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

Example 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!) F7 Q=+2.0mC 1 2 3 4 5 6 7 8 9 10 11 12 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 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

Example Three Charges Calculate force on +2mC charge due to other two charges Calculate force from +7mC charge Calculate force from –7mC charge Add (VECTORS!) F+7 Q=+2.0mC 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 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

Example Three Charges Calculate force on +2mC charge due to other two charges Calculate force from +7mC charge Calculate force from –7mC charge Add (VECTORS!) F+7 Q=+2.0mC F = k q1q2/r2 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

Adding Vectors F+7+F-7 Example F+7 F-7 Q=+2.0mC 5 m 4 m 6 m Q=+7.0mC 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

Adding Vectors F+7+F-7 Example y components cancel x components: F+7 Q=-7.0 mC Q=+7.0mC Q=+2.0mC 6 m 4 m F+7 5 m F-7 y components cancel x components: F = F+7,x + F-7,x F+7,x = (3/5)F+7 F-7,x = (3/5)F-7 F = (3/5)(5+5)x10-3 N=6 x 10-3 N F 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

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

ACT: E Field What is the direction of the electric field at point C? Left Right Zero Red is negative Blue is positive y C x

Comparison: Electric Force vs. Electric Field Electric Force (F) - the actual force felt by a charge at some location. Electric Field (E) - found for a location only – tells what the electric force would be if a charge were located there: F = Eq Both are vectors, with magnitude and direction. Add x & y components. Direction determines sign.

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

ACT: E Field II What is the direction of the electric field at point A, if the two positive charges have equal magnitude? Up Down Right Left Zero Red is negative Blue is positive y A B x

Electric Field of a Point Charge 0.81011 N/C Example 321011 N/C 251011 N/C 2.91011 N/C + E This is becoming a mess!!!

Electric Field Lines Closeness of lines shows field strength - lines never cross # 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

Preflight 2.5 Charge A is 1) positive 2) negative 3) unknown B X Y Charge A is 1) positive 2) negative 3) unknown Field lines start on positive charge, end on negative.

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

Preflight 2.8 The electric field is stronger when the A B X 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

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: electric field lines

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 _________.