## 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 5

The copy of the test used in class is available, with the multiple choice and free response sections separate. The questions below are nearly identical, except for minor formatting changes and typo fixes to various problems.

## Multiple Choice

1. What is $${\hat x} \times {\hat z}$$?
1. $${\hat y}$$
2. -$${\hat y}$$
3. 0
4. $${\hat x}$$
5. $${\hat z}$$
2. Two straight parallel wires both carry a current $$I$$ in the positive y-direction. These two wires experience a force:
1. In the x-direction
2. In the z-direction
3. Towards each other
4. Away from each other
5. Equal and opposite, so that the net force is zero
3. You fire an electron into a magnetic field and notice that its trajectory is a counterclockwise circle of radius $$R$$. You fire a proton into the same magnetic field with the same initial velocity. What do you expect the trajectory of the proton to be?
1. A straight line
2. A counterclockwise circle of radius less than $$R$$
3. A counterclockwise circle of radius greater than $$R$$
4. A clockwise circle of radius less than $$R$$
5. A clockwise circle of radius greater than $$R$$
4. You fire a neutron into the same magnetic field with the same initial velocity as in problem 3. What do you expect the trajectory of the neutron to be?
1. A straight line
2. A counterclockwise circle of radius less than $$R$$
3. A counterclockwise circle of radius greater than $$R$$
4. A clockwise circle of radius less than $$R$$
5. A clockwise circle of radius greater than $$R$$
5. You measure the magnetic field of a finite-length current-carrying wire at point P and find it to be 2.0 Tesla. You now double the length of the wire, keep the same current, and measure the magnetic field at a point twice as far from the wire as point P. What magnetic field do you expect to measure now?
1. 1.0 Tesla
2. 2.0 Tesla
3. .70 Tesla
4. 1.4 Tesla
5. .50 Tesla
6. A particle of mass $$m$$ and charge $$+q$$ is fired into a region with velocity $$v$$ in the $$+x$$ direction. In this region, there is an electric field $$E$$ in the $$+y$$ direction and a magnetic field. In order for the particle to move in a straight line, what must the magnetic field be?
1. $$E/v$$ in the $$+z$$ direction
2. $$E/v$$ in the $$-z$$ direction
3. $$E/(mv)$$ in the $$+z$$ direction
4. $$E/(qv)$$ in the $$-z$$ direction
5. $$E/(qv)$$ in the $$+z$$ direction
7. Which of the following changes would not increase the magnitude of the magnetic field inside a solenoid?
1. Increasing the number of turns of wire per unit length
2. Increasing the current
3. Lengthening the solenoid
4. Increasing the radius of the solenoid
5. All of the above would increase the magnetic field strength
8. You draw an Amperian loop around two wires carrying a current of the same magnitude in opposite directions. What can be said of the magnetic field at any point on the loop?
1. It is zero at all points on the loop
2. It is nonzero at all points on the loop
3. It depends on whether a net electric charge is present in the region
4. Ampere's law is incorrect in these circumstances
9. You bring a wire with a current of 1 milliamp towards a parallel wire with current 2 milliamps in the opposite direction. When the wires are 8 centimeters apart, what is the force per unit length between them in Newtons per meter?
1. $$3.1 \cdot 10^{-6}$$
2. $$4.9 \cdot 10^{-6}$$
3. $$3.1 \cdot 10^{-11}$$
4. $$3.9 \cdot 10^{-13}$$
5. $$5.0 \cdot 10^{-12}$$
10. Your silly friend tells you that he has discovered a magnetic field with field lines that point radially outward from a single point, just like the electric field from a point charge. Assuming your friend has not discovered a never-before-seen magnetic field source, which of Maxwell's equations does your friend's apparent discovery violate?
1. $$\iint E \cdot dA = q / \varepsilon$$
2. $$\iint B \cdot dA = 0$$
3. $$\oint E \cdot ds = - \frac{d}{d t} \Phi_B$$
4. $$\oint B \cdot ds = \mu I$$
5. Your friend isn't actually so silly
11. A closed loop wire of resistance $$R$$ and area $$A$$ is placed in a horizontal plane that is situated in a magnetic field described by $$B(t) = B_0 \sin(\omega t)$$. The magnetic field is perpendicular to the horizontal plane. What is the maximum instantaneous current in the loop?
1. $$A B_0 \cos(\omega) / R$$
2. $$A B_0 \sin(\omega) / R$$
3. $$A B_0 \omega / R$$
4. $$A B_0 R \omega$$
5. $$A B_0 / (\omega R)$$
12. A wire carries a current toward the top of the page. An electron is located to the right of the wire. In which direction should the electron be moving if it is to experience a magnetic force toward the wire?
1. Into the page
2. Out of the page
3. Toward the bottom of the page
4. Toward the top of the page
5. To the right
13. Magnetic field lines differ from electric field lines in that:
1. They are lines along which the magnitude of the field is constant
2. They have no associated direction
3. They are always circular
4. Their density conveys the magnitude of the field in a region
5. In reality they are always closed loops
14. A beam of electrons has speed $$107 m/s$$. It is desired to use the magnetic field of the Earth, $$5 \cdot 10^{–5} T$$, to bend the electron beam into a circle. What will be the radius of this circle?
1. One nanometer
2. One micrometer
3. One millimeter
4. One meter
5. One kilometer
15. A rectangular loop of wire in the plane of the page has dimensions $$a$$ by $$b$$ and includes a resistor $$R$$. The a length pieces of wire lie parallel to the $y$-axis, and the $$b$$ length pieces lie parallel to the $x$-axis. This loop is pulled with speed $$v$$ in uniform magnetic field $$B$$ pointing in the $$+z$$ direction. What is the magnitude and direction of the current through the resistor?
1. $$B a v / R$$, counterclockwise
2. $$B b v / R$$, counterclockwise
3. $$B a v / R$$, clockwise
4. $$B b v / R$$, clockwise
5. $$B b a / R$$, clockwise
16. You increase $$b$$ in the loop in problem 13, but keep $$a$$ the same. Which of the following changes occurs?
1. The current remains in the loop for more time
2. The current remains in the loop for less time
3. The current increases more rapidly
4. The current increases more slowly
5. The magnitude of the current increases
17. You increase $$a$$ in the loop in problem 13, but keep $$b$$ the same. What happens to the power dissipated in the resistor?
1. It increases
2. It remains the same
3. It decreases
4. It initially increases, then decreases
5. It initially decreases, then increases
18. The electromotive force is defined as which of the following?
1. The force required to move a test charge around a closed loop.
2. The force per unit charge required to move a test charge around a closed loop.
3. The work required to move a test charge around a closed loop.
4. The work per unit charge required to move a test charge around a closed loop.
5. The net force on a loop of wire in a magnetic field.
19. You are given a transformer containing two parallel solenoids, $$A$$ and $$B$$. $$A$$ has a set voltage and induces a voltage in $$B$$. You want to increase the current generated in $$B$$. Which of the following changes will accomplish this?
1. Decreasing the number of turns in $$A$$
2. Decreasing the number of turns in $$B$$
3. Removing the iron core from the transformer
4. Replacing the iron core with an aluminum one
5. None of the above
20. A current of uniform density flows through the plane of this page, from the bottom of the page to the top (assume you are an observer looking down at the page). What is the direction of the magnetic field generated by this current?
1. To your right in all of space
2. To your left in all of space
3. To your right above the page, to your left below it
4. To your left above the page, to your right below it
5. Parallel to the current
21. You want to generate a current from a source of mechanical energy. Which of the following laws may be invoked to create a device that does this?
1. Ampere's Law
2. The Biot-Savart Law
3. Faraday's Law
4. Gauss's Law
5. Coulomb's Law
22. A uniform magnetic field increases from $.05 T$ to $.10 T$ in ten seconds. A circular loop of wire of radius 1m exists perpendicular to this field. If this loop has resistance $$5 \Omega$$, how much energy in Joules will be lost in the resistor as the magnetic field increases?
1. $$1 \cdot 10^{-4}$$
2. $$5 \cdot 10^{-3}$$
3. $$1 \cdot 10^{-3}$$
4. $$5 \cdot 10^{-2}$$
5. $$1 \cdot 10^{-2}$$
23. Let $$r$$ be the distance from the central axis of a cylindrical wire. The magnetic field inside such a wire with uniform current density varies with:
1. $$r$$
2. the square of $$r$$
3. the inverse of $$r$$
4. the inverse of $$r^2$$
5. Nothing, the magnetic field inside the wire is constant
24. In a motor, the torque that creates mechanical energy is created by:
1. A positively charged object in a magnetic field
2. A negatively charged object in a magnetic field
3. A distribution of positive charge in an electric field
4. A distribution of negative charge in an electric field
5. A current in a magnetic field
25. In order to use Ampere's law to analytically derive the magnetic field from a solenoid, what shape should you make your Amperian loop?
1. A circle
2. An ellipse
3. A rectangle
4. An infinite line
5. A parabola
26. A wire bent at a $$90^\circ$$ angle carries a current $$I$$. It is directed down the $y$-axis and then to the right along the $x$-axis. The magnetic field at a point equidistant from both wires in the first quadrant:
1. Is a function of $$I$$ but not the distance from the wires
2. Is parallel to the diagonal
3. Is equal to zero
4. Is in the $+z$-direction
5. Is in the $-z$-direction
27. Although useful in different situations, Coulomb's law and Gauss's law encode the same information about a system. Which of Maxwell's equations encodes the same information as the Biot-Savart Law?
1. $$\iint E \cdot dA = q / \varepsilon$$
2. $$\iint B \cdot dA = 0$$
3. $$\oint E \cdot ds = - \frac{d}{d t} \Phi_B$$
4. $$\oint B \cdot ds = \mu I$$
5. None of them
28. Two long parallel wires carry currents in opposite directions. The first wire carries a current $$+I$$, while the second wire carries a current $$+3 I$$. At what fraction of the distance between the wires is the magnetic field zero, starting from the $$+I$$ wire?
1. $$\frac14$$
2. $$\frac13$$
3. $$\frac12$$
4. $$\frac23$$
5. $$\frac34$$
29. As one moves farther away from a charged object, the electric field approaches that of a point charge. As one moves farther away from a magnetic field source, the magnetic field approaches that of a…
1. Toroid
2. Solenoid
3. Infinitely long wire
4. Magnetic monopole
5. Magnetic dipole (ie a small bar magnet)

## Solutions

### Multiple Choice

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