ELECTRIC FORCE (Chapter 19)
Electric forces are important
 All interatomic and intermolecular forces are electric
o i.e. forces that determine properties of materials
Two kinds of charge: positive (+) and negative (-)
 opposite charges attract, like charges repel
Net charge in an isolated system is conserved (i.e. constant)
19
 Always an integral multiple of electron charge e  1.60  10 C


Classify materials by electrical properties
 Conductor: electrons flow freely (i.e. metals)
 Semiconductor: “controllable” electron flow (i.e. silicon, used in electronics)
 Insulator: electrons stay on atoms or molecules in material
Can separate positive and negative charges in materials:
Can charge a conductor by INDUCTION:
1.
Connection to ground allows charged rod to push
like charge away
o Creates charge imbalance in conductor
2.
Remove ground while charged rod remains in
place
o Conductor remains charged
3.
Charged rod removed
o Conductor retains a NET CHARGE
Insulators can be POLARIZED:
 Molecules in insulators:
o may be polar (have permanent electric dipoles)
o may be easily distorted to give induced electric dipole
 A charged object near an insulator may
align molecules
o Gives effective charge separation
 Material POLARIZED
COULOMB’S LAW (1777)
Experimental result:
 Force between two charged bodies
1
F

e
separated by r:
r2
o Inverse square law
Can measure electrical force with Torsion Balance
 Find torque from twist in wire
Electric Force is a vector: Magnitude AND Direction
Magnitude of Electric Force:
Fe  k e
q1 q2
r2
 Coulomb constant:
k e  8.99  10 N  m / C
9
2
2
OR
ke 
1
4 0
12
2
2
 Permittivity of free space:  0  8.854  10 C / N  m
But electric force is a vector so we need to talk about direction too!
Two charged particles exert force on each other: Newton’s 3rd Law
Forces have equal magnitude, opposite direction
 Notation:

F12 is the force on charge 2 caused by charge 1
Define special unit vector:
r̂12
is a unit vector that points FROM 1 TO 2
Then write Coulomb’s law as:

qq
F12  k e 1 2 2 r̂12
r
 Direction of force comes out easily if used correctly

q1q2

F
k
r̂12
e
2
Direction in Coulomb’s Law: 12
r
If both charges have same sign: ( i.e. so that product q1q2 is positive)
 then force on 2 is in same direction as r̂12
o i.e. force on 2 is AWAY from 1
o force is repulsive
If charges have opposite signs: ( i.e. so that product q1q2 is negative)
 then force on 2 is in opposite direction to r̂12
o i.e. force on 2 is TOWARD 1
o force is attractive


By Newton’s 3 Law: F21   F12
rd
(i.e. both forces attractive or both repulsive)
Net force on a charge due to several other charges:
 VECTOR SUM of all forces on that charge due to other charges
 Called Principle of SUPERPOSITON
 Each charge exerts a force on charge 1




 Resultant force is F1  F21  F31  F41
 says net force on charge 1 is sum of:
o force on 1 from 2,
o force on 1 from 3,
o force on 1 from 4
Example: Chapter 19, problem 14
Three point charges are located at corners of an
equilateral triangle as shown. Calculate the
resultant force on the 7.00-μC charge.
Example: Chapter 19, problem 7
Two small beads having positive charges 3q and q are fixed at opposite ends of a
horizontal, insulating rod, extending from the origin to the point x = d. A third
small charged bead is free to slide on the rod.
At what position is the third bead in
equilibrium? Can it be in stable equilibrium?