Two conductors in proximity form a

1
Two conductors in proximity form a capacitor
they have a capacity to hold a charge Q (Q on
one and -Q on the other) with a voltage
difference V.CQ/VNote Capacitance C is
italicized. Coulomb C is not. (Sorry!)Capacitan
ce is a property of the geometry of the
conductors (and depends on whether there is
vacuum or material between them, as we will see
later.) This is because of linearity
(superposition.) If I double the source charges,
I will double the field, and double the potential.
2
If I put 2 microcoulombs of charge on the sphere
and plate, there is a potential difference of 2
V.

• What is the capacitance?
• A 0
• B Cannot determine, since not symmetric
• C 1 microfarad 10-6 C/V
• D 106 farads

3
If I put 2 microcoulombs of charge on the sphere
and plate, there is a potential difference of 2
V.

• If I put 4 microcoulombs of charge on the sphere
  and plate, what will be the potential difference?
• A 0
• B 2 V
• C 4 V
• D 8 V

4
Two infinite parallel sheets carry charge
densities ?? What is the electric field at
point 1?
5
Two infinite parallel sheets carry charge
densities ?? What is the electric field at
point 2?
The potential difference between the plates is
d????
6
By superposition, the field in the dielectric is
the sum of the original capacitor field, plus the
field from the polarization surface charge.The
total field is thereforeA bigger than the
original capacitor fieldB smaller than the
original capacitor fieldC the same as the
original capacitor field
7
Answer smaller than the original field.We can
write that the new field is the original field,
divided by K, the dielectric constant

• What is the new potential across the capacitor?
• A same as the old potential, without the
  dielectric
• B bigger than the old potential, by a factor of
  K
• C smaller than the old potential, by a factor of
  K

8
If I put a charge Q on a parallel plate
capacitor and increase the plate separation, what
happens to V?

• A it increases
• B it decreases
• C it stays the same

9
If I put a charge Q on a parallel plate
capacitor and increase the plate separation, what
happens to V?

• The field is the same, but the distance is
  larger. So V increases.
• What happens to the potential energy U?
• A it increases
• B it decreases
• C it stays the same

10
If I put a charge Q on a parallel plate
capacitor and increase the plate separation, what
happens to V?

• The field is the same, but the distance is
  larger. So V increases.
• What happens to the potential energy U?
• A it increases
• The energy density u is the same, but there is
  more volume.
• Where did this energy come from??

11
If I put a charge Q on a parallel plate
capacitor and insert a dielectric, what happens
to V?

• A it increases
• B it decreases
• C it stays the same

12
If I put a charge Q on a parallel plate
capacitor and insert a dielectric, what happens
to V?

• The field in the dielectric is reduced by a
  factor of K. So the potential goes down.
• What happens to the potential energy?
• A it goes up by a factor of K
• B it goes up by a factor of K2
• C it goes down by a factor of K
• D it goes down by a factor of K2
• E it stays the same.

13
If I put a charge Q on a parallel plate
capacitor and insert a dielectric, what happens
to V?

• What happens to the potential energy?
• It may be counterintuitive, but the potential
  energy goes down by a factor of K (not K2).
• UQ2/(2C) the capacitance goes up by a factor of
  K.
• Note the energy density for a given E field in a
  dielectric is
• The field goes down by a factor of K, but epsilon
  adds a factor of K.

14
If the potential energy goes down, where does the
energy go?

• The field pulls the dielectric into the
  capacitor, giving it kinetic energy. (Very small,
  here.)
• Application Optical tweezers

15
Batteries dont store charge. They store
energy.A chemical battery works because
electrons like to leave some materials to go to
others. The change in energy when the electron
goes downhill becomes available as electric
POTENTIAL between the battery terminals
16
Lead Acid (Car) Battery
The rxn on the right will not go in the direction
indicated unless the electrolyte soln potential
is closer than 1.685 V to the electrode
potential. i.e. the electrode can be no more
than 1.685 V higher in potential than the
electrolyte soln.
Pb2 is in the form of solid lead sulfate on the
electrodes. When discharged, both electrodes
turn into lead sulfate.
17
Lead Acid (Car) Battery
The rxn on the left will not go in the direction
indicated unless the electrolyte potential is
closer than 0.356 V to the - electrode potential.
i.e. the - electrode can be no more than 0.356
V lower in potential than the electrolyte soln.
18
Lead Acid (Car) Battery
Overall, then, the reactions will STOP when the
potential between the /- electrodes is
2.041V. Only a tiny tiny tiny amount of charge
needs to build up on the electrodes for the
reaction to stop. How much? But if you connect
the electrodes with a resistive wire, the
reaction will start to go as the potential drops
a hair below 2.041V.
19
Lead Acid (Car) Battery
What happens if you force the potential
difference to be higher than 2.041 V? The
reactions run backwards! Lead sulfate turns into
lead oxide and lead (metallic). This is charging
the battery.
20
Lead Acid (Car) Battery
Note that the rxn doesnt make a big reservoir
of electrons. The battery doesnt die because
it runs out of stored electrons. It doesnt
store electrons. It pumps electrons on
demand, i.e. when the potential falls below
2.041 V.
21
The two electrodes of an ideal V volt battery are
shown. The field lines for the electric field
between the electrodes are shown when nothing is
attached to the electrodes. The electrodes have a
separation d.A resistive wire of length L is
then attached to the battery.What is the
electric field in the wire, when steady state is
reached?

• A 0
• B it varies, but averages to V/d
• C it varies, but averages to V/L
• D it is V/L everywhere in the wire
• E no way to determine

22
The two electrodes of an ideal V volt battery are
shown. The field lines for the electric field
between the electrodes are shown when nothing is
attached to the electrodes. The electrodes have a
separation d.A resistive wire of length L is
then instantaneously attached to the
battery.What is the electric field in the wire,
immediately after attaching it?

• A 0
• B it varies, but averages to V/d
• C it varies, but averages to V/L
• D it is V/L everywhere in the wire
• E no way to determine

23
Where on this wire will negative charges build
up (a tiny amount)
B
A
24
(No Transcript)
25
Assume wires have zero resistance
26
Assume wires have zero resistance
27
No E field in electrostatics.
28
A same B 3R C 9R D R/3 E R/9
29
On left, both are equally bright. Bulb A on the
right is brighter, As V2/R is bigger.
30
If the Rs are all the same, which arrangement
has the lowest Ref ? B
Which has the highest Ref ? A
Which has a lower Ref C or d? D
31

• If the 2 cm long resistor is 3 ohms, what is the
  resistance of the 1 cm long resistor (with half
  the radius)? (Both are of the same material.)
• A 1 ohm
• B 1.5 ohms
• C 2 ohms
• D 3 ohms
• E 6 ohms

32

• What is the current through the battery?
• A 0 amps
• B 0.5 amps
• C 1 amp
• D 2 amps
• E 3 amps

33

• What is the power delivered by the battery? In
  watts
• A 0
• B 1
• C 2
• D 3
• E 4

34

• What is the magnitude of the E field the
  physically larger resistor (3 ohms)? (in V/m)
• A 0
• B 100
• C 200
• D 300
• E 400

35

• What is the magnitude of the E field the
  physically smaller resistor (6 ohms)? (in V/m)
• A 0
• B 100
• C 200
• D 300
• E 400

36

• What is the current through the battery? In amps
• A 0
• B 1/9
• C 1/6
• D 2/9
• E 2/3

37

• What is the E field in the 3 ohm resistor? (in
  V/m)
• A 0
• B 16
• C 33 1/3
• D 78
• E 200

38
Are R1 and R2 in parallel, in series, or
neither?A parallelB seriesC neither
39
Which junction formula is correct?
40
Which loop formula is correct?
41
At steady state, what is current I1?
42
At steady state, if the voltage at a 0, what is
the voltage at b?