Transcript PE electric

Chapter 18
Electrical Energy
and
Capacitance
18.1 Electrical Potential Energy
Objectives
1. Define electrical potential energy
2. Compare the electrical potential energy
for various charge distributions
A Look Back at
Gravitational Potential Energy
PEgrav = mgh
PEgrav=mgh
h
PEgrav=0
Electric Potential Energy
Potential associated with an object
due to its position relative to a
source of electric force
Consider: Uniform Electric Field
Charge Movement in E Field vs PEelectric
If the charge is
moving….
+ Charge
- Charge
With E
Loses PEelectric
Gains PE electric
Opposite E
Gains PEelectric
Loses PEelectric
Electrical Potential Energy
(in a uniform field)
PEelectric = -qEd
q = charge (C)
E = electric field strength (N/C)
d = displacement (m) from the
reference point in the
direction of the field
Electrical Potential Energy for a Pair of Charges
PEelectric = kC q1q2
r
…because point charges produce
non-uniform electric fields
Regarding PEelectric for point charges…
• The reference point for electrical potential
energy is assumed to be at infinity. Note
that PEelectric goes to zero as r goes to infinity.
• Because like charges repel, positive work must
be done to bring them together. So, PEelectric
is positive for like charges and negative for
unlike charges.
• For determining PEelectric for more than two
charges, calculate PEelectric for each pair then
add the energies.
Problem:
In one model of the hydrogen atom, an electron
in its lowest energy state moves in a circular
orbit about the nucleus (a single proton) at a
distance of 5.29x10-11m. Find the electrical
potential energy of the hydrogen atom.
Which equation for PEelectric?
PEelectric = kC q1q2
r
Answer: PEelectric = -4.35x10-18 J
18.2 Potential Difference
Objectives
1. Distinguish between electrical potential
energy, electric potential, and potential
difference.
2. Compute the potential difference for
for various charge distributions.
Water Analogy
Electric Potential
…is the electrical potential energy
associated with a charged particle
divided by the charge of the particle
V = PEelectric
q
Potential Difference
…is the change in electrical potential
energy associated with a charged
particle divided by the charge of the
particle.
V=
PEelectric
q
units = J/C = volts (V)
What’s another name for PE?
Hint:What do we have to do to a particle
if we want to increase it’s PE?
PE aka “Work” (W)
So, ΔV = PEelec = W
q
q
units for PE and for work = joules (J)
More About Potential Difference
• Potential difference is often referred to as
“voltage”.
• As a 1C charge moved through a potential
difference of 1V, the charge gains (or loses)
1J of energy.
• Common potential differences (voltages)
are 12V for a car battery and 120V
between the two slots in a household
electrical outlet.
Potential Difference in a Uniform
Electric Field
We know
V=
PEelectric
q
And PEelectric = -qEd (uniform field)
So
V = -qEd
q
V = -E d
(where
d is displacement from a reference
point in the direction of the electric field)
V = -E
d
Notice…..new units for E !!
V units is volts (V)
d is in meters (m)
...therefore E units must be ??
E is in V/m
Potential Difference at Some
Location Near a Point Charge
We know
V=
PEelectric
q
And PEelectric = kC q1q2 (for point charges)
r
So
V = kC q1q2
q1r
V = kC q
r
(compares the potential difference between a point
at infinity and some location near a point charge)
Questions
1. Find the potential difference between a point
infinitely far away from and a point 1.0 cm
from a proton.
2. A proton is released from rest in a uniform Efield with a magnitude of 8.0x104 V/m. The
proton moves 0.50 m as a result. Find:
a) The potential difference between the initial
and final positions of the proton.
b) The change in electrical potential energy of
the proton as a result of this displacement.
Answers
1. 1.44 x 10-7 V
2. a) -4.0 x 104 V
b) -6.4 x 10-15 J
PEelectric, Electric Potential, and
Potential Difference in a Battery
• The potential difference between the
positive and negative terminals is
9V, where the electric potential
at the negative terminal is 0V, and
the electric potential at the positive
terminal is 9V.
• When hooked to an electrical device,
the charge moves inside the battery
from negative to positive terminal.
The battery does work on the charge
in order to move it from the (-) to the
(+) terminal, so PEelectric increases.
More on PEelectric, Electric Potential
and Potential Difference
18.3 Capacitance
Objectives
1. Relate capacitance to the storage of
electrical potential energy in the form
of separated charges
2. Calculate the capacitance of various
devices
3. Calculate the energy stored in a
capacitor
Capacitance
…is the ability of a conductor to
store energy in the form of
electrically separated charges
Parallel-plate Capacitor
Parallel conductive plates in a circuit with a charge source (V).
Close the switch and the charge flows until the voltage across the
plates equals the applied voltage. Charge flows from one plate to the
other, leaving behind a plate that is equally (but oppositely) charged.
Open the switch and charge (and electrical potential energy) are stored.
Capacitance – Basic Equation
C=Q
V
capacitance = magnitude of charge on each plate
potential difference
C = farads (F) = C/V
Capacitance and PEelectric
PEelectric = ½ Q V
and since
C=Q
V
substituting gives us:
and
PEelectric = ½ C V2
PEelectric = Q2
2C
Questions
1. A parallel-plate capacitor has a charge of
6.0x10-6 C when charged by a potential
difference of 1.25V.
a) Find its capacitance
b) How much potential energy is stored
when this capacitor is connected to a 1.5V
battery?
Answers:
a) 4.8x10-6 F
b) 5.4x10-6 J