PHY 132 First Practice Midterm and Solutions, 2/2002 (Laszlo Mihaly)

The first midterm will be on Friday, February 22, 11:35-12:30, during lecture time. Chapters 21-25 (including) of the textbook will be covered.

The exam will be at two different places. If your given name (first name) starts with letters A to K, go to the old Student Union Auditorium. Enter under the bridge, go straight, turn left.) For first names starting with letters L-Z the exam will be in Harriman Hall. There will be assigned seating at the exam, so you MUST go to the right place, otherwise you are going to waste valuable time by walking during the exam.  Here are two examples: John Smith should go to the old Student Union. Xiuping Kong should be in Harriman. Check out the places before the exam.

Exams are closed books and notes, but you will be allowed to bring your own notes on a single sheet of regular size white paper. The text on the paper should be written with your own hand (no photographic, xerox etc. copies) and it should be readable without the use of any instruments (magnifying glass, microscope, etc). You may use both sides of the paper. Otherwise, use only the paper that is distributed in the exam room. Numerical constants needed for the exam will be printed on the exam booklet.

Bring a photo ID to the exams. Acceptable IDs: Stony Brook student ID, driver's license, green card/passport. If you do not have an ID, and you want to take the exam, we reserve the right of making a photo of you on the spot. Also bring a pen/pencil and a handheld calculator capable of doing simple arithmetic and trigonometric functions to the exam. We can not provide a replacement calculator (or allow exchange of calculators) if yours does not work or you forgot to bring one. Notebooks computers are not allowed.

No communication between students is allowed during the exams. No devices with infrared ports or any other communication options. No beepers, cell phones, buzzers, etc. Any evidence of cheating will be reported to the academic hearing officer and will also result in a stiff grade penalty. Ask for permission if you want to leave the room. Do not remove the text of the exam, or any other notes, from the room until the exam is completely over. When finished, copy all results to the front page of the exam booklet.

Grading/complaints: Problems 1,2,3: 10 points for correct answer, partial credit possible. Problems 4-7: 5 points each, no partial credit. No guessing: The graders may check your solution to see if the work handed in justifies your choices in the multiple choice questions. The solutions will be posted on the course WEB page. The graded exam will be handed back to you by your recitation instructor. If you feel that a mistake was made, return the exam and a brief written statement of your grievance to your recitation instructor. Except for trivial mistakes (like incorrect addition of the scores by the grader), the returned exam will be accepted only on the same day that you received the graded exam in recitation. Preferably, you should ask for the re-grading at the end of the recitation session. Do not change your solution in any way. The contested exams may be compared to a xerox copy made by the grader. If you make notes on the exam sheet, use a writing instrument that is very different from the pen/pencil used during the exam. If partial credit is contested, the whole exam will be re-graded. Your grade may go up, down or remain unchanged.

1. Two horizontal infinite plane sheets are separated by a distance d = 1.00cm. The lower sheet has a negative charge with uniform surface charge density -s. The upper sheet has a positive charge with uniform surface charge density +s (s = 3.6nC/m2). What is the electric field magnitude and direction
a.) below the lower sheet
b.) in between the two sheets and
c.) above the upper sheet.

a.) below the lower sheet: zero field
b.) in between the two sheets and: E=s/e0 = 406 V/m, pointing downwards
c.) above the upper sheet: zero field 2. A solid, infinite long, insulating cylinder of radius a =29cm carries a uniform volume charge density r=5.4nC/m3 .
a.) What is the electric field magnitude just outside of the surface of the cylinder?
b.) Draw a sketch of the electric field magnitude versus the distance from the center of the axis, r.
c.) Draw a similar sketch for metallic cylinder of the same total charge and radius.

a.) E = 1/2pe0l/r andl = a2p r . At the surface r = a and we get E = ra/2e0 = 88.4V/m 3. Eight point charges of equal magnitude q = 0.125nC are placed on the corners of a cube of edge a = 0.10m . Assuming that the electrostatic potential is zero at a point at infinity, what is the potential at the center of the cube? All 8 charges are of equal distance from the center. The potential is the sum of the 8 equal contributions: V = 104V 4. A spacecraft of approximately spherical shape and radius a = 10m carries a net charge of Q = 1mC. (Assume that the spacecraft is an insulator, and the charge is uniformly distributed.) A small piece of rock, mass m = 1g, is floating far away from the spacecraft, so that the relative velocity of the two objects is zero. The rock collects a negative charge of q = - 5mC, and it is attracted to the spacecraft by the electrostatic force. What will be the velocity of the rock when it hits the spacecraft?
A 30,000m/s
B 3,000m/s
C 1,500m/s
D 300m/s
E 150 m/s
F none of the above The electric potential of the spacecraft will be the same as that of a point charge, V =1/4pe0Q/r. The potential and the kinetic energy of the rock is zero when it is far away. The potential energy becomes U = -1/4pe0Qq/a when it hits the spacecraft. The kinetic energy is 1/2mv2. Using energy conservation, we get v=3,000 m/sec. 5. A parallel plate capacitor has 6.45J of energy stored in it. The separation of the plates is 1.40mm. the capacitor is disconnected from the source, so the charge on the plates remains constant. What is the energy stored in the capacitor, if the separation is decreased to 0.7mm?
A 25.8J
B 12.9J
C 6.45J
D 3.225J
E 1.61J
F none of the above With constant charge, the energy is expressed as U=(1/2) Q2/C. When the distance is decreased, the capacitance increases by a factor of two - the energy decreases to 3.225J.

6. Two conducting plates are placed one above the other inside a metal box. The equipotential lines in the Figure are of 1V separation. The lower plate is at -12V potential, The upper plate is at +12V. The electric field is approximately zero
A at point A only
B at point B only
C at point C only
D at points A and C
E none of the above

The field is close to zero in the corner, at point C. This can be seen from the drawing, since the equipotential lines are widely spaced. (The thick line representing the metallic box is also an equipotential line.) Another way of proving this: the field must be perpendicular to the metal surface. If the two surfaces meet at a right angle the field can not be perpendicular to both therefore it must be zero. 7. A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new wire compares to the resistance of the original one?
A four times smaller
B four times larger
C two times smaller
D two times larger
E same
F none of the above The length is halved, and the cross section is doubled. The resistance is four times smaller.