PHYS 1102 EXAM
Spring 2008
PHYS 1102 EXAM - II SECTION: (Circle one) 001 (TH 9:30 AM to 10:45AM) 002 (TH 3:30 PM to 4:45 PM)
Your Name:
Student ID:
You have 1 hr 45 minutes to complete the test PLEASE DO NOT START TILL YOU ARE INSTRUCTED TO DO SO
You must show all your work on the answer sheets provided to get full credit. NO OTHER SHEET IS TO BE ATTACHED TO YOUR ANSWERS.
All multiple choice questions are 5 points each. For questions 15 -17 Draw clear well labeled diagrams and show the chosen coordinate system, wherever applicable Write down known parameters Determine the physical principles that apply Work out the problem algebraically, showing all your steps neatly. (show all your steps to get full credit) Give reasons for your answers Put a Box around your final answers Points will be deducted for answers without units or with incorrect units.
-1-
Spring 2008
1. When a light bulb is connected to a 4.5 V battery, a current of 0.16 A passes through the bulb filament. What is the resistance of the filament? (a) 440 Ω (b) 9.3 Ω (c) 0.72 Ω (d) 28 Ω (e) 1.4 Ω 2. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? (a) It is a maximum if the particle is stationary. (b) It is zero if the particle moves perpendicular to the field. (c) It is a maximum if the particle moves parallel to the field. (d) It acts in the direction of motion for a positively charged particle. (e) It depends on the component of the particle's velocity that is perpendicular to the field. 3. An electron traveling due south enters a region that contains a uniform magnetic field that points due east. In which direction will the electron be deflected? (a) east (b) west (c) up (d) down (e) south 4. A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure. Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. What is the direction of the net magnetic force that acts on the loop? 1.20 m y (a) (b) (c) (d) (e)
+x direction –x direction +y direction –y direction 30° with respect to the +x direction
10.0 A
x
2.00 A 1.00 m
5. Two loops carry equal currents I in the same direction. The loops are held in the positions shown in the figure and are then released. Which one of the following statements correctly describes the subsequent behavior of the loops? (a) Both loops move to the left. (b) The loops remain in the positions shown. (c) The top loop moves to the right; the bottom loop moves to the right. (d) The loops repel each other. (e) The loops attract each other.
-2-
I
I
Spring 2008
6. Two long, straight wires are perpendicular to the plane of the paper as shown in the drawing. Each wire carries a current of magnitude I. The currents are directed out of the paper toward you. Which one of the following expressions correctly gives the magnitude of the total magnetic field at the origin of the x, y coordinate system? μ I (a) B = 0 2d y μ I (b) B = 0 2d μ0 I d (c) B = 2πd x μ I O (d) B = 0 d πd μ I (e) B = 0 2πd 7. The figure shows a uniform magnetic field that is normal to the plane of a conducting loop, which has a resistance R. Which one of the following changes will cause an induced current to flow through the resistor? x x x x x (a) decreasing the area of the loop (b) decreasing the magnitude of the magnetic field x x x x x (c) increasing the magnitude of the magnetic field (d) rotating the loop through 90° about an axis in the plane of the x x x x x paper (e) all of the above R x
x
x
x
8. In the figure the bar is in contact with a pair of rails and is in motion with velocity v. A uniform magnetic field (pointing downward) is present. The induced current through the resistor R is (a) From b to a (clockwise) (b) Zero (c) From a to b (counterclockwise)
v
B
R
-3-
x
Spring 2008
The figure shows a simple RC circuit consisting of a 10.0-µF capacitor in series with a resistor. Initially, the switch is open as suggested in the figure. The capacitor has been charged so that the potential difference between its plates is 100.0 V. At t = 0 s, the switch is closed. The capacitor discharges exponentially so that 2.0 s after the switch is closed, the potential difference between the capacitor plates is 37 V. In other words, in 2.0 s the potential difference between the capacitor plates (hence its charge) is reduced to 37 % of its original value.
R
10 µF
Switch
9. Calculate the electric potential energy stored in the capacitor before the switch is closed. (a) 0.01 J (b) 0.02 J (c) 0.03 J (d) 0.04 J (e) 0.05 J 10. Determine the numerical value of the resistance R. (a) 1.0 × 105 Ω (b) 2.0 × 105 Ω (c) 5.0 × 105 Ω (d) 1.0 × 106 Ω (e) 2.5 × 106 Ω
BONUS questions 11. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero magnetic field directed eastward is then applied to the region. In what direction, if any, will each electron be moving after the field is applied? electron A electron B (a) at rest westward (b) northward eastward (c) at rest eastward (d) southward downward, toward the earth (e) upward, away from earth westward
The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of 1.5 Ω and a radius of 0.024 m. The magnetic field is • • • • • • • • directed out of the paper as shown. Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular • • • • • • • • B R loop. 12. What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s? (a) 2.8 x 10–3 A, clockwise (b) 4.5 x 10–3 A, clockwise (c) 4.5 x 10–3 A, counterclockwise (d) 9.0 x 10–3 A, clockwise (e) 9.0 x 10–3 A, counterclockwise
-4-
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Spring 2008
13. If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, what is the magnitude of the average induced emf in the loop? (a) 8.6 x 10–3 V (b) 9.8 x 10–2 V (c) 2.7 x 10–2 V (d) 5.4 x 10–2 V (e) 6.4 x 10–2 V
14. If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, at what rate is energy dissipated in R? (a) 1.8 x 10–2 W (b) 3.6 x 10–2 W (c) 3.8 x 10–3 W (d) 2.7 x 10–4 W (e) 4.9 x 10–4 W
-5-
Spring 2008
15. For the circuit shown below (a) Write down three equations using Kirchoff’s loop rule (for loop ABEF and loop BCDE) and junction rule (at junction B). (b) Solve the above equations to determine the magnitude of the potential difference across the 5.0 resistor in the drawing (V1 = 7.0 V and V2 = 16.0 V). (c) Which end of the resistor is at the higher potential (i.e. left end or right end) ? (15 points)
-6-
Spring 2008
16. In the circuit below, all bulbs are identical (i.e. they have the same filament resistance, R) (a) Find the current through each of the bulbs in term of the battery voltage ‘V’ and the resistance of each bulb ‘R’ (or use V = 120Volts, R = 60Ω ). Label the currents IA, IB, IC, …etc. (b) Rank the brightness of the bulbs in order, from most to least bright. Explain briefly the reason for your ranking. (c) If bulb C is removed from its socket what happens to the brightness of each of the remaining bulbs (A, B, D). Explain with reasons or show calculations in support of your answer. (20 points)
A
B
C
D
-7-
Spring 2008
17. A positively charged particle of mass 6.40 10-8 kg is traveling due east with a speed of 30 m/s and enters a 0.32 T uniform magnetic field (shaded square region). The particle moves through onequarter of a circle in a time of 5.80 10-3 s, at which time it leaves the field heading due south. All during the motion the particle moves perpendicular to the magnetic field. (a) Determine the direction of the magnetic field and show it on the diagram (i.e. is it pointing left, right, up, down, into or out of the page?) (out of page) (b) determine the radius of the particle’s circular path. (0.111 m) (c) Calculate what must be the centripetal force required to keep this particle moving in its circular path ? (d) What is the magnitude of the magnetic force acting on the particle? 0.00052 N (e) What is the magnitude of the charge on the particle? 5.42e-05 C (15 points)
v
-8-
PHYS 1102 EXAM - II SECTION: (Circle one) 001 (TH 9:30 AM to 10:45AM) 002 (TH 3:30 PM to 4:45 PM)
Your Name:
Student ID:
You have 1 hr 45 minutes to complete the test PLEASE DO NOT START TILL YOU ARE INSTRUCTED TO DO SO
You must show all your work on the answer sheets provided to get full credit. NO OTHER SHEET IS TO BE ATTACHED TO YOUR ANSWERS.
All multiple choice questions are 5 points each. For questions 15 -17 Draw clear well labeled diagrams and show the chosen coordinate system, wherever applicable Write down known parameters Determine the physical principles that apply Work out the problem algebraically, showing all your steps neatly. (show all your steps to get full credit) Give reasons for your answers Put a Box around your final answers Points will be deducted for answers without units or with incorrect units.
-1-
Spring 2008
1. When a light bulb is connected to a 4.5 V battery, a current of 0.16 A passes through the bulb filament. What is the resistance of the filament? (a) 440 Ω (b) 9.3 Ω (c) 0.72 Ω (d) 28 Ω (e) 1.4 Ω 2. Which one of the following statements concerning the magnetic force on a charged particle in a magnetic field is true? (a) It is a maximum if the particle is stationary. (b) It is zero if the particle moves perpendicular to the field. (c) It is a maximum if the particle moves parallel to the field. (d) It acts in the direction of motion for a positively charged particle. (e) It depends on the component of the particle's velocity that is perpendicular to the field. 3. An electron traveling due south enters a region that contains a uniform magnetic field that points due east. In which direction will the electron be deflected? (a) east (b) west (c) up (d) down (e) south 4. A long, straight wire carries a 10.0-A current in the +y direction as shown in the figure. Next to the wire is a square copper loop that carries a 2.00-A current as shown. The length of each side of the square is 1.00 m. What is the direction of the net magnetic force that acts on the loop? 1.20 m y (a) (b) (c) (d) (e)
+x direction –x direction +y direction –y direction 30° with respect to the +x direction
10.0 A
x
2.00 A 1.00 m
5. Two loops carry equal currents I in the same direction. The loops are held in the positions shown in the figure and are then released. Which one of the following statements correctly describes the subsequent behavior of the loops? (a) Both loops move to the left. (b) The loops remain in the positions shown. (c) The top loop moves to the right; the bottom loop moves to the right. (d) The loops repel each other. (e) The loops attract each other.
-2-
I
I
Spring 2008
6. Two long, straight wires are perpendicular to the plane of the paper as shown in the drawing. Each wire carries a current of magnitude I. The currents are directed out of the paper toward you. Which one of the following expressions correctly gives the magnitude of the total magnetic field at the origin of the x, y coordinate system? μ I (a) B = 0 2d y μ I (b) B = 0 2d μ0 I d (c) B = 2πd x μ I O (d) B = 0 d πd μ I (e) B = 0 2πd 7. The figure shows a uniform magnetic field that is normal to the plane of a conducting loop, which has a resistance R. Which one of the following changes will cause an induced current to flow through the resistor? x x x x x (a) decreasing the area of the loop (b) decreasing the magnitude of the magnetic field x x x x x (c) increasing the magnitude of the magnetic field (d) rotating the loop through 90° about an axis in the plane of the x x x x x paper (e) all of the above R x
x
x
x
8. In the figure the bar is in contact with a pair of rails and is in motion with velocity v. A uniform magnetic field (pointing downward) is present. The induced current through the resistor R is (a) From b to a (clockwise) (b) Zero (c) From a to b (counterclockwise)
v
B
R
-3-
x
Spring 2008
The figure shows a simple RC circuit consisting of a 10.0-µF capacitor in series with a resistor. Initially, the switch is open as suggested in the figure. The capacitor has been charged so that the potential difference between its plates is 100.0 V. At t = 0 s, the switch is closed. The capacitor discharges exponentially so that 2.0 s after the switch is closed, the potential difference between the capacitor plates is 37 V. In other words, in 2.0 s the potential difference between the capacitor plates (hence its charge) is reduced to 37 % of its original value.
R
10 µF
Switch
9. Calculate the electric potential energy stored in the capacitor before the switch is closed. (a) 0.01 J (b) 0.02 J (c) 0.03 J (d) 0.04 J (e) 0.05 J 10. Determine the numerical value of the resistance R. (a) 1.0 × 105 Ω (b) 2.0 × 105 Ω (c) 5.0 × 105 Ω (d) 1.0 × 106 Ω (e) 2.5 × 106 Ω
BONUS questions 11. Two electrons are located in a region of space where the magnetic field is zero. Electron A is at rest; and electron B is moving westward with a constant velocity. A non-zero magnetic field directed eastward is then applied to the region. In what direction, if any, will each electron be moving after the field is applied? electron A electron B (a) at rest westward (b) northward eastward (c) at rest eastward (d) southward downward, toward the earth (e) upward, away from earth westward
The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of 1.5 Ω and a radius of 0.024 m. The magnetic field is • • • • • • • • directed out of the paper as shown. Note: The area of the non-circular portion of the wire is considered negligible compared to that of the circular • • • • • • • • B R loop. 12. What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s? (a) 2.8 x 10–3 A, clockwise (b) 4.5 x 10–3 A, clockwise (c) 4.5 x 10–3 A, counterclockwise (d) 9.0 x 10–3 A, clockwise (e) 9.0 x 10–3 A, counterclockwise
-4-
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Spring 2008
13. If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, what is the magnitude of the average induced emf in the loop? (a) 8.6 x 10–3 V (b) 9.8 x 10–2 V (c) 2.7 x 10–2 V (d) 5.4 x 10–2 V (e) 6.4 x 10–2 V
14. If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, at what rate is energy dissipated in R? (a) 1.8 x 10–2 W (b) 3.6 x 10–2 W (c) 3.8 x 10–3 W (d) 2.7 x 10–4 W (e) 4.9 x 10–4 W
-5-
Spring 2008
15. For the circuit shown below (a) Write down three equations using Kirchoff’s loop rule (for loop ABEF and loop BCDE) and junction rule (at junction B). (b) Solve the above equations to determine the magnitude of the potential difference across the 5.0 resistor in the drawing (V1 = 7.0 V and V2 = 16.0 V). (c) Which end of the resistor is at the higher potential (i.e. left end or right end) ? (15 points)
-6-
Spring 2008
16. In the circuit below, all bulbs are identical (i.e. they have the same filament resistance, R) (a) Find the current through each of the bulbs in term of the battery voltage ‘V’ and the resistance of each bulb ‘R’ (or use V = 120Volts, R = 60Ω ). Label the currents IA, IB, IC, …etc. (b) Rank the brightness of the bulbs in order, from most to least bright. Explain briefly the reason for your ranking. (c) If bulb C is removed from its socket what happens to the brightness of each of the remaining bulbs (A, B, D). Explain with reasons or show calculations in support of your answer. (20 points)
A
B
C
D
-7-
Spring 2008
17. A positively charged particle of mass 6.40 10-8 kg is traveling due east with a speed of 30 m/s and enters a 0.32 T uniform magnetic field (shaded square region). The particle moves through onequarter of a circle in a time of 5.80 10-3 s, at which time it leaves the field heading due south. All during the motion the particle moves perpendicular to the magnetic field. (a) Determine the direction of the magnetic field and show it on the diagram (i.e. is it pointing left, right, up, down, into or out of the page?) (out of page) (b) determine the radius of the particle’s circular path. (0.111 m) (c) Calculate what must be the centripetal force required to keep this particle moving in its circular path ? (d) What is the magnitude of the magnetic force acting on the particle? 0.00052 N (e) What is the magnitude of the charge on the particle? 5.42e-05 C (15 points)
v
-8-
