Phy207 Exam I (Form1) Professor Zuo Fall Semester Signature: Name:

Transcription

1 Phy207 Exam I (Form1) Professor Zuo Fall Semester 2015 On my honor, I have neither received nor given aid on this examination Signature: Name: ID number: Enter your name and Form 1 (FM1) in the scantron sheet. Attempt all problems. Multiple choice questions 1-14 are worth 5pts each and the essay problem 15 is worth 30 pts. This is a closed book exam, you must work independently! No collaboration is allowed. Prohibited items: any electronic devices including cell phones and calculators, pens, backpacks, notes, books. Anyone found cheating during the exam will automatically receive an F grade for the course and sent to the honor s court. Put an X next to your discussion section: [ ] Dr. Mezincescu 5P, 11:00 11:50 a.m. [ ] Dr. Zuo 5Q, 12:30 1:20 p.m. [ ] Dr. Zuo 5R, 2:00 2:50 p.m. [ ] Dr. Barnes 5S, 3:30 4:20 p.m. [ ] Dr. Barnes 5T, 5:00 5:50 p.m.

2 1. Two point charges are arranged as shown. In which region could a third charge +1 C be placed so that the net electrostatic force on the third charge be zero? A) I only B) I and II only C) III only D) I and III only II only 2. The figure below shows the electric field lines of two charges. Which of the following describes possible values of the charges (left, right)? A) (+32nC, -8nC) B) (+32nC, -4nC) C) (-16nC, +2nC) D) (+16nC, +4nC) (+12nC, -4nC) 3. Positive charge +Q is uniformly distributed on the upper half of a semicircular rod and negative charge Q is uniformly distributed on the lower half. What is the direction of the electric field at point P, the center of the semicircle? A) Zero B) C) D)

3 4. The diagrams show four possible orientations of an electric dipole in a uniform electric field Rank them according to the magnitude of the torque exerted on the dipole by the field, least to greatest. A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1, 2, 4, 3 D) 3, then 2 and 4 tie, then 1 1, then 2 and 4 tie, then 3 5. Consider Gauss law:. Which of the following is true? A) must be the electric field due to the enclosed charge B) If q = 0 then 0 everywhere on the Gaussian surface C) If the three particles inside have charges of +q, +q and 2q, then the integral is zero D) On the surface is everywhere parallel to If a charge is placed outside the surface, then it cannot affect at any point on the surface 6. Two large insulating parallel plates carry positive charge of equal magnitude that is distributed uniformly over their inner surfaces. Rank the points 1 through 5 according to the magnitude of the electric field at the points, least to greatest. A) 1, 2, 3, 4, 5 B) 5, 4, 3, 2, 1 C) 1 and 4 and 5 tie, then 2 and 3 tie D) 2 and 3 tie, then 1 and 4 tie, then 5 2 and 3 tie, then 1 and 4 and 5 tie

4 For the next three questions, consider that a total positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer radius R2. A particle with charge q is placed at the center of the cavity. 7. The magnitude of the electric field at a point inside the cavity, a distance r from the center, is: A) B) C) q/40r 2 D) (q + Q)/40r 2 R 2 R 1 q 8. The Surface charge density at the inner surface of the conducting shell R1 is given by: A) 0 B) C) D) None of above 9. The magnitude of the electric field outside the shell at a distance r from the center is given by A) Q/40r 2 B) q/40r 2 C) (q + Q)/40r 2 D)

5 For the next five questions, consider a uniformly charged disk of radius R. The total charge on the disk is Q. To find the electric field at a point P (x>0) on the x-axis which is perpendicular to the disk with the origin at the center of the disk, it is necessary to consider the contribution from an infinitesimally thin ring of radius a and width da on the disk, as shown. 10) What is the surface charge density on the disk? A) /2 B) / C) / D) 3/4 / 11) The charge dq on the infinitesimal ring of radius a and width da is given by A) B) 2 C) Q D) 12) The electric field at point P due to this ring is given by A) B) C) D) 13) Using the result above, the total electric field can be calculated to be A) / B) 21 / C) / D) 2/ None of above 14) In the limit of, the electric field can be reduced from above to be A) 0 B) C) 2 D) 4 None of above

6 [15] A very long solid insulating cylinder of radius R carries a volume charge density where is a positive constant and r is the distance from the axis. A) Find the total charge per unit length along the axis direction of the cylinder (hint: find the charge contained in an infinitesimal cylindrical shell first). B) Find the electric field E(r) everywhere (r<r and r>r). C) Graph qualitatively E(r) as a function of r. A) Consider the charge inside an infinitesimal R cylindrical shell of radius r and thickness dr dq= 2 2 Total charge per unit length is then B) The Gaussian surface here should be a concentric cylindrical surface because of the charge symmetry. For points outside, the charge enclosed is the total charge above 2 = 3 For points inside, charge enclosed is only part of the total charge C) 3 E(r) R r