Physics 212 Lecture 2

1. Physics 212 Lecture 2 Today's Concept: The Electric Field Continuous Charge Distributions

2. Music • Who is the Artist? • Bill Frisell • Cindy Cashdollar • Daniel Lanois • Marc Ribot • Tony Rice Great musician/album names. All these people were at the Ellnora Guitar Festival this year. Physics 212 Lecture 2

3. Our Comments • If your TA doesn’t show up – go to undergrad office 231/3 (or home page for telephone numbers of discussion and lab masters) • Please operate only your own clicker • Unfortunately we really can’t help with PreLecture, Checkpoint or homework physics questions by email – too many students: Office Hours, CARE (see link), your friends • Fridays 2:00 – 7:00 p.m. in 271 Loomis • Sundays 2:00 – 9:00 p.m. in 143 Loomis • Mondays 11:00 a.m. – 9:00 p.m. in 143 Loomis • Quite a bit of homework this week • Don’t panic!

4. q2 q2 q1 F4,1 F4,1 F2,1 F2,1 q1 F1 F1 F1 F1 F2,1 F2,1 F3,1 F3,1 F3,1 q4 q4 F3,1 F4,1 F4,1 q3 q3 MATH: Coulomb’s Law (from last time) If there are more than two charges present, the total force on any given charge is just the vector sum of the forces due to each of the other charges: +q1 -> -q1 direction reversed 33

5. q2 q4 q3 Electric Field “Electric fields and also their use with lines of charge really confuse me! “ “How fields add together“ The electric field E at a point in space is simply the force per unit charge at that point. Electric field due to a point charged particle Superposition E4 E2 E Field points toward negative and away from positive charges. E3 08

6. Checkpoint 1 “Field directions were confusing.” Two equal, but opposite charges are place on the x axis. The positive charge is placedto the left of the origin and the negative charge to the right, as shown in the figure above. What is the direction of the electric field at point A? A. Up B. Down C. Left D. Right E. Zero What is the direction of the electric field at point B? A. Up B. Down C. Left D. Right E. Zero simulation 09

7. Checkpoint 2 E E In which of the two cases below is the magnitude of the electric field at the point labeled Athe largest? A Case 1 B Case 2 C Same “the two positive charges would cancel eachother out in the x direction since they both have fields that point away from them, while the charges in case one have fields that both point in the same direction.” “In two there is a component of the field pointing away.” “The coulomb forces exerted at point A are at right angles in both cases, so that the magnitude stays the same.” 12

8. Two Charges Two charges q1 and q2 are fixed at points (-a,0) and (a,0) as shown. Together they produce an electric field at point (0,d) which is directed along the negative y-axis. y (0,d) q1 q2 x (-a,0) (a,0) • Which of the following statements is true: • Both charges are negative • Both charges are positive • The charges are opposite • There is not enough information to tell how the charges are related 22

9. - - + + + - 23

10. Checkpoint 3 “although the charge on the right is doubled, the force on q by the charge is inversely proportional to the square of the distance between the charges, so the force is effectively halved compared to the charge on the left. “ INTERESTING: statement is correct, but given in support of “to the left” !! “radius gets squared so it moves to the right even though the second charge is stronger.” “The forces from each charge will have the same force because of their relative distances.” A positive test charge q is released from rest at a distance r away from a charge of +Q and a distance 2r away from a charge of +2Q. How will the test charge move immediately after being released? A. To the left B. To the right C. Stay still D. Other 12

11. Example +q P d d -q +q “Just some more examples would be cool” Calculate E at point P. What is the direction of the electric field at point P, the unoccupied corner of the square? Need to know d & q Need to know d (E) (B) (A) (D) (C) 20

12. Continuous Charge Distributions l = Q/L Linear Example: dE pt for E r charges dq = ldx “my head is spinning, what does the dQ mean?” Summation becomes an integral (be careful with vector nature) WHAT DOES THIS MEAN ?? Integrate over all charges (dq) r is vector from dq to the point at which E is defined 25

13. Charge Density • Some Geometry “What exactly is charge density, how is it calculated?” • Linear (l=Q/L) Coulombs/meter • Surface (s = Q/A) Coulombs/meter2 • Volume (r = Q/ V) Coulombs/meter3 • What has more net charge?. • A sphere w/ radius 2 meters and volume charge density r = 2 C/m3 • A sphere w/ radius 2 meters and surface charge density s = 2 C/m2 • Both A) and B) have the same net charge. 28

14. Checkpoint 4 Two infinite lines of charge are shown below. Both lines have identical charge densities +l C/m. Point A is equidistant from both lines and Point B is located above the top line as shown. How does EA, the magnitude of the electric field at point A compare to EB, the magnitude of the electric field at point B? A. EA < EB B. EA = EB C. EA > EB “cancel at A, sum at B“ “Both fields are parallel and both lines are parallel and identical.” “b is twice as far from the bottom one as the other, therefore smaller E.” 29

15. Calculation y P r dq=ldx h x We know: x a What is ? (B) (E) (A) (D) (C) “I really think it would be nice to go over how to find the electric field with the infinite lines of charge with the integrals” Charge is uniformly distributed along the x-axis from the origin to x = a. The charge denisty is l C/m. What is the x-componen t of the electric field at point P: (x,y) = (a,h)? 33

16. Calculation P y r h q1 q2 x x a dq=ldx What is ? (B) (A) (D) (C) q2 Charge is uniformly distributed along the x-axis from the origin to x = a. The charge denisty is l C/m. What is the x-componen t of the electric field at point P: (x,y) = (a,h)? We know: 33

17. Calculation P y r h q1 q2 x x a dq=ldx What is ? (A) (B) (C) neither of the above q2 “The concept I found most difficult was integrating to find electric field when the charge is distributed over a distance.” Charge is uniformly distributed along the x-axis from the origin to x = a. The charge denisty is l C/m. What is the x-componen t of the electric field at point P: (x,y) = (a,h)? We know: cosq2 DEPENDS ON x !! 33

18. Calculation P y r h q1 q2 x x a dq=ldx What is ? (A) (B) (C) (D) q2 Charge is uniformly distributed along the x-axis from the origin to x = a. The charge denisty is l C/m. What is the x-componen t of the electric field at point P: (x,y) = (a,h)? We know: 33

19. Calculation P y r h q1 q2 x x a dq=ldx What is ? q2 Charge is uniformly distributed along the x-axis from the origin to x = a. The charge denisty is l C/m. What is the x-componen t of the electric field at point P: (x,y) = (a,h)? We know: 33

20. Observation P y r h q1 q2 x x a Note that our result can be rewritten more simply in terms of q1. dq=ldx q2 Charge is uniformly distributed along the x-axis from the origin to x = a. The charge denisty is l C/m. What is the x-componen t of the electric field at point P: (x,y) = (a,h)? Exercise for student: Change variables: write x in terms of q Result: obtain simple integral in q 33

21. Notes • Preflight + Prelecture 3 due by 8:00 AM Tuesday Jan. 24 • Homework 1 is due Tuesday Jan. 24 • Labs start Monday Jan. 23 • Discussion Quiz next week will be on Coulomb’s Law and E