Coulomb’s Law and Electric Fields

Recall Coulomb’s Law Example Magnitude of the force between charges q1 and q2 separated a distance r: F = k q1q2/r2 k = 9x109 Nm2/C2 Force on nucleus of Hydrogen from e- Example + - r = 1x10-10 m Qp=1.6x10-19 C Qe = -1.6x10-19 C F Calculate force on electron due to proton F = (9x109)(1.6x10-19)(1.6x10-19)/(10-10)2 N = 2.3x10-8 N (to the right) 5

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 If a tree falls in the forest, and no one is around to hear it, does it make a sound? E E = (9109)(1.610-19)/(10-10)2 N = 1.41011 N/C (to the right) 21

What is the direction of the electric field at point B? Left Right Zero Since charges have equal magnitude, and point B is closer to the negative charge net electric field is to the left y A B x 23

E Field What is the direction of the electric field at point C? Left Right Zero Red is negative Blue is positive Away from positive charge (right) Towards negative charge (right) Net E field is to right. y C x 25

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. 26

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 37

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 39

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 42

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. 44

Compare the ratio of charges QA/ QB 1) QA= 0.5QB 2) QA= QB 3) QA= 2 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 45

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 46

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 47

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!) 48

(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 50

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