Storage by Electrons:
Electric Fields and Capacitors
But first, a discussion of the exam
What type of forces could act on e-?
Gravity, if . . .
• another mass is around.
Electricity, if . . .
• another charged object is around.
Magnetism, if . . .
• the e- is in a magnetic field
The weak nuclear force, if . . .
• any other fermion is around
Gravity’s force between e- and p+
Force between two objects due to gravity:
m1m2
F G 2
r
m1 = me = 9.11 E-31 kg
m2 = mproton = 1.67 E-27 kg
r = 1 nm = 10-9 m = 1 E-9 m
F = 1.01 E-49 N
Electrical force between e- and p+
Force between two objects due to Coulomb
(electric) attraction:
q1q2
F k 2
r
q1 = qe = 1.602 E-19 C
q2 = qproton = 1.602 E-19 C
r = 1 nm = 10-9 m
F = 2.31 E-10 N
Comparing forces between e- and p+
Electric:
Gravity:
Nuclear:
F= 2 E-10 N
F= 1 E-49 N
F < 1 E -100,000 N
A 1kg mass needs ~10N of force to prevent it
from falling on the surface of the earth so
electric force seems small. However,
~1E23 electrons per cubic centimeter.
 enormous forces possible from electric
charges
Coulomb’s Law
1 q1q2
F
2
4 0 r
1
4 0
 8.99  10 N  m /C
9
2
 9.0  10 N  m /C
9
2
2
2
 0  8.85  10 C /N  m
12
2
2
Forces on Charges
Unlike charges attract.
Like charges repel.
How can a force act at a distance?
If I took my electron away from the proton
and brought a positron (positive e) near the
proton, the positron would . . .
• accelerate away from the proton
So, does my proton exert a force if no one is
around to feel it?
• Force, no. But we can define an electric
field which describes the force a charge
would feel if it came near the proton
The Electric Field
F
E
q0
• When E is known, the force, F, on a charge, q0, is given
by:
• F = q0E
• The direction of E is the direction of the force on a positive
charge.
The Electric Field
F
E
q0
For a point charge q, the force on q0 is,
1 qq0
F
2
4 0 r
Then, at q0’s location,
F
1 q
E 
2
q0 4 0 r
Electric Field of a Positive Point
Charge
•The picture shows the electric field vector at
several points.
Electric Field Lines
•Electric field lines show the direction of E at
any point.
•The magnitude of E is proportional to the
density of electric field lines.
•Electric field lines originate on positive
charges and terminate on negative charges,
unless they extend to infinity.
Electric Field Lines for a
Negative Point Charge
Consider Two Point Charges
•The two fields point toward the negative charges that produce them, and
must be added as vectors to get the final result.
Addition of Electric Field
(continued)
The horizontal components of the two vectors add to
zero, so the resultant points downward. Its
magnitude is equal to the sum of the vertical
components of the two vectors. Since it is an
equilateral triangle, each vector makes an angle of
30° with the vertical direction. Then:
E1vertical = E1 cos 30°
and
E = 2 E1 cos 30°
Addition of Electric Field
(continued)
The answer is:
E = 2(1.0 × 105 N/C) cos 30°
E = 1.7 × 105 N/C
Downward
What do you think?
What do you think the field from a positive point
charge will look like?
How will the field change if the charge is negative?
How will the field lines change if the magnitude of
the charge is increased?
What do you think the field lines for a pair of
oppositely charged point charges (one positive,
one negative) look like?
Field around a Positive Charge
Since forces obey the law of linear superposition (i.e., they
add), electric fields add too!
Class 10 Activity
• Start Activity 10 on WebCT Tools.
• Wait for class before completing parallel
plate part of the activity.
Charges in Conductors
 Electric fields are created when positive charges
and negative charges are separated
 A uniform electric field existing over a region sets
up a potential difference between points in that
region: DV=EDx, where Dx is the distance along
a field line.
 If I apply a potential difference across a
conducting object (including semiconductors),
charges experience a force, and charge carriers
will flow until the potential difference is removed.
What if charge can’t flow?
 Consider charge separated by two metal
plates
– A potential difference exists between the plates
– An electric field exists between the plates,
pointing from positive plate to negative plate
– No current can flow
Introducing, . . . Capacitance
The battery provides
the work needed to
move the charges
and increase their
potential energy
Before the next class, . . .
• Start Homework 12 (Due Monday, Feb. 25)
• Do Activity 10 Evaluation by Midnight
tonight
• Do the Readings for Class 10 (if you have
not completed already)
• Do Reading Quiz