Download Electric Potential

Electric Potential Energy
Work is defined as the product of displacement d
and a parallel applied force F.
Work = Fd; Units: 1 J = 1 N m
Potential Energy U is defined as the ability to do work
by virtue of position or condition. (Joules)
Kinetic Energy K is defined as the ability to do work
by virtue of motion (velocity). (Also in Joules)
Work (Fd) is positive if an applied force F is
in the same direction as the displacement d.
B
F
m
mg
A
d
Consider work against g to move m
from A to B, a vertical height h.
Work = Fh = mgh
At level B, the potential energy U is:
U = mgh (gravitational)
B
F
m
mg
h
g
A
The external force does positive work;
the gravity g does negative work.
The external force F against the g-field increases the
potential energy. If released, the field does work.
An external force F moves +q from
A to B against the field force qE.
Work = Fd = (qE)d
At level B, the potential energy U is:
U = qEd (Electrical)
The E-field does negative work;
External force does positive work.
B ++++
Fe
+q + d
qE
E
A - - - -
The external force F against the E-field increases the
potential energy. If released, the field does work.
Suppose a negative charge –q is
moved against E from A to B.
Work by E = qEd
At A, the potential energy U is:
U = qEd (Electrical)
No external force is required !
B ++++
F=qE
-q
d
E
A - - - -
The E-field does positive work on –q decreasing the
potential energy. If released from B nothing happens.
Equation for Work in a Uniform Electric Field
The work W done by the
electric field E to move the
charge a distance d (in a uniform electric field)
is
W = Fd = qEd
where F = qE, since E = F/q
Work = -ΔPE
The electrostatic force is
conservative – potential
energy can be defined.
Change in electric potential
energy is negative of work
done by electric force:
ΔPE = U =
Where d is the distance between charged plates
What about a Non-Uniform Field?
Electric PE for a point charge
(relative to some source point charge)
Or, PE Between Two Charges.
Δ P.E. = W = F d = F r =
ΔP.E. = U =
r =
(as measured from infinity)
Note: A reference point of PE = 0 is conventionally
set at infinity because at this location, the electrical
force on a charged particle due to a source charge
would be zero.
A
•
8 cm
+2 nC
+Q
+6 µC
U = 1.35 mJ
Positive potential energy
A
•
•
B
12 cm
8 cm
Questions:
If +2 nC moves from A to B,
does field E do + or – work?
Does P.E. increase or decrease?
+Q
•
C
4 cm
+6 µC
Moving
positive q
+2 nC
If +2 nC moves from A to C (closer to +Q)…
the field E does negative work and P.E.
increases.
A
•
•
B
12 cm
8 cm
From Ex-1: UA = + 1.35 mJ
ΔU = UB – UA = 0.9 mJ – 1.35 mJ
+Q
+6 µC
ΔU = -0.450 mJ
Note that P.E. has decreased as work is done by E.
A
•
•
B
12 cm
8 cm
Questions:
If -q moves from A to B, does
field E do + or – work? Does
P.E. increase or decrease?
+Q
•
C
4 cm
+6 µC
Moving
negative q
-
What happens if we move a –2 nC charge from A to B
instead of a +2 nC charge. This example follows . . .
A
•
From Ex-1: UA = -1.35 mJ
8 cm
•
B
12 cm
+Q
+6 µC
2
Nm
(9 × 10 9 2 )(6 × 10 −6 C)(−2 × 10 −9 C)
C
UB =
= −0.900mJ
0.12m
UB – UA = -0.9 mJ – (-1.35 mJ)
ΔU = +0.450 mJ
€
A – charge moved away from a + charge gains P.E.
Example 4: Electric Potential Energy
Two alpha particles (helium nuclei), each consisting of
two protons and two neutrons, have an electrical potential
energy of 6.32 x 10-19 J. What is the distance between
these particles?
PE = 6.32x10-19 J ;
q1 = q2 = +2e = 3.2x10-19 C ;
PE = k (q1q2)/ r
k (q1q2) / PE = r
(8.99x109)(3.2x10-19)(3.2x10-19)
r = 1.46 x 10-9 m
/ (6.32x10-19) = r
r=?
Electric Field
.
E
r
++
+
+
++Q++
E is a Vector
An electric field is a property of
space allowing prediction of the
force on a charge at that point.
The field E exists independently
of the charge q and is found from:
P.
r
+ ++
+
++Q++
Potential
U = qV = (-2 x 10-9C)(400 J/C);
U = -800 nJ
Analogy between gravitational and electrical
potential energy:
Analogy between gravitational and electrical
potential energy:
Electrical potential energy depends on charge,
but electrical potential does not.
A potential of one volt at a given point means that
a charge of one coulomb placed at that point will
experience a potential energy of one joule.
P.
r
+ ++
+
++Q++
Potential
The potential due to a positive charge is
positive; The potential due to a negative
charge is negative. (Use sign of charge.)
Analogy between gravitational and electrical
potential energy:
Analogy between gravitational and electrical
potential energy:
Electrical potential energy depends on charge,
but electrical potential does not.
Electrostatic Potential Energy and
Potential Difference
Electric potential is defined as
potential energy per unit charge:
kQ
=
r
Unit of electric potential: the volt (V).
€ 1 V = 1 J/C.
Electric Potential vs Electric Potential
Energy
•  Which charge has
more electric
potential?
•  Which has more
electric potential
energy?
Electric Potential vs Electric Potential
Energy
•  Electric Potential (voltage) is independent
of charge (it is energy per charge)
•  Electric Potential Energy is charge
dependent
P.
r 6 cm
-- -Q- -- -
Negative V at
Point P :
VP = -750 V
Q = -5 nC
U = 3.00 mJ
Since P.E. is positive, E will do + work if q is released.
The Electric Potential V in the vicinity of a number
of charges is equal to the algebraic sum of the
potentials due to each charge.
Q1 - r1
r3
Q3 -
•
A
r2
+
Q2
Potential is + or – based on sign of the charges Q.
B •
2 cm
Q1 + +3 nC
6 cm
A •
2 cm
VA = 450 V – 2250 V;
VA = -1800 V
Q2 = -5 nC
B •
2 cm
Q1 + +3 nC
6 cm
A •
2 cm
VB = 1350 V – 450 V;
VB = +900 V
Q2 = -5 nC
Potential Difference: ΔV =VAB = VB - VA
WorkAB (Work BY E-field) = -qΔV
The positive and negative signs of the charges may
be used mathematically to give appropriate signs.
B •
VA = -1800 V
VB = +900 V
2 cm
Q1 + +3 nC
6 cm
A •
VAB = +2700 V
Q2
2 cm
- -5 nC
Work = -5.40 mJ
Thus, an external force was required to move the charge.
VA = -1800 V
VB = +900 V
B •
2 cm
Q1 + +3 nC
6 cm
A •
VBA = -2700 V
Q2
-
Work = +5.40 mJ
The work is done BY the E-field this time !
2 cm
-5 nC
VA + + + +
Constant E field: F = qE
+q
F = qE
VB - - - VAB = -Ed
The potential difference between two oppositely
charged parallel plates is the product of E and d.
E
VA + + + +
E
+q
F = qE
VB - - - -
-
U
V = →U = Vq
q
-
U = −qEd
€
The E-field expressed in volts per meter (V/m) is
€ and is equivalent to
known as the potential gradient
the N/C. The volt per meter is the better unit for
current electricity, the N/C is better electrostatics.
Example 8: Electric Potential Energy
A charge moves a distance of 2.0 cm in the direction of a
uniform electric field having a magnitude of 215 N/C. The
electrical potential energy of the charge decreases by
6.9x10-19 J as it moves. Find the magnitude of the charge
on the moving particle.
ΔPE = -6.9x10-19J ; d = 2cm = 0.02m ;
ΔPE = -qEd
- ΔPE / Ed = q
- (-6.9x10-19J) / ((215)(0.02)) = q
1.6 x 10-19 C = q
E = 215 N/C ;
q=?
Electric Potential
Energy and Potential
Electric Potential Near
Multiple charges:
WorkAB = q(VA – VB)
Oppositely Charged
Parallel Plates:
Work BY E-field
Work done on charge (by external force)? Yes
Electric PE is greatest at:
A
Electric potential is greatest at:
or
B
A or B
or
No
Work done on charge (by external force)? Yes
Electric PE is greatest at:
A
Electric potential is greatest at:
or
B
A or B
or
No
Work done on charge to get from A to B?
Yes or No
Electric PE is greatest at:
A
Electric potential is greatest at:
or
B
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
What if the test charge were negative?
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Potential due to an electric field is assumed, by definition,
to originate from a positive source charge (field lines go
out from positive to negative).
An electron moving to a higher potential (closer to the
field line origins) will be losing potential energy. So ΔPE is
negative, and, since q is also negative (in ΔV = ΔPE / q),
ΔV is positive, moving from A to B.
The opposite will hold if it is being moved closer to a like
(negative) charge. In that case it will be moving along the
direction of the electric field lines.
Also, it helps if you think of electric potential as a property
of the field, but think of PE as a property of the charge.
Read more in our book, p.572
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Work done on charge? Yes
or
No
Electric PE is greatest at:
or
B
A
Electric potential is greatest at:
A or B
Potential Difference
•  Batteries provide
potential difference
between one end of the
circuit and the other
Potential Difference
•  Batteries provide
potential difference
between one end of the
circuit and the other
•  Positive charges flow
from high to low electric
potential
The terminals of a battery are
defined as follows:
Potential Difference
•  Batteries provide
potential difference
between one end of the
circuit and the other
•  Positive charges flow
from high to low electric
potential
Potential Difference
•  Batteries provide
potential difference
between one end of the
circuit and the other
•  Positive charges flow
from high to low electric
potential
•  Negative charges flow
from _____ to _____
electric potential.
Potential Difference
•  Batteries provide
potential difference
between one end of the
circuit and the other
•  Positive charges flow
from high to low electric
potential
•  Negative charges flow
low to _____
high
from _____
electric potential.
The diagram shows a light bulb connected to a 12-V car
battery. The + and - terminals are shown.
a. As a + charge moves through the battery
gains (gains, loses)
from D to A, it ________
potential energy and ________ (gains, loses)
electric potential. The point of highest energy
within a battery is the ______ (+, -) terminal.
b. As a + charge moves through the external
circuit from A to D, it ________ (gains, loses)
potential energy and ________ (gains, loses)
electric potential. The point of highest energy
within the external circuit is closest to the
______ (+, -) terminal.
VA = VB > VC = VD
c. Use >, <, and = signs to compare the
electric potential (V) at the four points of the
circuit.
The diagram shows a light bulb connected to a 12-V car
battery. The + and - terminals are shown.
a. As a (-) charge moves through the battery
from A to D, it ________ (gains, loses)
potential energy and ________ (gains, loses)
electric potential. The point of highest energy
within a battery is the ______ (+, -) terminal.
b. As a (-) charge moves through the external
circuit from D to A, it ________ (gains, loses)
potential energy and ________ (gains, loses)
electric potential. The point of highest energy
within the external circuit is closest to the
______ (+, -) terminal.
VA = VB > VC = VD
c. Use >, <, and = signs to compare the
electric potential (V) at the four points of the
circuit.
Equipotential Lines
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
The surface of a conductor is
an equipotential.
Equipotential Lines
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by
an electron moving through a potential
difference of one volt.
The Electron Volt, a Unit of Energy
(Another Approach)
One electron volt (eV) is the amount of energy
experienced by an electron (or proton) when
it drops its potential by 1 V.
1eV = ΔPEe = qeΔV = (1.6 x 10-19C) (1V)