Coulomb’s Law and Electric Fields 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

Recall Coulomb’s Law Magnitude of the force between charges q1 and q2 separated a distance r: F = k q1q2/r2 k = 9x109 Nm2/C2 Force is attractive if q1 and q2 have opposite sign repulsive if q1 and q2 have same sign Units: q’s have units of Coulombs (C) charge on proton is 1.6 x 10-19 C r has units of m F has units of N Calculate force on electron due to proton

Coulomb Law practice: Three Charges Example Coulomb Law practice: Three Charges Calculate force on +2mC charge due to other two charges Draw forces Calculate force from +7mC charge Calculate force from –7mC charge Add (VECTORS!) F+7 Q=+2.0mC 1 2 3 4 5 6 7 8 9 10 11 12 4 m F-7 First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Perhaps need to show this can be done with cosine and sine too. Preflight: What is direction of force on third charge due to dipole 6 m Q=+7.0mC Q=-7.0 mC

Three Charges – Calculate forces Example Three Charges – Calculate forces Calculate force on +2mC charge due to other two charges Draw forces Calculate force from +7mC charge Calculate force from –7mC charge Add (VECTORS!) Calculate magnitudes F+7 Q=+2.0mC 4 m F-7 First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Perhaps need to show this can be done with cosine and sine too. Preflight: What is direction of force on third charge due to dipole 6 m Q=+7.0mC Q=-7.0 mC

Three charges – Adding Vectors F+7+F-7 Example Three charges – Adding Vectors F+7+F-7 Calculate components of vectors F+7 and F-7: F+7 Q=+2.0mC 5 m 4 m F-7 First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Preflight: What is direction of force on third charge due to dipole 6 m Q=+7.0mC Q=-7.0 mC

Three charges – Adding Vectors F+7+F-7 Example Three charges – Adding Vectors F+7+F-7 Add like components of vectors F+7 and F-7: F+7 Q=+2.0mC F Final vector F has magnitude and direction 5 m 4 m F-7 First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Preflight: What is direction of force on third charge due to dipole 6 m Q=+7.0mC Q=-7.0 mC Double-check with drawing

Electric Field Example 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 Example + r = 1x10-10 m Qp=1.6x10-19 C E If a tree falls in the forest, and no one is around to hear it, does it make a sound? E = (9109)(1.610-19)/(10-10)2 N = 1.41011 N/C (to the right)

Preflight 2.3 What is the direction of the electric field at point B? Left Right Zero y A B x

Preflight 2.2 What is the direction of the electric field at point A? Up Down Left Right Zero y A B x

ACT: E Field What is the direction of the electric field at point C? Left Right Zero y A C B x

E Field from 2 Charges Example Calculate electric field at point A due to two unequal charges Draw electric fields Calculate E from +7mC charge Calculate E from –3.5mC charge Add (VECTORS!) A Note: this is similar to (but a bit harder than) my earlier example. 4 m First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Preflight: What is direction of force on third charge due to dipole 6 m Q = +7.0mC Q = –3.5 mC

Comparison: Electric Force vs. Electric Field Electric Force (F) – the actual force felt by a real 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, with magnitude and direction.

Electric Field Map Electric field defined at any location (we did three: A, B, C) y A C B x

Electric Field Lines This is becoming a mess!!! Closeness of lines shows field strength (lines never cross) Number of lines at surface  Q Arrow gives direction of E (Start on +, end on –) After field lines up ask to compare efield at two points of equal distance This is becoming a mess!!!

Preflight 2.5 A B X Y Charge A is 1) positive 2) negative 3) unknown

Preflight 2.6 Compare the ratio of charges QA/ QB X Y X A B Y Compare the ratio of charges QA/ QB 1) QA= 0.5QB 2) QA= QB 3) QA= 2 QB

Preflight 2.8 1) True 2) False B X Y The magnitude of the electric field at point X is greater than at point Y 1) True 2) False

ACT: E Field Lines B A Compare the magnitude of the electric field at point A and B 1) EA>EB 2) EA=EB 3) EA<EB

E inside of conductor Conductor  electrons free to move Electrons feels electric force - will move until they feel no more force (F=0) F=Eq: if F=0 then E=0 E=0 inside a conductor (Always!)

Preflight 2.10 (1) Negative (2) Zero (3) Positive B X Y "Charge A" is actually a small, charged metal ball (a conductor). The magnitude of the electric field inside the ball is: (1) Negative (2) Zero (3) Positive

Demo: E-field from dipole y A C B x

Recap E Field has magnitude and direction: Electric Field Lines E  F/q Calculate just 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

To Do Do your preflight by 6:00 AM Wednesday.