1.(10 points, suggested time 20 minutes)The figures above show a rectangular conducting loop at three instants in time. The loop moves at a constantspeed v into and through a region of constant, uniform magnetic field B directed into the page. The magneticfield is zero outside the region.
(a) In a coherent paragraph-length response, compare the magnitude and direction of the current at times t1, t2,and t3. Include an explanation of why there is or is not a current and the direction of the current if one is present. Use fundamental physics concepts and principles in your explanation.
(b) The loop is removed. A proton traveling to the right in the plane of the page, as shown below, then enters the region of magnetic field with a speed v=3.0*105m/s. The magnitude of the field is 0.030 T. The effects of gravity are negligible.
i. Calculate the magnitude of the force on the proton as it enters the field.
ii. On the figure below, sketch a possible path of the proton as it travels through the magnetic field. Clearly label the path P1.
iii. A second proton now enters the magnetic field at the same point and from the same direction but at a greater speed than the first proton. On the figure above, draw the path of the second proton as it travels through the field. Clearly label the path P2.
iv. Next an electric field is applied in the same region as the magnetic field, such that there is no net force on the first proton as it enters the region. Calculate the magnitude and indicate the direction of the electric field relative to the coordinate system shown in part (b).
2. (12 points, suggested time 25 minutes)
Students are given resistor 1 with resistance R1 connected in series with the parallel combination of a switch S and resistor 2 with resistance R2, as shown above. The circuit elements cannot be disconnected from each other,and other circuit components can only be connected at points A and B. The students also are given an ammeter and one 9 V battery. The teacher instructs the students to take measurements that can be used to determine R1 and R2.
(a) Complete the diagram below to show how the ammeter and the battery should be connected to experimentally determine the resistance of each resistor. Describe the experiment by listing the measurements to be taken and explaining how the measurements would be used to calculate resistances R1 and R2.
Complete the Diagram Describe the Experiment
A second group of students is given a combination of circuit elements that is similar to the previous one but has an initially uncharged capacitor in series with the open switch, as shown above. The combination is placed in a circuit with a power supply so that the potential difference between A and B is maintained at 9 Volts. The students close the switch and immediately begin to record the current through point B. The initial current is 0.9 A, and after a long time the current is 0.3 A.
i. Compare the currents through resistor 1, resistor 2, and the switch immediately after the switch is closed to the currents a long time after the switch is closed. Specifically state if any current is zero.
ii. Calculate the values of R1 and R2.
iii. Determine the potential difference across the capacitor a long time after the switch is closed.
A third group of students now uses the combination of circuit elements with the capacitor. They connect it to a 9 V battery that they treat as ideal but which is actually not ideal and has internal resistance.
(c) How does the third group’s value of R1 calculated from the data they collected compare to the second group’s value? Explain your reasoning with reference to physics principles and/or mathematical models.