1. A proton is traveling to the left when it enters the space between two oppositely charged parallel plates, as shown above. Which of the four labeled paths will the proton take?
2. The figures above represent two fields. The figure on the left represents the uniform gravitational field very near Earth’s surface. The figure on the right represents the uniform electric field E near the center of the region between very large parallel plates. Which of the following describes the shape of the isolines of potential for the gravitational field and the electric field in these regions?
(A) Isolines are straight, vertical lines for both the gravitational and electric fields.
(B) Isolines are straight, horizontal lines for both the gravitational and electric fields.
(C) Gravitational isolines are straight, while electric isolines are curved.
(D) Gravitational isolines are curved, while electric isolines are straight.
3. The figure above shows a model of an electromagnetic wave, where E is the electric field and B is the magnetic field. In what direction is the energy of the wave transmitted?
(A) Along the x-axis only
(B) Along the y-axis only
(C) Along the z-axis only
(D) In a direction that is at a nonzero angle to each of the axes
4. Three identical conducting spheres, S1, S2, and S3, are supported by insulating thread, as shown above. Initially, sphere S1 has a net positive charge and the other two spheres are uncharged. Spheres S1 and S2 are brought into contact and then separated. Next, spheres S2 and S3 are brought into contact and then separated. Which of the following shows the signs of the final net charges on the spheres?
Questions 5-7 refer to the following material.
The circuit shown above contains four identical lightbulbs with constant resistance, a capacitor C, which is initially uncharged, and a switch S. The switch is initially open.
5. Which of the following correctly ranks the potential differences △V1 , △V2 , △V3 , and △V4 across the bulbs while the switch is open?
(A) △V1 = △V2 = △V3 = △V4
(B) △V1 ＞ △V2 = △V3 = △V4
(C) △V1 ＞ △V2 ＞ △V3 = △V4
(D) △V1 ＞ △V2 ＞ △V3 ＞ △V4
1. (10 points, suggested time 20 minutes)
Three samples of a gas, X, Y, and Z, are prepared. Each sample contains the same number of molecules, but the samples are at different temperatures. The temperature of sample X is TX , the temperature of sample Y is lower than that of sample X, and the temperature of sample Z is lower than that of sample Y (TX > TY > TZ) .
(a) The graph below shows the distribution of the speeds of the molecules in sample Y. On the graph, sketch and label possible distributions for sample X and sample Z.
The three samples with initial temperatures TX > TY > TZ are placed in thermal contact, with sample Z in the middle, as shown below, and the samples are insulated from their surroundings. The samples can exchange thermal energy but not gas molecules. The samples eventually reach equilibrium, with a final temperature greater than TY .
X Z Y
(b) In a few sentences, describe the change over time in the average kinetic energy of the molecules of each sample, from initial contact until they reach equilibrium. Explain how these changes relate to the energy flow between the pairs of samples that are in contact.
(c) Indicate whether the net entropy of sample X increases, decreases, or remains the same as a result of the process of reaching equilibrium.
____ Increases ____ Decreases ____ Remains the same
(d) For the three-sample system, indicate whether the entropy of the system increases, decreases, or remains the same.
____ Increases ____ Decreases ____ Remains the same
2. (12 points, suggested time 25 minutes)
Students are given some resistors with various resistances, a battery with internal resistance, and an ammeter. They are asked to determine the emf e and internal resistance r of the battery using just this equipment. Working with the circuit shown above, they insert each resistor into the circuit and measure the current I in the circuit each time they insert a resistor. From their data, the students generate a graph of 1/I as a function of the resistance R of each resistor, as shown above.
i. Write an algebraic equation describing the circuit that includes ε , R, r, and I.
ii. Use your equation and the graph to calculate the emf of the battery and the internal resistance of the battery.
The students are now given a voltmeter and a new resistor X to use with the resistors, battery, and ammeter they already have. They are asked to determine whether resistor X is ohmic.
i. Using standard symbols for circuit elements, as in the previously shown circuit, draw a diagram of a circuit that the students could use to determine whether resistor X is ohmic, including the appropriate placement of the meters. Clearly label your diagram.
ii. Describe the procedure you would use with your circuit to get enough data to determine whether resistor X is ohmic.
iii. What would you graph using your data, and what would you look for on your graph to determine whether resistor X is ohmic?
(c) Would your procedure or data analysis in part (b) need to be different if the internal resistance of the battery was nonohmic? Justify your answer.