Exam 1 Review: Fluids, Electrostatics, Capacitance
Supplemental Instruction
IowaStateUniversity / Leader: / German and Karl
Course: / Phys 222
Instructor: / Dr. SoerenPrell
Date: / 02/17/2014

Introduction (10min)

  1. Please write down in the note card provided any question you have about the material covered in the exam, past exams, class slides/worksheets/homework. Be as specific as you can, we will go over some of these questions at the end of the review
  1. Complete the following table with the correct equations

Geometry / Force / Electric Field / Potential
Point Charge / / /
Infinite Line / / /
Infinite Sheet / / /
Inside conductor sphere / N/A / /
Inside insulator sphere
Uniform charge distr. ρ / N/A / /
Outside conductor sphere / N/A / /
Outside insulator sphere
Uniform charge distr. ρ / N/A / /

Please do not start the next section until you are indicated to do so

Part 1 (30min)

Please work individually for 20 min in the following multiple-choice problems

1)“Two identical objects are submerged in a liquid at different heights. Then, the object submerged the deepest will experience a larger net force.” This statement

  1. Is true
  2. Is false
  3. Can’t be evaluated because more info about the shape of the object is needed
  4. Can’t be evaluated because more info about the difference in depths is needed

2)The best way increase the energy stored in an isolated capacitor is to

  1. Insert a dielectric with K = 2
  2. Double distance between plates
  3. Double area of the plates
  4. Double the charge on the plates

3)At equilibrium, the electric field just outside the surface of a charged conductor

  1. Can have nonzero components perpendicular to and parallel to the surface of the conductor.
  2. Is always perpendicular to the surface of the conductor
  3. Is perpendicular to the surface of the conductor only if it is a sphere, a cylinder, or a flat sheet.
  4. Is always parallel to the surface.
  5. Is always zero because the electric field is zero inside conductors.

4) The equivalent capacitance of two identical parallel plate capacitors (A = 0.1 m2, d = 0.5 m) connected in series is,

  1. ε0/5
  2. 2ε0/5
  3. 0.1 ε0
  4. I need information on the charge and voltage on each capacitor

5)A point charge (-3nC) is located at y = 0cm and another charge (-5nC) is located at y = 6cm. The point where the net E field is zero is located at,

  1. 1.27 cm
  2. 2.62 cm
  3. 5.43 cm
  4. Such point does not exist

6)A large cylindrical tank with a radius of 10 m is filled with water up to a level h = 6.00 m. The tank is being emptied with a siphon hose (10 cm diameter) whose end is 3.00 m below the bottom of the container. What is the initial speed of water as it exits the hose?

  1. 3.94 m/s
  2. 5.10 m/s
  3. 7.67 m/s
  4. 10.8 m/s
  5. 13.3 m/s

7)An infinite plane of charge coincides with the xy plane and has a surface charge density of +σ. If the potential at the origin is zero, determine the potential at the point (d, 0, d)

Please do not start working on Part 2 until you are indicated to do so

Part 2 (30 min)

Please work individually for 20 min in the following multiple-choice problems

1)When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, the distance would have to be changed to

2)Read the statements below and choose which letter option is correct

  1. The more closely-spaced the electric field lines are, the stronger the electric field
  2. Electric field lines are always perpendicular to equipotential lines
  3. The more closely-spaced the equipotential lines are, the stronger the potential
  4. Electric field lines start at negative charges and end in positive charges
  1. Only I, II and III are true
  2. Only I and II are true
  3. Only I and IV are true
  4. Only II and III are true
  5. We said A was the correct answer during the session but that is incorrect. For III, the potential gradient would be larger if the equipotentials are close, but the potential has a constant value along the equipotential lines regardless how close they are to one another.

3)A spherical buoy filled with air (p = 10 kg/m3) has been tied to the bottom of a lake (p = 1000 kg/m3). The buoy weighs 400g and has a volume of 1000 cm3. If the buoy is completely submerged, what is the tension of the cable holding the buoy?

  1. 5.98 N
  2. 13.95 N
  3. 97.2 N
  4. 45.56 N

4)A charge q = 2.00 µC is placed at the origin in a region where there is already a uniform electric field E = (100 N/C) i. Calculate the flux of the net electric field through a Gaussian sphere of radius 10.0 cm centered at the origin.

  1. 5.52·105 Nm2/C
  2. Zero
  3. 1.13·105 Nm2/C
  4. 2.26·105 Nm2/C

5)A U-shaped tube is initially filled with water, each arm having a height of 30cm. Then, a 15cm column of oil (density 0.80g/cm3) is added to one of the sides. What is the new height of the side that does not have oil?

  1. 24 cm
  2. 30 cm
  3. 36 cm
  4. 37.5 cm

6)Two coaxial long metallic thin cylinders have been given opposite charges. The inner cylinder has a radius of r1 and a linear charge density of +λ, while the outer one has a radius of r2 and a linear charge density of -2λ. The magnitude of the E-field between the cylinders as a function of the radial distance is,

Challenge Problem: An electric dipole of dipole moment = (5.00 × 10-10 C · m) is placed in an electric field = (3.00 × 106 N/C) + (2.00 × 106 N/C) . What is the magnitude of the torque that the electric field exerts on the dipole?

  1. 1.80·10-3 Nm
  2. 1.50·10-3 Nm
  3. 2.50·10-3 Nm
  4. 0 Nm
  5. 1.00·10-3 Nm

Please do not start working on Part 3 until you are indicated to do so

Part 3 (30 min)

Please work individually for 20 min in the following multiple-choice problems

1)A point charge was placed in an electric field pointing in the positive x direction. After being released, the charge will move,

  1. Toward the positive x direction
  2. Toward the negative x direction
  3. Need more information about the magnitude of the charge and E field
  4. Need more information about the sign of the charge

2)A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?

3)The capacitors C1, C2, C3 and C4 in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance of this capacitor network?

  1. 10 µF
  2. 20 µF
  3. 1.0 µF
  4. 3.0 µF
  5. 5.0 µF

4)Four dipoles, each consisting of a +10-µC charge and a −10-µC charge, are located in the xy-plane with their centers 1.0 mm from the origin, as shown. A sphere passes through the dipoles, as shown in the figure. What is the electric flux through the sphere due to these dipoles?

  1. 11.0·105 Nm2/C
  2. 9.0·106 Nm2/C
  3. 0 Nm2/C
  4. 4.5·106 Nm2/C
  5. -9.0·106 Nm2/C

5)Three point charges, which initially are infinitely far apart, are placed at the corners of an equilateral triangle with sides d. Two of the point charges are identical and have charge q. If zero net work is required to place the three charges at the corners of the triangle, what must the value of the third charge be?

  1. 2q
  2. -4q
  3. 4q
  4. -1/2q

6)A small metallic ball (d = 0.1cm, m = 2 g) has been charged with -3μC and placed above a very large charged sheet of metal. If the ball is levitating 2cm above the sheet, calculate the surface charge density of the sheet.

  1. -0.06 μC/ m2
  2. -2.96·10-4μC/ m2
  3. 0.15 μC/ m2
  4. -0.12 μC/ m2

Challenge Problem:A semicircular wire (of radius R) has been given a total charge of q, which is distributed uniformly along its length. What is the value of the electric field at the center of the semicircle?

  1. 0

Closing (20 min)

What questions do you have about the exam material?

Next SI sessions before the exam:

  • Tuesday 6:10pm, 1051 Gilman
  • Wednesday 7:10pm, 1051 Gilman

Good luck on the exam!