Electric Potential Energy & Electric Potential Honors Physics Mr. Kuffer.
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Transcript of Electric Potential Energy & Electric Potential Honors Physics Mr. Kuffer.
Electric Potential Energy & Electric Potential
Honors Physics Mr. Kuffer
We Know… Coulomb’s Law
If either Q1 or Q2 increases the Force increases
If either Q1 or Q2 decreases the Force decreases
If r, the distance between the two charges, increases the force decreases
If r, the distance between the two charges, decreases the force increases
Because r appears as 1/r2 the dependence on r is strong
Q1 r Q2
We know… Coulomb’s Law
Double r. F decreases by a factor of 4
If r -> r/3 F increases by a factor of 9
If r decreases to ¼ of its value,
F becomes 16 times as large
Q1 r Q2
We know… The Electric Field
The electric field is the force on a small charge, divided by the charge:
Fields play an intermediate role in the force between bodies.We treat fields as a property of space. Charges create fields. Given the field we can calculate the forces on ANY charged objects
Field Lines
The electric field between two closely spaced, oppositely charged parallel plates is constant.
Today’s Topics
• Electric Potential Energy• Electric Potential• Electric Equi-potential Lines
Recall… Work
• You do work when you push an object up a hill• The longer the hill the more work you do: more
distance• The taller the hill, the more work you do: more force
The work, W, done on an object by an agent exerting a constant force is the product of the component of the force in the direction of the displacement and the magnitude of the displacement
dFW ||
Energy is capacity to do worknote Ep aka UG
• Gravitational Potential Energy• Kinetic Energy• Energy can be converted into other forms of
energy • When we do work on any object we transfer
energy to it • Energy cannot be created or destroyed
mghUG
2
2
1mvK
GU
GUKW
Potential Energy
The presence of charges can give rise to a potential energy (PE)
Ug doing work!! Ue doing work!!
Potential EnergyWe determined the
potential energy Uel of a spring by asking how much work we do to compress it.
We can determine the potential energy of a charge distribution by how much work we do to bring the charge to its position
Potential of a Parallel-Plate Capacitor
Slide 21-24
Potential Energy• High Gravitational PE. Ball will roll down hill
• High Electrical Potential Energy• Positive charge will move away
• Positive charge will “fall” from high • potential energy to low PE +
• Negative charge “falls” from high PE to• low PE -
•
Electric Potential Energycharges also have electrical potential energy
EEF 0q
+Q
+Q
d
FdW
Edq0
EdqU e 0
vNote the loss in potential Energy.Hence the ‘-’ sign
Electric Potential Energy
• Work done (by electric field) on charged particle is qEd
• Particle has gained Kinetic Energy (qEd)• Particle must therefore have lost
Potential Energy U=-qEd
Electrostatic Potential Energy
Change in electric potential energy is work done against electric force (from b to a):
PEa – PEb = qEd
a---
Compare Ug b---
Ug = mg (a-b) =mgh
Electric Potential
• Just as Electric field depends on space and allows us to compute force on any charge, Electric Potential depends on space and allows us to calculate Uelec for any charge.
(Not Electric Potential Energy)
Electric Potential
0q
UV
compare with the Electric Field and Coulomb Force
0q
FE
If we know the potential field this allows us to calculate changes in potential energy for any charge introduced
VqU 0 EF 0q
Electrostatic Potential Energy and Potential Difference
Electric potential is defined as potential energy per unit charge:
Unit of electric potential: the volt (V).
1 V = I J/C.
qVU elec
q
UV elec
Greater at B, Greater yet at C
Ue= qV
Ue= q V Ue(B) = 10 nC * 400V
Electrostatic Potential Energy and Potential Difference
Analogy between gravitational and electrical potential energy:
A
B
Which has higher potential energy A, B or C the same?
A and B are the same distance from sphere
A
B
Which has higher potential energy A, B or C the same?
A and B are the same distance from sphere
A
B
Which is at a higher potential (voltage)A,B or C the same?
A and B are the same distance from sphere
A
B
Which is at a higher potential (voltage)A,B or C the same?
(electric potential is a "property" related only to the electric field itself)
A and B are the same distance from sphere
Careful here!Potential is a measure per individual charge!
Electrostatic Potential Energy and Potential Difference
Only changes in potential can be measured, allowing free assignment of V = 0… where there is no change there is no potential difference.
Vba = Vb – Va = Ue(b) –Ue (a)
q
Therefore Potential (V) is unaffected by position change within equipotential surfaces!
For Potential Difference… defining ‘zero’ is arbitrary… just like choosing a frame of reference for Ug
Electric Potential
Electric Potential is a scalar
it is defined everywhere
but it does not have any direction
it doesn’t depend on a charge being there
Super Fun Review Challenge!
Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f?
+ i f
Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f?
+ i f
Is the change in Ue ΔU, A) positive B) negativeC) zeroas a negative charge moves from point labeled i to f?
+ i f
Is the change in Ue ΔU, A) positive B) negativeC) zeroas a negative charge moves from point labeled i to f?
+ i f
Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f? + -
i f
Is the change in Ue ΔU, A) positive B) negativeC) zeroas a positive charge moves from point labeled i to f? + -
i f
Conceptual Example Problem
Slide 21-17
The correct order of electrical potentials from largest to smallest is A)V1>V2>V3B)V1=V2> V3C)V1=V2 =V3D)V3>V2=V1E)V3>V2>V1
Note: q1, q2, & q3 are positive test charges
Conceptual Example Problem
Slide 21-17
The correct order of electrical potentials from largest to smallest is A)V1>V2>V3B)V1=V2> V3 C)V1=V2 =V3D)V3>V2=V1E)V3>V2>V1
Note:1 and 2 share an equipotential surface.
Conceptual Example Problem
Slide 21-17
The correct order of electrical potentials from largest to smallest is A)V1>V2>V3B)V1=V2> V3C)V1=V2 =V3D)V3>V2=V1E)V3>V2>V1
Note: q1, q2, & q3 are positive test charges
Conceptual Example Problem
Slide 21-17
The correct order of electrical potentials from largest to smallest is A)V1>V2>V3B)V1=V2> V3C)V1=V2 =V3D)V3>V2=V1E)V3>V2>V1
Note: We are asked about the Electric Potential… not the Force the charge Feels!
Energy Conservation in Electric Potentials
• Just as for mechanical systems Energy is conserved. We can change potential energy to kinetic energy and vice versa.
• Kf + qVf = Ki + qVi
• Kf –Ki = qVi –q Vf =-q(Vf –Vi)
ΔK = -qΔV
The more Potential is lost… the more Kinetic is gained
Charged Particle Moving Through a Potential Difference
Slide 21-18ΔK = -qΔV
Charged Particle Moving Through a Potential Difference
Slide 21-18
Be careful! Things are reversed for negative charge.Negative charge speeds up if it moves from region of lower to higher potential: ΔK = -qΔV
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy (not charge) gained by an electron moving through a potential difference of one volt.
Slide 21-19
Example ProblemA proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point?
Slide 21-20