 ## By Pavel Panchekha & Jeffrey Prouty

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Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

# Delve AP Physics C Quiz 4

The copy of the test used in class is available, with the multiple choice and free response sections separate. The questions are mostly identical, with a minor change to question 7.

## Multiple Choice

1. You want to determine how much charge is on an insulating sphere. Which of the following could give you enough information to do this?

1. Another sphere of known charge, a ruler, and a conducting wire
2. Another sphere of known charge, a ruler, and a spring scale
3. A ruler, a spring scale, and a conducting wire
4. A ruler, a conducting wire, and a conducting sphere
5. A spring scale, a conducting wire, and another sphere of known

charge

2. A point charge with charge +q is situated a distance -d from the origin along the x-axis. A second point charge is situated at +d from the origin along the x-axis. What is the electric field at the origin if the second point charge has a charge of -q?
1. $$k q / d^2$$
2. $$- k q / d^2$$
3. $$0$$
4. $$2 k q / d^2$$
5. $$- 2 k q / d^2$$
3. In the same configuration as in problem 2, what is the net force on a charge of -Q at the origin?
1. $$k Q q / d^2$$
2. $$- k Q q / d^2$$
3. $$0$$
4. $$2 k Q q / d^2$$
5. $$- 2 k Q q / d^2$$
4. How much work would be required to bring the charge from problem 3 from infinitely far away on the +y-axis to the origin?
1. $$k Q q / d$$
2. $$- k Q q / d$$
3. $$0$$
4. $$2 k Q q / d$$
5. $$- 2 k Q q / d$$
5. Three positive charges are situated on the vertices of an isolated equilateral triangle of side length l. If each has charge +q, what is the potential energy of this configuration of charges?
1. $$k q^2 / l$$
2. $$2 k q^2 / l$$
3. $$3 k q^2 / l$$
4. $$4 k q^2 / l$$
5. $$6 k q^2 / l$$
6. A dense cloud of positive charge sits at the origin. From very far away, you bring a negatively charged ball towards but not into the cloud and situate it north of the origin. Which direction must you bring the charge from to minimize the amount of work done in this process?
1. North
2. South
3. East
4. West
5. The direction from which you bring the ball is irrelevant
7. Two point charges of mass m and charge -q are initially held together at a distance d and then released. How fast is each charge moving after the distance between them has doubled?
1. $$Q \sqrt{\frac{3k}{4md}}$$
2. $$Q \sqrt{\frac{3k}{8md}}$$
3. $$Q \sqrt{\frac{k}{4md}}$$
4. $$Q \sqrt{\frac{k}{1md}}$$
5. $$Q \sqrt{\frac{k}{2md}}$$
8. Which of the following is true of the relationship between electric field lines and equipotential lines?
1. They both describe lines along which electric field and electric potential respectively have constant values
2. They never intersect with each other
3. They are perpendicular at all points of intersection
4. They are parallel at all points of intersection
5. All of the above
9. Which of the following is a vector quantity?
1. Electric field
2. Charge
3. Potential energy
4. Electric flux
5. Electric potential
10. A ring of charge has a total charge Q spread evenly throughout and a radius R. What is the electric potential at the center of the ring?
1. $$k Q / R$$
2. $$k Q / 2 R$$
3. $$2 k Q / R$$
4. $$4 k Q / R$$
5. $$k Q / 4 R$$
11. When choosing a Gaussian surface, which of the following is not a characteristic that allows one to easily compute the electric field?
1. The electric field being normal to the surface
2. The electric field being parallel to the surface
3. The electric field being constant along the surface
4. The electric field being stronger on the surface than in nearby regions
5. The surface having a known surface area
12. Four point charges are randomly distributed in space. A closed surface contains two of them; the other two are outside the surface. Which of the following is true?
1. The electric field at a point on the surface is not affected by the outside charges
2. The electric potential at a point on the surface is not affected by the outside charges
3. The electric field at a point on the surface is not affected by the inside charges
4. The electric potential at a point on the surface is not affected by the inside charges
5. The electric flux through the surface is not affected by the outside charges
13. A constant electric field of 5 N/C is directed along the positive z-axis in all of space. A 0.5m by 0.25m sheet of paper is held in the xy-plane and then rotated 30 degrees about the x-axis. What is the electric flux through the paper?
1. $$0.31 Nm^2/C$$
2. $$0.54 Nm^2/C$$
3. $$0.63 Nm^2/C$$
4. $$0.75 Nm^2/C$$
5. $$0$$
14. Suppose we replace the paper in problem 13 with a cube of edge length 0.5m. The bottom face of the cube sits in the xy-plane and then the entire cube is rotated 30 degrees about the x-axis. What is the electric flux through the cube?
1. $$0.31 Nm^2/C$$
2. $$0.54 Nm^2/C$$
3. $$0.63 Nm^2/C$$
4. $$0.75 Nm^2/C$$
5. $$0$$
15. Which of the following surfaces cannot ever be used when applying Gauss's law?
1. A sphere
2. An cylinder
3. A cube
4. A hemispherical shell (bowl)
5. A tetrahedron
16. An infinitely long insulating cylinder has volume charge density p and radius R. What is the electric field a distance r away from the axis of the cylinder outside the cylinder (r > R)?
1. $$p R^2 / 2 r \varepsilon$$
2. $$p R^2 / r \varepsilon$$
3. $$0$$
4. $$p r / 2 \varepsilon$$
5. $$p r / \varepsilon$$
17. For the same cylinder, what is the electric field a distance r away from the axis of the cylinder inside (r < R)?
1. $$p R^2 / 2 r \varepsilon$$
2. $$p R^2 / r \varepsilon$$
3. $$0$$
4. $$p r / 2 \varepsilon$$
5. $$p r / \varepsilon$$
18. For which of the following charged bodies does the electric field created outside not depend on one's distance from the body?
1. An infinite plane
2. An infinite wire
3. A point charge
4. A spherical shell of charge
5. A ring of charge
19. You have a 2 Ohm resistor, a 5 Ohm resistor, and a 10 Ohm resistor. What is the effective resistance of these three resistors when all are placed in a circuit in series?
1. 18 Ohms
2. 17 Ohms
3. 13 Ohms
4. 10/7 Ohms
5. 7/10 Ohms
20. You have a 2 Ohm resistor, a 5 Ohm resistor, and a 10 Ohm resistor. What is the effective resistance of these three resistors when all are placed in a circuit in parallel?
1. 18 Ohms
2. 17 Ohms
3. 13 Ohms
4. 1.25 Ohms
5. 0.8 Ohms
21. Two resistors combined produce a greater effective resistance when placed in series than when placed in parallel in a circuit. This is the case because:
1. The new resistor has a greater cross-sectional area
2. The new resistor has a decreased cross-sectional area
3. The new resistor has a greater length
4. The new resistor has a decreased length
5. Two resistors in parallel actually produce a greater effective resistance
22. A positive current in one direction through a wire indicates:
1. Electrons are flowing in that direction
2. Protons are flowing in that direction
3. Electrons are flowing in the opposite direction
4. Protons are flowing in the opposite direction
5. None of the above occur
23. Which of the following does not determine the resistance of a wire?
1. The material from which the wire is constructed
2. The length of the wire
3. The cross-sectional area of the wire
4. The mass of the wire
5. The resistance of a wire depends on all of the above

For the following questions use the circuit diagram below. Assume all wires have negligible resistance: Figure 1: For use in problems 24-29

1. What is the current at point A in Amperes?
1. 9/7
2. 6/7
3. 3/7
4. 2/7
5. 1/7
2. What is the current at point B in Amperes?
1. 9/7
2. 6/7
3. 3/7
4. 2/7
5. 1/7
3. What is the current at point C in Amperes?
1. 9/7
2. 6/7
3. 3/7
4. 2/7
5. 1/7
4. What is the potential difference between points A and B in Volts?
1. 10/7
2. -10/7
3. 110/7
4. -110/7
5. 0
5. What is the potential difference between points B and C in Volts?
1. 10/7
2. -10/7
3. 110/7
4. -110/7
5. 0
6. What is the power dissipated in the 10 Ohm resistor in Watts?
1. 810/49
2. 90/49
3. 90/7
4. 60/7
5. 30/7

## Solutions

### Multiple Choice

 1-10 B D D C C E E C A A 11-20 D E B E D A D A B D 21-29 C C D B C A E D B