Phy207 Exam I (Form1) Professor Zuo February 16, Signature: Name:

Transcription

1 Phy207 Exam I (Form1) Professor Zuo February 16, 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 are worth 5pts each and the essay problem is 30 pts. There is a formula sheet attached the end. 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.

2 1) A charge q is placed at x=0 and another charge 9q is placed at x=l. Find the point on the axis where the electric field is zero. A) x= L/2 B) x=l/2 C) X=L/4 and x= L/2 D) X=L/4 E) x=3l/4 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) E) (12nC, 4nC) 3) A conducting spherical shell of inner radius a and outer radius b carries a total charge of 2q. There is a q at the center of the cavity. What is the surface charge density at the outer surface? A) 0 B) /4 C) 2/4 D) 3/4 E)/4 4) If the potential in a region is given by V(x,y,z) = xy 3z 2, then the z component of the electric field in that region is A) y B) x C) x + y D) 6z 3 E) None of above 5) If a conductor has a surface charge density at a given point, the electric field just outside the surface is given by: A) /2 B) / C) 0 D) E) Not enough info is given

3 [6] A solid conducting sphere of radius R carries a positive charge and is very far from any other charges. Which one of the following graphs best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere? [7] Three equal charges of q each are placed on an equilateral triangle of side length l, what is the electric potential energy of the system? A) B) C) D) E) None of above [8] A uniform electric field is directed along the x axis from left to right, so E x = 500 V/m. An electron at rest is released from x=0, what is the kinetic energy of the electron at x = 2 m? A) 2000 ev B) 1000 ev C) 500 ev D) 0 ev E) 1000 ev

4 For the next six problems, consider a uniformly charged disk of radius R. The total charge on the disk is Q. To find the electric potential and 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. 9) What is the surface charge density on the disk? A) /2 B) / C) / D) 3/4 E) / 10) The charge dq on the infinitesimal ring of radius a and width da is given by A) B) 2 C) Q D) E) 11) The electric potential at point P due to this ring is given by A) / B) C) / D) E) 12) Using the result above, the total potential can be calculated to be A) / B) 2 C)/ D) 2/ E) None of above 13) From electric potential, the electric field can be easily obtained to be A) / B) 21 / C) / D) / E) 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 E) None of above

5 [15] A solid insulating sphere of radius R carries a volume charge density 1 where is a positive constant. A) Find the total charge contained by the sphere. B) Find the electric field everywhere (r<r and r>r). C) Graph qualitatively the E(r) as a function of r. D) Find the electric potential for a point inside the sphere V(r<R) assuming V(r= ) = 0. Solution: A) For spherical charge distribution, the total charge can be calculated by summing the contributions from infinitesimal spherical shells Some might find it unbelievable, how is it possible that the total charge is zero!!! If you examine the density expression, it should not be surprising since the charge density changes sign inside the sphere. B) For points outside the sphere, E=0, since there are no net charge enclosed by any Gaussian surface for r>r. For points inside the sphere, the total charge enclosed is not the total charge but a fraction of it The electric field is then given by C)

6 A plot of the function (x x 2 /5) is shown above, assuming R=5. It shows the electric field has a maximum at R/2, but always positive. D) The electric potential is zero outside the sphere. Inside the sphere, it can be calculated by