there will be a quiz next class period, feb 1, covering ch 22 and the beginning of ch 23 (what we...
TRANSCRIPT
There will be a quiz next class period, Feb 1, covering Ch 22 and the beginning of Ch 23 (what we cover in class today)
Definitions
• Electric potential—Potential energy per unit charge at a point in an electric field
• Path integral (line integral)—An integral performed over a path such as the path a charge q follows as it moves from one point to another
• Volt—The unit of electric potential. 1V = 1 J/C
• Electron volt (eV)—the energy that an electron (or proton) gains or loses by moving through a potential difference of 1 V.
• Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential
Electric Potential
• Electric force is a conservative force, therefore there is a potential energy associated with it.
• We can define a scalar quantity, the electric potential, associated with it.
€
V =U
q= −
r E • d
r l
A
B
∫
€
WEfield =r F E • d
r l = q
r E • d
r l
dU = −qr E • d
r l
ΔU = −qr E • d
r l
A
B
∫
Electric Potential Energy
Concepts of work, potential energy and conservation of energy
For a conservative force, work can always be expressed in terms of potential energy difference
( )b
a b b aa
W F d l U U U
Energy Theorem
For conservative forces in play,total energy of the system is conserved
a a b bK U K U
• The line integral used to calculate V does not depend on the path taken from A to B; therefore pick the most convenient path to integrate over
Electric Potential
• We can pick a 0 for the electric potential energy
• U is independent of any charge q that can be placed in the Electric field
• U has a unique value at every point in the electric field
• U depends on a location in the E field only
rU 0
0a bW Fd q Ed 0U q Ey 0 ( )a b a bW U q E y y
Potential energy U increases as the test charge q0 moves in the
direction opposite to the electric force : it decreases as it moves in the same direction as the force acting on the charge
0F q E
Electric Potential Energy of Two Point Charges
02
cosb
a
rb
a b ea r
qqW F d l k dl
r
01 1
a b ea b
W k qqr r
Example: Conservation of energy with electric forces
A positron moves away from an – particle
-particle
positron
0
31
100
60
9.1 10
7000
2
10
3 10 /
p
p
m kg
m m
q e
r m
V m s
What is the speed at the distance ?What is the speed at infinity?Suppose, we have an electron instead of positron. What kind of motion we would expect?
1002 2 10r r m
Conservation of energy principle
0 0 1 1K U K U
Electric Potential Energy of the System of Charges
Potential energy of a test charge q0
in the presence of other charges0
04i
ii
q qU
r
Potential energy of the system of charges(energy required to assembly them together)
0
1
4i j
iji j
q qU
r
Potential energy difference can be equivalently described as a work done by external force required to move charges into the certain geometry (closer or farther apart). External force now is opposite to the electrostatic force
( )a b b a extW U U F d l
Electric potential is electric potential energy per unit charge
Finding potential (a scalar) is often much easier than the field (which is a vector). Afterwards, we can find field from a potential
0
UV
q Units of potential are Volts [V]
1 Volt=1Joule/Coulomb
If an electric charge is moved by the electric field, the work done by the field
0 0
( )a ba b
W UV V
q q
Potential difference if often called voltage
Two equivalent interpretations of voltage:
1.Vab is the potential of a with respect to b, equals the work done by the electric force when a UNIT charge moves from a to b.
2. Vab is the potential of a with respect to b, equals the work that must be done to move a UNIT charge slowly from b to a against the electric force.
Potential due to the point charges
0
1
4
dqV
r Potential due to a continuous
distribution of charge
Finding Electric Potential through Electric Field
0
ba b
a ba
WV V E d l
q
Some Useful Electric Potentials
• For a uniform electric field
• For a point charge
• For a series of point charges
€
V = −r E • d
r l = −
r E • d
r l = −
r E •
r l ∫∫
rq
kV e
i
ie r
qkV
Potential of a point charge
Moving along the E-field lines means moving in the direction of decreasing V.
As a charge is moved by the field, it loses it potential energy, whereas if the chargeis moved by the external forces against the E-field, it acquires potential energy
Positive Electric Charge Facts
• For a positive source charge– Electric field points away from a positive source charge
– Electric potential is a maximum
– A positive object charge gains potential energy as it moves toward the source
– A negative object charge loses potential energy as it moves toward the source
Negative Electric Charge Facts
• For a negative source charge– Electric field points toward a negative source charge
– Electric potential is a minimum
– A positive object charge loses potential energy as it moves toward the source
– A negative object charge gains potential energy as it moves toward the source