Electric Fields and Capacitors
The basis of Electric storage
A Learning Summary
• Two objects are just resolved when the central
diffraction maximum of one object is at the first
minimum of the other. (Rayleigh’s criterion)
1.22 1.22
  sin

d
d
1
R
 As before, q is approximately tan q = y/L
 Circular aperture has diameter d
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
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
Nuclear force between e- and p+
Force between two objects due to the weak
nuclear force:
F  GF se
 mW cr / 2 h
s = 2mc2E = 1 GeV2 = 2.5 E-20 J2
mW = 1.42 E-25 kg
r = 1 nm = 10-9 m
GF = 4.52 E 14 J-2
F < 1 E -100,000 N
Comparing forces between e- and p+
Electric: F= 2.31 E-10 N
Gravity: F= 1.01 E-49 N
Nuclear: F < 1 E -100,000 N
If I had 1% more electrons than protons, and
I stood an arm’s length away from a
similarly imbalanced person, the force
between us would be great enough to lift a
weight the size of . . .
• The earth!
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
How can a force act at a distance?
A charge creates an
electric field that
fills space, whether
or not any other
charge is around to
feel its effects!
Make Predictions for the Activity, then
Answer Questions 1-7 of the Activity
What’s a Field?
Electric field E = F/q,
where q is the charge
feeling the force
Since forces obey the law of
linear superposition (i.e., they
add), electric fields add too!
What does a “field” look like?
Finish the Activity, working as far as
you can in the time allowed
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 semi-conductors),
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, . . . The Capacitor
Introducing, . . . Capacitance
The battery provides
the work needed to
move the charges
and increase their
potential energy
What determines capacitance?
C = e0 A/d
More about capacitors
More about capacitors
U = Vq = Ve
1 eV = 1.602 x 10-19 J
= energy to move
electron through 1 volt