Transcript electric potential difference

Ch 25 – Electric Potential
A difference in electrical potential
between the upper atmosphere and
the ground can cause electrical
discharge (motion of charge).
Ch 25 – Electric Potential
So far, we’ve discussed electric force and fields.
Now, we associate a potential energy function with electric force.
This is identical to what we did with gravity last semester.
gravity

m1m2
Fg  G 2 rˆ
r
m

g  G 2 rˆ
r
m1m2
U g  G
r
electricity
Fe  ke
q1 q2
r2

q
E  ke 2 rˆ
r
?
Ch 25.1 – Electric Potential and Potential Difference
• Place a test charge, q0, into an E-field. The charge will experience a
force:


F  q0 E
• This force is a conservative force.
• Pretend an external agent does work to move the charge through the
E-field.
• The work done by the external agent equals at least the negative of
the work done by the E-field.
Ch 25.1 – Electric Potential and Potential Difference
• Let’s introduce a new symbol:

ds
• We’re talking about moving charges
through some displacement.
• The “ds” vector is a little tiny step of
displacement along a charge’s path.
Ch 25.1 – Electric Potential and Potential Difference
• If q0 moves through the E-field by a little step ds, the E-field does
some work:
 
dWEfield  F  ds
• As the E-field performs this work, we say that the potential energy
of the charge-field system changes by this amount.
• This is the basis for our definition of the potential energy function.
Ch 25.1 – Electric Potential and Potential Difference
• If q0 moves through the E-field by a little step ds, the E-field does
some work:
 
dWEfield  F  ds

 
 
dU  dWEfield  F  ds  q0 E  ds

 
U  U B  U A  q0  E  ds
B
A
Ch 25.1 – Electric Potential and Potential Difference
 
U  U B  U A  q0  E  ds
B
A
The change in electrical potential energy
of a charge-field system as the charge
moves from A to B in the field.
The integral accounts for the motion of the charge through a 1-D
path. It’s called a “path” or “line” integral.
Ch 25.1 – Electric Potential and Potential Difference
 
U  U B  U A  q0  E  ds
B
A
The change in electrical potential energy
of a charge-field system as the charge
moves from A to B in the field.
Because electric force is conservative, the value of the integral does
not depend on the path taken between A and B.
Ch 25.1 – Electric Potential and Potential Difference
 
U  U B  U A  q0  E  ds
B
Potential Energy refresher:
A
Potential Energy measures the energy a system has due
to it’s configuration.
We always care about changes in potential energy – not
the instantaneous value of the PE.
The zero-point for PE is relative. You get to choose what
configuration of the system corresponds to PE = 0.
The change in electrical potential
energy of a charge-field system as
the charge moves from A to B in
the field.
Ch 25.1 – Electric Potential and Potential Difference
• What we’re about to do is different than anything you saw in
gravitation.
• In electricity, we choose to divide q0 out of the equation.
 
U
V 
  E  ds
q0
A
B
• We call this new function, ΔV, the “electric potential difference.”
Ch 25.1 – Electric Potential and Potential Difference
B
 
U
V 
  E  ds
q0
A
Potential difference between two points in
an Electric Field.
• This physical quantity only depends on the electric field.
• Potential Difference – the change in potential energy per unit
charge between two points in an electric field.
• Units: Volts, [V] = [J/C]
Ch 25.1 – Electric Potential and Potential Difference
B
 
U
V 
  E  ds
q0
A
Potential difference between two points in
an Electric Field.
• Do not confuse “potential difference” with a change in “electric
potential energy.”
• A potential difference can exist in an E-field regardless the
presence of a test charge.
• A change in electric potential energy can only occur if a test
charge actually moves through the E-field.
Ch 25.1 – Electric Potential and Potential Difference
• Pretend an external agent moves a charge, q, from A to B without
changing its speed. Then:
W  U
But: V  U
q0
W  qV
Ch 25.1 – Electric Potential and Potential Difference
• Units of the potential difference are Volts:
1 V  1 J/C
• 1 J of work must be done to move 1 C of charge through a
potential difference of 1 V.
Ch 25.1 – Electric Potential and Potential Difference
• We now redefine the units of the electric field in terms of volts.
1 N/C  1 V/m
E-field units in terms of
volts per meter
Ch 25.1 – Electric Potential and Potential Difference
• Another useful unit (in atomic physics) is the electron-volt.
1 eV  1.6010-19 C  V  1.6010-19 J
The electron-volt
• One electron-volt is the energy required to move one electron
worth of charge through a potential difference of 1 volt.
• If a 1 volt potential difference accelerates an electron, the electron
acquires 1 electron-volt worth of kinetic energy.
Quick Quiz 25.1
Points A and B are located in a region where there is an
electric field.
How would you describe the potential difference
between A and B? Is it negative, positive or zero?
Pretend you move a negative charge from A to B. How
does the potential energy of the system change? Is it
negative, positive or zero?
Ch 25.2 – Potential Difference in a Uniform E-Field
Let’s calculate the potential difference between A and B separated by a
distance d.
Assume the E-field is uniform, and the path, s, between A and B is
parallel to the field.
 
V   E  ds
B
A
Ch 25.2 – Potential Difference in a Uniform E-Field
Let’s calculate the potential difference between A and B separated by a
distance d.
Assume the E-field is uniform, and the displacement, s, between A and
B is parallel to the field.
 
V   E  ds
B
A
B
V   Edscos
1
A
B
V   E  ds
A
V   Ed
Ch 25.2 – Potential Difference in a Uniform E-Field
V   Ed
The negative sign tells you the potential at B is lower
than the potential at A.
VB < VA
Electric field lines always point in the direction of
decreasing electric potential.
Ch 25.2 – Potential Difference in a Uniform E-Field
Now, pretend a charge q0 moves from A to B.
The change in the charge-field PE is:
U  q0 V  q0 Ed
If q0 is a positive charge, then ΔU is negative.
When a positive charge moves down field, the
charge-field system loses potential energy.
Ch 25.2 – Potential Difference in a Uniform E-Field
Electric fields accelerate charges… that’s what
they do.
What we’re saying here is that as the E-field
accelerates a positive charge, the charge-field
system picks up kinetic energy.
At the same time, the charge-field system loses an
equal amount of potential energy.
Why? Because in an isolated system without
friction, mechanical energy must always be
conserved.
Ch 25.2 – Potential Difference in a Uniform E-Field
If q0 is negative then ΔU is positive as it moves
from A to B.
U  q0 V  q0 Ed
When a negative charge moves down field, the
charge-field system gains potential energy.
If a negative charge is released from rest in an
electric field, it will accelerate against the field.
Ch 25.2 – Potential Difference in a Uniform E-Field
Consider a more general case.
Assume the E-field is uniform, but the path, s, between A and B is not
parallel to the field.
 
V   E  ds
B
A
Ch 25.2 – Potential Difference in a Uniform E-Field
Consider a more general case.
Assume the E-field is uniform, but the path, s, between A and B is not
parallel to the field.
 
 B 
 
V   E  ds   E   ds   E  s
B
A
A
 
U  q0V  q0 E  s
Ch 25.2 – Potential Difference in a Uniform E-Field
 
V   E  s
If s is perpendicular to E (path C-B), the
electric potential does not change.
Any surface oriented perpendicular to the
electric field is thus called a surface of
equipotential, or an equipotential
surface.
Quick Quiz 25.2
The labeled points are on a series of
equipotential surfaces associated with
an electric field.
Rank (from greatest to least) the work
done by the electric field on a
positive charge that moves from A to
B, from B to C, from C to D, and
from D to E.
EG 25.1 – E-field between to plates of charge
A battery has a specified potential difference ΔV between its terminals and
establishes that potential difference between conductors attached to the
terminals. This is what batteries do.
A 12-V battery is connected between two plates as shown. The separation
distance is d = 0.30 cm, and we assume the E-field between the plates is
uniform. Find the magnitude of the E-field between the plates.
EG 25.1 – Proton in a Uniform E-field
A proton is released from rest at A in a uniform E-field of magnitude 8.0 x
104 V/m. The proton displaces through 0.50 m to point B, in the same
direction as the E-field. Find the speed of the proton after completing
the 0.50 m displacement.