electric potential. gravitational potential energy b hbhb f = mg haha a gpe = mgΔh gpe = mgh a –...
TRANSCRIPT
Electric Potential
Gravitational Potential Energy
B
hB
F = mg
hA
A GPE = mgΔh
GPE = mghA – mghB
GPE = Work (W) required to raise or lower the book.
-Where W = (Fgravity)(Δh)
Electric Potential Energy+ + + + + + + + +
- - - - - - - - - -
+
Fe = qoE
A
dA+
Fe = qoE
B
dB
•Does a proton at rest at point A have more or less potential energy than it would at point B? More
ΔEPE = qoEΔd
ΔEPE = qoEdA – qoEdB
-WE(AB) = qoEdA – qoEdB
-WE(AB) = FedA – FedB
Electric Potential Energy of Point Charges Much like the book is attracted to the earth due to gravity,
two unlike charges are attracted to one another. Conversely, like charges repel. It takes positive work to move unlike charges away from
one another and negative work to move them closer together.
F = kqqo
r2
Ue = Fr = kqqo
r
+q
-qo
rE
EPE
Electric Potential Energy and Work of Point Charges
+q
-qo
rA
A
+q
-qo
rB
B
To change the energy level from UA to UB, it requires positive work (W).
-W = UB – UA
-W = kqqo – kqqo
rB rA
Electric Potential Energy1. What would happen if the charged particle q was fixed in
place and then particle qo was suddenly released from rest?
A. It would accelerate away from q.B. It would accelerate towards q.C. It would stay where it is.
2. How would the potential energy of thissystem change?
A. It would increase.B. It would decrease.C. It would remain the same.
+q
-qo
Electric Potential
SI Units: joule/coulomb = 1 volt (V)
The Electric Potential Difference is equal to the Work required to move a test charge from infinity to a point in an electric field divided by the magnitude of the test charge.
The Electric Potential is the energy per unit of charge (J/C).
ooAB q
W
q
EPEVVV
r
kqqEPE o Since
AB r
kq
r
kqV
Point Charges only
Example 1: Electric Potential
An object with 2.5C of charge requires 1.00x10-
3 Joules of energy to move it through an electric field. What is the potential difference through which the charge is moved?
VV
CJV
C
J
q
WV
400
/400
105.2
001.06
Relationship Between Electric Potential and Distance(point charges)
Consider relationship between V and r.
What happens to V as rB goes to ?
•As r increases, i.e., as rB , V 0.
•The relationship above reduces to: V = kq/rThe sign of the charge will determine if the electric potential is positive or negative.When two or more charges are present, the total electric potential is the sum total from all the charges present in the system.
-WAB kq kq
qo rB rA
VB - VA = = -
Electric Potential(point charges) Consider the following system of three point charges.
What is the electric potential that these charges give rise to at some arbitrary point P?
Use superposition to determine V.
kQ1 kQ2 kQ3
r1 r2 r3
Note that the electric potential can be determined from any arbitrary point in space.
P
Q1
Q3
Q2
r1r2
r3
+ +V =
Electric Potential and Electrical Potential Energy/Work (point charges)
If we now move a test charge from infinity to point P, we can determine the potential energy of the system or the work required to the test charge to its new location.
Remember: work = energy.qo
Q1
Q3
Q2
r1r2
r3
31 2
1 2 3
o
o
U W q V
QQ QW kq
r r r
Example 2: Two Point ChargesTwo point charges, +3.00 µC and -6.10 µC, are separated by
1.00 m. What is the electric potential midway between them?
A
-6.10 μC
B
+3.00 μC
0.5 m0.5 mVtotal = VA + VB = kqA/rA + kqB/rB
VA = (8.99 x 109 Nm2/C2)(-6.10 x 10-6C) = -109678 V
0.5mVB = (8.99 x 109 Nm2/C2)(3.00 x 10-6C) = 53,940 V
0.5m
Vtotal = -55700 V
Characteristics of a Capacitor
Uniform Electric Field
Two equal and oppositely charged plates
+++++++++++++++
---------------
E
• Since the electric field is constant, the force acting on a charged particle will be the same everywhere between the plates.
• Fe = qoE
B
qo
qo
A
qo
C
FA = FB = FC
Electric Potential and Work in a Capacitor
qo
A
F = qoE
qo
B
F = qoE
dA
dB
+++++++++++++++
---------------
(Ue) -WAB
qo qo
WAB = F·dB - F·dA
WAB = qoEd
V = =
If WAB = qoEd, then what is WCD?
qo
D
C
WCD = 0 Joules because the force acts perpendicular to the direction of motion.
•Do you remember that W = F·d·cos?
Electric Potential of a Capacitor – An alternative From mechanics, W = Fd. From the previous slide, W = qoEd
From the reference table, V = W/qo
V = WAB/qo = Fd/qo = qoEd/qo = Ed
+++++++++++++++
---------------
UniformElectricField
qo
A
F = qoE
B
d
Two equal and oppositely charged plates
Example 3:Parallel PlatesA spark plug in an automobile engine consists of two metal
conductors that are separated by a distance of 0.50 mm. When an electric spark jumps between them, the magnitude of the electric field is 4.8 x 107 V/m. What is the magnitude of the potential difference V between the conductors?
V = Ed
V = (4.8 x 107 V/m)(5.0 x 10-4m)
V = 24,000V
d
Example 4: Parallel Plates
A proton and an electron are released from rest from a similarly charged plate of a capacitor. The electric potential is 100,000 V and the distance between the two plates is 0.10 mm.
1. Which charge will have greater kinetic energy at the moment it reaches the opposite plate?
2. Determine the amount of work done on each particle.3. Determine the speed of each particle at the moment it
reaches the opposite plate.4. Determine the magnitude of the force acting on each
particle.5. Determine the magnitude of the acceleration of each
particle.
Example 4: Parallel Plates(cont.)
Begin by drawing a picture and listing what is known: V = 100,000V d = 0.10 mm = 1.0 x 10-4m qe = qp = 1.6 x 10-19C (ignore the sign. We are
only interested in magnitude.)
+++++++++++++++
---------------
p+
e-
d
Example 4: Parallel Plates(#1 & #2) For #1, you could answer #2 first to
verify. The answer is that the kinetic energy of both
particles will be the same • Why?• because of the formula needed in question #2
applies to both charges, and work = energy.
• Hence: Wproton = Welectron
qprotonV = qelectronV
Wproton = Welectron = (1.6x10-19C)(100,000V)
Wproton = Welectron = 1.6x10-14 J
Example 4: Parallel Plates(#3) Apply the work-energy theorem to determine the
final speed of the electron and proton.W = KE
Since the initial kinetic energy is equal to 0J:W = KEf
W = ½ mvf2
Proton:
Electron:
146
27
(2)( ) (2)(1.6 10 )4.38 10 /
( ) (1.67 10 )fproton
W Jv m s
m kg
148
31
(2)( ) (2)(1.6 10 )1.87 10 /
( ) (9.11 10 )felectron
W Jv m s
m kg
Example 4: Parallel Plates(#4) Since F = qE, it will be the same for both
particles because their charges are the same and the electric field is uniform between two parallel plates.
We also know that W = Fd. Since we know the distance between the plates and the work done to move either charge from one plate to another, we can determine the force as follows:
1410
4
1.6 101.6 10
1.0 10
W JF N
d m
Example 4: Parallel Plates(#5) Since we have the force acting on each particle,
we can now calculate the acceleration of each particle using Newton’s 2nd Law.
1016 2
27
1020 2
31
1.6 109.6 10 /
1.67 10
1.6 101.8 10 /
9.11 10
proton
electron
F Na m s
m kg
F Na m s
m kg
Equipotential Lines Equipotential lines denote where the electric potential is
the same in an electric field. The potential is the same anywhere on an equipotential
surface a distance r from a point charge, or d from a plate. No work is done to move a charge along an equipotential
surface. Hence VB = VA (The electric potential difference does not depend on the path taken from A to B).
Electric field lines and equipotential lines cross at right angles and point in the direction of decreasing potential.
Equipotential Lines
Parallel Plate Capacitor
Electric Field Lines
+++++++++++++++
---------------
Decreasing Electric Potential / Voltage
Lines of Equipotential
Note: Electric field lines and lines of equipotential intersect at right angles.
Equipotential Lines
Point Charge
+
Lines of Equipotential
Electric Field Lines
Decreasing Electric Potential / Voltage
Note: Electric field lines and lines of equipotential intersect at right angles.
Note: A charged surface is also an equipotential surface!
Equipotential Lines (Examples) http://www.cco.caltech.edu/~phys1/java/phys1/E
Field/EField.html
Key Ideas Electric potential energy (U) is the work required to bring a
positive unit charge from infinity to a point in an electric field.
Electric potential (V) is the change in energy per unit charge as the charge is brought from one point to another.
The electric field between two charged plates is constant meaning that the force is constant between them as well.
The electric potential between two points is not dependent on the path taken to get there.
Electric field lines and lines of equipotential intersect at right angles.
Electric Potential Energy and Work in a Uniform Electric Field
qo
A
F = qoE
qo
B
F = qoE
dA
dB
+++++++++++++++
---------------
WAB = EPEB – EPEA
WAB = FdB – FdA
WAB = qoEdB – qoEdA
WAB = qoE(dB – dA) = qoEd
Note: The force acting on the charge is constant as it moves from one plate to another because the electric field is uniform.