Download Electric Potential and Energy

Electric Potential
and Energy
Objectives
Define work and relate it to energy
Define electric potential difference, and
relate it to the work done on an electric
charge in an electric field
Define capacitance
Write equations for work, electric potential,
and capacitance
Use equations to solve problems
Work is Energy
Charge is stored at a “potential” or “voltage”
– A battery stores a certain amount of charge at a
specific voltage
– When the charge runs out, the battery is “dead”
– Unit of work is a joule (J), just like energy
Work is done to move a charge in
an electric field
Work is equal to a force exerted over a
distance
W=F·d
More Specifically
Positive work is stored energy
Negative work is released energy
Work is only done if there is a component
of the electric field in the direction of the
motion
– If the motion is perpendicular to the electric
field lines, no work is done
– The electric field is constant in that direction
Work
W  F d
F
E
q
F  qE
b g
W  q E d
W
 E  d  V
q
∆V = Voltage or
“potential difference”
Volts
Unit is joules per coulomb, or volt (V)
Potential difference, or voltage (V)
W
V
q
Example
Moving a charge of 3.2 x 10-19 coulombs
between two points in an electric field
requires 4.8 x 10-18 joules of energy.
What is the potential difference between
these points?
Solution
q  3.2 x10
19
W  4.8 x10
C
18
J
18
W 4.8 x10 J
V 
19
q 3.2 x10 C
V  15V
Example
Electric field between two parallel plates
+++++++++++++++++++++++++
V = 60 V
d = 3.0 cm
------------------------------------
What is the magnitude of the
electric field between them?
Textbook, Pg. 491
Example
An elementary charge is moved through a
potential difference of 1 volt
Calculate the amount of work done on the
charge
Solution
V  1V
19
q  16
. x10 C
W
 V  W  qV
q
19
W  1V  16
. x10 C  16
. x10
or 1 electronvolt (eV)
19
J
Electrical Energy
At A an electron has 100 eV of electric
potential energy
At B the electron has 100 eV of kinetic
energy
++++++++++++++++++++++++++++++++++
B
100 V
A
e
Capacitance
Capacitance depends on the structure of
the device
A capacitor with a given amount of charge,
will have a specific potential difference
q
C
V
Capacitance
Unit of capacitance is the farad (F)
One farad equals one coulomb per volt
A
C
d
For a parallel
plate capacitor
WARNING
Capacitors can be
lethal
Summary
Electric potential difference
– Work done per unit charge to move a charged
body in an electric field
– Unit is joule per coulomb, or “volt”
Capacitance
– Ratio of an object’s stored charge to its
potential difference
– Measured in farads
Equations
F
E   F  qE
q
E = Electric Field
W  F d  W  q  E d
W = Work = Electric
Potential Energy
W
  E  d  V
q
q
C
V
V = Potential Difference
= Electric Potential
b g
F = Force
q = Charge
C = Capacitance
Practice Problems
Pg. 493 #5 – 8