1.(10 points, suggested time 20 minutes)
The figure above shows a particle with positive charge +Q traveling with a constant speed v0 to the right and inthe plane of the page. The particle is approaching a region, shown by the dashed box, that contains a constantuniform field. The effects of gravity are negligible.
（a）i. On the figure below, draw a possible path of the particle in the region if the region contains only an electric field directed toward the bottom of the page.
ii. On the figure below, draw a possible path of the particle in the region if the region contains only a magnetic field directed out of the page.
iii.For which of the previous situations is the motion more similar to that of a projectile in only agravitational field near Earth’s surface, and why?
(b) Another region of space contains an electric field directed toward the top of the page and a magnetic field directed out of the page. Both fields are constant and uniform. A horizontal beam of protons with a variety of speeds enters the region, as shown above. Protons exit the region at a variety of locations, including points 1 and 2 shown on the figure. In a coherent, paragraph-length response, explain why some protons exit the region at point 1 and others exit at point 2. Use physics principles to explain your reasoning.
2. (12 points, suggested time 25 minutes)
The two circuits shown above contain an ideal variable power supply, an ohmic resistor of resistance R, an ammeter A, and two voltmeters VPS and VR. In circuit 1 the ammeter has negligible resistance, and in circuit 2 the ammeter has significant internal ohmic resistance r. The potential difference of the power supply is varied, and measurements of current and potential difference are recorded.
(a) The axes below can be used to graph the current measured by the ammeter as a function of the potential difference measured across the power supply. On the axes, do the following.
•Sketch a possible graph for circuit 1 and label it 1.
•Sketch a possible graph for circuit 2 and label it 2.
(b) Let △VPS be the potential difference measured by voltmeter VPS across the power supply, and let I be the current measured by the ammeter A. For each circuit, write an equation that satisfies conservation of energy,in terms of △VPS, I, R, and r, as appropriate.
Circuit 1 Circuit 2
(c) Explain how your equations in part (b) account for any differences between graphs 1 and 2 in part (a).
(d) In circuit 2,R=40Ω. When voltmeter VPS reads 3.0 volts, voltmeter VR reads 2.5V. Calculate the internal resistance r of the ammeter.
(e) Voltmeter VR in circuit 2 is replaced by a resistor with resistance 120Ω to create circuit 3 shown below. Voltmeter VPS still reads 3.0V.
i. Calculate the equivalent resistance uppercase Req of the circuit.
ii. Calculate the current in each of the resistors that are in parallel.