Coulomb’s Law and Electric Fields - UIUC

1 Physics 102: Lecture 02. coulomb 's Law and Electric Fields Today we will . get some practice using coulomb 's Law learn the concept of an Electric Field Physics 102: Lecture 2, Slide 1. Recall coulomb 's Law Force between charges q1 and q2 separated distance r: 1 2 coulomb constant . 2 9 109 2. / 2. Opposite charges attract, like charges repel Physics 102: Lecture 2, Slide 2. coulomb Law practice: Three Charges Calculate force on +2 C charge due to other two charges Draw forces Calculate force from +7 C charge F+7. Calculate force from 7 C. 7 C charge Add (VECTORS!) Q=+ C. F-7. 4m 6m Q=+ C Q= C. Physics 102: Lecture 2, Slide 3. Three Charges Calculate forces Calculate force on +2 C charge due to other two charges Draw forces Calculate force from +7 C charge Calculate force from 7 C.

2 7 C charge F+7. Add (VECTORS!). Q=+ C. Calculate magnitudes F-7. 4m 6m Q=+7 0 C. Q=+ C Q= 7 0 C. Q= Physics 102: Lecture 2, Slide 4. Three charges Adding Vectors F+7+F. F-77. Calculate components of vectors F+7 and F-7: F+7. Q=+ C. F-7. 4m 6m Q=+ C Q= C. Physics 102: Lecture 2, Slide 5. Three charges Adding Vectors F+7+F. F-77. Add like components of vectors F+7 and F-7: F+7. Q=+ C. F. Final vector F has magnitude andd direction di ti F-7. 4m 6m Q=+ C Q= C. Double-check with drawing Physics 102: Lecture 2, Slide 6. Electric Field Charged particles create Electric Fields . Direction is the same as for the force that a + charge would feel at that location. Magnitude given by: E F/q = kq/r2. Qp= C. +. E. r = 1x10-10 m E = (9 109)( 10-19)/(10-10)2 N = 1011 N/C (to the right).

3 Physics 102: Lecture 2, Slide 7. CheckPoint What is the direction of the Electric field at point A? 7% 1) Up y 7% 2) Down A. 2% 3)) Left B. x 53% 4) Right 32% 5) Zero Physics 102: Lecture 2, Slide 8. ACT: E Field What is the direction of the Electric field at point C? Left e Away from positive charge (right). B. Right Towards negative charge (right). C Zero C. Net E field is to right. right y A. C B. x Physics 102: Lecture 2, Slide 9. E Field from 2 Charges Calculate Electric field at point A due to two unequal charges Draw Electric Fields Calculate E from +7 C charge charge Calculate E from C g Add (VECTORS!). A. Note: this is similar to ((but a bit harder than) my earlier example. 4m We ll do some of this We'll here you try the rest at home! 6m Q = + C Q = C. Physics 102: Lecture 2, Slide 10.

4 E Field from 2 Charges Calculate Electric field at ppoint A due to charges g Calculate E from +7 C charge Calculate E from C charge E7. Add*. E = k q/r2 A. E3. 4m 6m Q=+ C Q= C. Physics 102: Lecture 2, Slide 11. Adding Vectors E7+E3. Decompose into x and y components. components E7. E7y=E7 (4/5). ( / ). A . E7x=E7 (3/5). 4m . 6m Q=+ C Q= C. Physics 102: Lecture 2, Slide 12. Adding Vectors E7+E3. Decompose into x and y components. Add components. E7. A Etotal E3. 4m Ex = 10+3 N/C. 6m Q=+ C Q= C. 1 0 10+3 N/C. Ey = 10. Physics 102: Lecture 2, Slide 13. Comparison: Electric l i Force vs. Electric l i Field ld Electric Force (F) the force felt by a charge at some location Electric Field (E) found for a location only (any location) tells what the Electric force would be if a + charge were located there: F = Eq Both are vectors, vectors with magnitude and direction.

5 Direction Ok, what is E actually good for? Physics 102: Lecture 2, Slide 14. Electric Field Map Electric field defined at any location y A. C B. x Physics 102: Lecture 2, Slide 15. Electric Fields : A useful record-keeping tool! Calculate once for fixed charges, use to find force on other charges (like ions/electrons in neurons, heart tissue, tiss e and cell membranes). Eisenberg, BU. Physics 102: Lecture 2, Slide 16. Electric Field Lines Closeness of lines shows field strength (lines never cross). Number of lines at surface Q. Arrow gives direction of E (Start on +, end on ). Physics 102: Lecture 2, Slide 17 This is becoming a mess!!! CheckPoint X. A B. Y. Charge A is Field lines start on positive charge, end on negative. 1) positive 2) negative 3) unknown 93%. Physics 102: Lecture 2, Slide 18.

6 4% 3%. CheckPoint / ACT. X. X. A B. A Y B. Y. Compare the ratio of charges QA/ QB # lines proportional to Q. A) QA= B) QA= QB C) QA= 2 QB. Physics 102: Lecture 2, Slide 19. 15% 17% 53%. CheckPoint X. A B. Y. The Electric field is stronger when the lines are located closer to one another. The magnitude of the Electric field at point X is greater than at point Y. 1) True 2) False Density of field lines gives E. 18% 82%. Physics 102: Lecture 2, Slide 20. E inside of conductor Conductor electrons free to move El Electrons feels f l Electric l i force f - will ill move until il they feel no more force (F=0). F=Eq: F E if F F=0. 0 th then E. E=00. E=0 inside a conductor (Always!). Physics 102: Lecture 2, Slide 21. Demo: E-field E field from dipole y A. C B. x Physics 102: Lecture 2, Slide 22.

7 Recap E Field has magnitude and direction: E F/q Calculate jjust like coulomb 's law Careful when adding vectors Electric Field Lines Density gives strength (# proportional to charge.). Arrow gives direction (Start + end on ). Conductors Electrons free to move E = 0. Physics 102: Lecture 2, Slide 23. To Do Campus closed on Monday; no office hours. Homework 1 due Wednesday, Jan 23 @ 8 AM! Do your Checkpoint by 8:00 AM Wednesday. Physics 102: Lecture 2, Slide 24.