Physics 102 Homework #9Due Noon, Tuesday, March 30, 2010

. . . .Reading:

This week: Knight, Jones, & Field §20.6, §21.1-21.7Next week: Knight, Jones, & Field §21.8-21.9, §22

. . . .

Problems: Four problems will be selected at random from among those problems indicatedwith asterisks for grading. You need not to submit solutions to the non-asterisk problems.

1. * Each figure below shows two small charged spheres surrounded by a thick hollowconducting metal sphere. In figure (a) the small spheres are oppositely charged; infigure (b) they have the same charge. In each case, the conducting metal sphere isneutral (no net charge). Make a copy of each figure on your homework paper. Addpluses and minuses to the figure to show the charge distribution within the conductor.Sketch the electric fields, if any, both inside and outside the sphere.

(a)

ConductingMetal Sphere

(b)

ConductingMetal Sphere

2. (a) KJF Problem 20.33.(b) Where is the electric field strongest?

(Answers at the end of this assignment.)

3. * The last page of this assignment has a topographic map of the area around theBryn Mawr campus. Remove this page from the assignment paper and submit it aspart of your homework solution. Extra copies of the topographic map are available inthe “returned homework” bin in the hall near my office and can also be obtained bydownloading and printing a copy of this assignment from the course website.

Lines on the map indicate points of constant elevation. Elevations are given in feet.For this problem, interpret the elevation contours are equipotentials associated withan electric charge distribution.

Draw the following things on the map.

(a) At a place where the electric field points to the east, draw an arrow indicatingthe direction of ~E and label it “E.”

(b) At a place where the electric field points to the west, draw an arrow indicatingthe direction of ~E and label it “W.”

(c) At a place where the electric field points to the south, draw an arrow indicatingthe direction of ~E and label it “S.”

(d) At a place where the electric field points to the north, draw an arrow indicatingthe direction of ~E and label it “N.”

(e) At a place where ~E is zero, draw a dot and label it “0.”(f) At the place where |E| is maximum, draw an arrow indicating the direction of

~E and label it “max.” (If you aren’t sure about the absolute maximum on thegraph, at least find a place where it is very large.)

Notes: (i) There are many possible answers. (ii) Background colors on the maphave the following meanings: green indicates wooded areas; pink indicates urban andresidential areas in which not all buildings are drawn; and white indicates everythingelse. Ignore these colors while working the problem.

4. * Four charges are located at the corners of a square. The upper left and lowerright corners have charge +q. The upper right and lower left corners have charge−q. Sketch the equipotentials. Draw negative equipotentials as dashed lines, positiveequipotentials as solid lines, and zero potential as a heavy solid line.

5. * In last week’s homework, you sketched the field lines around two charges, q1 =−0.6 µC and q2 = +1.8 µC, located 15 cm apart, with q1 to the left of q2. Make a newcopy of that sketch (with the field lines), and add to it the pattern of equipotentiallines around these charges. Draw negative equipotentials as dashed lines, positiveequipotentials as solid lines, and zero potential as a heavy solid line. (This is a lot ofinformation to put on a single plot, so make it large and draw with some care.)

6. Some region has a uniform electric field 10.0 V/m due east. An object with charge−50.0 nC is in the field. The object is moved by an external force 1.0 m north, then5.0m east, then 2.0m south, and finally 5.0 m east. The object begins and ends its thismotion with zero velocity. What is the change in potential it experiences? How muchwork was done on it by the external force? (Answer at the end of this assignment.)

7. * KJF Multiple-Choice Questions 21.23 through 21.27.

8. KJF Problem 21.72. (Answer at the end of this assignment.)

9. KJF Problem 21.5.

10. * KJF Problem 21.56.

11. KJF Conceptual Question 21.9.

12.(a,b) KJF Problem 21.55.(c) If the proton is released from rest at point A, will it fly away from the charges,

or fly toward one of the charges, or what?

13. KJF Problem 21.25.

Answers to selected problems:

(2) a. b. Just above and below the sphere.

(6) 100 V, 5.0× 10−6 J.(8) The drawing doesn’t give enough information to determine precise values. Estimatedvalues of ~E are around 40 V/cm down at point 1 and 75 V/cm up at point 2.