 pF
(5) none of these
30. Suppose the electric company charges 10 cents per kWh. How much does it cost to use a 125 W lamp 8 hours a day for
30 days?
(1) $3.00
(2) $1.50
(3) $2.25
(4) $1.88
(5) $3.38
31. Suppose the electric company charges 10 cents per kWh. How much does it cost to use a 125 W lamp 6 hours a day for
30 days?
(1) $2.25
(2) $1.50
(3) $3.00
(4) $1.88
(5) $3.38
32. Suppose the electric company charges 10 cents per kWh. How much does it cost to use a 125 W lamp 4 hours a day for
30 days?
(1) $1.50
(2) $3.00
(3) $2.25
(4) $1.88
33. Two unknown point charges Q1 and Q2 are joined by a line. At a point on the
line one-fourth of the way from Q1 to Q2 the electric field is zero. What is the
ratio Q1 /Q2 ?
(1)
1
9
(2)
9
16
(3)
3
4
(4)
1
16
(5) $3.38
1
E=0
4
Q1
C
(5)
Q2
1
4
34. Two separate capacitors with capacitances C1 = 5F and and C2 = 4F are charged. Both have the same charge Q. The
charged capacitors are then brought in contact with each other, positive plate to positive plate (the total charge stays
the same). What is the percent change in the total energy ((Uf − Ui )/Ui ) ∗ 100? A negative sign here indicates that the
final total energy is less than the initial total energy.
(1) −1.23
(2) +1.23
(3) −4
(4) +4
(5) None of these