PHYS 202
FINAL EXAM
Summer 2020
1. NAME:
2. Answer all questions.
3. All questions are multiple choice.
4. Please circle your answers.
5. Total Points 25.
1. Two charges are placed a certain distance apart. The probe charge is at some point on a line connecting the
charges but not between them. The force exerted on the probe charge is 0. What is the most general thing we
can say about the charges?
Figure 1
(a) The same sign and magnitude.
(b) Opposite signs but the same magnitude.
(c) The same sign but must have different magnitudes.
(d) Opposite signs but must have different magnitudes.
(e) Zero magnitude necessarily for both of them.
2. A 1.0-C point charge is 15 m from a second point charge, and the electric force on one of them due to the other
2
is 1.0 N. What is the magnitude of the second charge? (𝑘 = 1/4𝜋𝜀0 ≈ 8.99 × 109 N ⋅ m2 /C )
(a) 10 nC
(b) 25 nC
(c) 25 C
(d) 0.025 C
(e) 1.0 C
3. A small glass bead has been charged to 8.0 nC. What is the magnitude of the electric field 2.0 cm from the
2
center of the bead? (𝑘 = 1/4𝜋𝜀0 ≈ 8.99 × 109 N ⋅ m2 /C )
(a) 3.6 × 10−6 N/C
(b) 1.4 × 10−3 N/C
(c) 3.6 × 103 N/C
PHYS 202: FINAL EXAM
(d) 1.8 × 105 N/C
4. A 3.0-𝜇C positive point charge is located at the origin and a 2.0 𝜇C positive point charge is located at 𝑥 = 0.00
m, 𝑦 = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is
zero.
(a) 𝑥 = 0.00 m, 𝑦 = 0.55 m
(b) 𝑥 = 0.00 m, 𝑦 = 0.67 m
(c) 𝑥 = 0.00 m, 𝑦 = 1.5 m
(d) 𝑥 = 0.00 m, 𝑦 = 0.60 m
5. A thin, circular disk of radius 30.0 cm is oriented in the 𝑦𝑧-plane with its center at the origin. The disk carries
a total charge of +3.00 𝜇C distributed uniformly over its surface. Calculate the magnitude of the electric field
2
due to the disk at the point 𝑥 = 15.0 cm along the x-axis. (𝜀0 = 8.85 × 10−12 C /N ⋅ m2 )
(a) 9.95 × 105 N/C
(b) 4.98 × 105 N/C
(c) 3.31 × 105 N/C
(d) 2.49 × 105 N/C
(e) 1.99 × 105 N/C
6. Which of the following statements about Gauss’s law are correct? (There may be more than one correct
choice.)
(a) Only charge enclosed within a Gaussian surface can produce an electric field at points on that surface.
(b) Gauss’s law is valid only for symmetric charge distributions, such as spheres and cylinders.
(c) If a Gaussian surface is completely inside an electrostatic conductor, the electric field must always be zero
at all points on that surface.
(d) If there is no charge inside of a Gaussian surface, the electric field must be zero at points of that surface.
(e) The electric flux passing through a Gaussian surface depends only on the amount of charge inside that
surface, not on its size or shape.
7. If the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.
(a) True
(b) False
8. A solid nonconducting sphere of radius 𝑅 carries a charge 𝑄 distributed uniformly throughout its volume. At
a certain distance 𝑟1(𝑟1 < 𝑅) from the center of the sphere, the electric field has magnitude 𝐸. If the same
charge 𝑄 were distributed uniformly throughout a sphere of radius 2𝑅, the magnitude of the electric field at
the same distance 𝑟1 from the center would be equal to:
PHYS 202: FINAL EXAM
(a) 8𝐸
(b) 𝐸/8
(c) 𝐸/2
(d) 2𝐸
(e) 𝐸
9. How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference
of 1.00 V? The proton is 1836 times heavier than an electron, and 𝑒 = 1.60 × 10−19 C.
(a) 1836 J
(b) 1.602 × 10−19 J
(c) 1.602 × 10−19 eV
(d) 2.941 × 10−16 J
(e) 1.0 J
10. A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity.
(a) The potential at the center of the sphere is the same as the potential at the surface.
(b) The potential at the center is the same as the potential at infinity.
(c) The potential at the center of the sphere is zero.
(d) The potential at the surface is higher than the potential at the center.
(e) The potential is highest at the center of the sphere.
11. Three point charges of −2.00 𝜇C, +4.00 𝜇C, and +6.00 𝜇C are placed along the x-axis as shown in the figure.
What is the electrical potential at point 𝑃 (relative to infinity) due to these charges? (𝑘 = 1/4𝜋𝜀0 ≈ 8.99 ×
2
109 N ⋅ m2 /C )
Figure 2
(a) −307 kV
PHYS 202: FINAL EXAM
(b) +307 kV
(c) −154 kV
(d) +154 kV
(e) 0 kV
12. A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the
sphere’s radius were twice as large, but the charge on the sphere were the same, what would be the potential
on the surface relative to infinity?
(a) 25 V
(b) 200 V
(c) 100 V
(d) 50 V
(e) 400 V
13. When two or more capacitors are connected in parallel across a potential difference
(a) the equivalent capacitance of the combination is less than the capacitance of any of the capacitors.
(b) each capacitor carries the same amount of charge.
(c) the potential difference across each capacitor is the same.
(d) All of the above choices are correct.
(e) None of the above choices are correct.
14. Three capacitors are connected as shown in Fig. 2. What is the equivalent capacitance between points 𝐴 and
𝐵?
Figure 3
(a) 1.7 𝜇F
(b) 4.0 𝜇F
(c) 8.0 𝜇F
(d) 7.1 𝜇F
(e) 12.0 𝜇F
PHYS 202: FINAL EXAM
15. In Fig. 3, three capacitors with capacitances 𝐶1 = 4 𝜇F, 𝐶2 = 3 𝜇F, and 𝐶3 = 2 𝜇F, are connected to a battery
of voltage 𝑉 = 12V. What is the charge on capacitor 𝐶2 ?
Figure 4
(a) 8 𝜇C
(b) 2.0 𝜇C
(c) 84.0 𝜇C
(d) 32.0 𝜇C
(e) 16.0 𝜇C
16. Two large non-conducting plates of surface area 𝐴 = 0.25 m2 carry equal but opposite charges 𝑞 = 75 𝜇C.
What is the energy density of the electric field between the two plates?
(a) 0
(b) 1.7 × 107 J/m3
(c) 3.4 × 107 J/m3
(d) 5.1 × 1015 J/m3
(e) 2.5 × 1015 J/m3
17. A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 6.0 × 10−2 m2 . What is the
capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the
plates?
(a) 32 × 10−12 F
(b) 16 × 10−14 F
(c) 3.7 × 10−12 F
(d) 3.7 × 10−14 F
(e) 32 × 10−14 F
18. An electric current produces
(a) a magnetic field.
PHYS 202: FINAL EXAM
(b) an electric field.
(c) an electromagnetic field.
(d) a gravitational field.
(e) a universal field.
19. An electron traveling toward the north with speed 4.0 × 105 m/s enters a region where the Earth’s magnetic
field has the magnitude 5.0 × 10−5 T and is directed downward at 45∘ below horizontal. What is the magnitude
of the force that the Earth’s magnetic field exerts on the electron? (charge of electron, 𝑒 = 1.60 × 10−19 C)
(a) 2.3 × 10−19 N
(b) 3.2 × 10−19 N
(c) 2.3 × 10−18 N
(d) 2.3 × 10−20 N
(e) 3.2 × 10−18 N
20. A proton starting from rest travels through a potential of 1.0 kV and then moves into a uniform 0.040-T magnetic field. What is the radius of the proton’s resulting orbit? (mass of proton, 𝑚𝑝 = 1.67 × 10−27 kg and
𝑒 = 1.60 × 10−19 C)
(a) 0.17 m
(b) 0.19 m
(c) 0.11 m
(d) 0.080 m
(e) 0.14 m
21. An electron enters a magnetic field of 0.75-T with a velocity perpendicular to the direction of the field. At
what frequency does the electron traverse a circular path? (𝑚𝑒 = 9.11 × 10−31 kg; 𝑒 = 1.60 × 10−19 C)
(a) 4.8 × 10−11 Hz
(b) 1.8 × 10−7 Hz
(c) 2.1 × 1010 Hz
(d) 2.1 × 1014 Hz
(e) 3.2 × 1018 Hz
22. A straight wire that is 0.60 m long is carrying a current of 2.0 A. It is placed in a uniform magnetic field of
strength 0.30 T. If the wire experiences a force of 0.18 N, what angle does the wire make with respect to the
magnetic field?
(a) 30∘
(b) 60∘
PHYS 202: FINAL EXAM
(c) 90∘
(d) 25∘
(e) 35∘
23. A circular loop of wire of radius 0.50 m is in a uniform magnetic field of 0.30 T. The current in the loop is 2.0
A. What is the magnetic torque when the plane of the loop is parallel to the magnetic field?
(a) 0.470 m.N
(b) 0.41 m.N
(c) 0.59 m.N
(d) 0.52 m.N
(e) 0
24. A force 𝐹 ⃗ = (6 × 10−3 N)𝑥̂ − (4 × 10−3 N)𝑦 ̂ − (8 × 10−3 N)𝑧 ̂ is acting on a charge 𝑞 = 2 × 10−9 C moving inside
a uniform magnetic field with a velocity 𝑣 ⃗ = (2 × 106 m/s)𝑥̂ + (3 × 106 m/s)𝑦.̂ Calculate the components of the
magnetic field knowing that the 𝑥-component of the field is equal to zero.
(a) 𝐵⃗ = (2T)𝑦 ̂ − (1T)𝑘 ̂
(b) 𝐵⃗ = −(3T)𝑦 ̂ + (2T)𝑘 ̂
(c) 𝐵⃗ = −(2T)𝑦 ̂ + (1T)𝑘 ̂
(d) 𝐵⃗ = (4T)𝑦 ̂ − (0.5T)𝑘 ̂
(e) 𝐵⃗ = −(4T)𝑦 ̂ + (0.5T)𝑘 ̂
25. A rectangular coil, with corners labeled ABCD, of length 𝐿 and width 𝑤 is placed in a magnetic field 𝐵 as
shown in Figure 5. If there is a current 𝐼 flowing through this coil, what is the direction of the force acting on
section AB of this coil?
Figure 5
(a) in the opposite direction of the magnetic field
(b) in the direction of the magnetic field
(c) perpendicular to and into the page
PHYS 202: FINAL EXAM
(d) perpendicular to and out of the page
(e) none
PHYS 202: FINAL EXAM