Reading Quiz
We have a point charge at the origin.At which point, A, B,or C, is the electricpotential the smallest?
1. A2. B3. C4. They are all the same.
A
BC
Answer: 3
The electric potential for a single point charge is equal to kq/r. The electric potential will be the largest when r is the smallest and the electric potential is smallest when r is the greatest.
Last Time
1) Learned about electric field.2) Learned how to obtain electric
fields for various charge configurations.
3) Studied effects of electric field.4) Charge induction5) Learned about electric flux, Gauss’
law.
Today
1) Review from last time.2) Electric potential3) Electric potential energy4) Conservation of energy again5) Applications
Show Van de Graaff accelerator
Review some special results
• The electric (or Coulomb) force is anotherforce to be added to the net force.
• F = qE when we have a charge q in a E.• We use to help find electric field.• We have rules to help us find E lines.• E inside a conductor is 0.• E outside a conductor is ⊥ to surface.
0q
e = 1.6 x 10-19 C, electron charge
Electric Flux
Use an imaginary surface, called a Gaussian surface, to surround any area you choose. The electric flux through the surface is proportional to the electric charge inside.
0where is the permittivity of free space.o
qεε
Φ = q is charge inside surface
Work Problem 19-73.Part c)What is relationship between electric field on Earth and Moon if Q is the same?
1) Emoon > EEarth2) Emoon < EEarth3) Emoon = EEarth4) Can’t possibly tell.
2
2
kQR
E =
0
WorkF q EW F s
U W F s
== ∆
∆ = − = − ∆
Ignore gravity
The charge q0 feels a force due to E.The electric field E does work on the charge.The charge has a higher potential energy on the left than it does on the right.
Electric Potential V
0 0
Unit: J/C = volt, VU WVq q∆ −
∆ ≡ =
Electric potential, or potential, is one of the most useful concepts in electromagnetism. This is a biggie!!
Electric Field and Electric Potential
What is the relationship?Potential must be related to electric field.
0
0
0 0
Solve for ,
W F s q E sW q E sVq q
V E sE
VEs
= ∆ = ∆− − ∆
∆ = =
∆ = − ∆
∆= −
∆
The Electric Potential for a Constant Electric Field
VEs
∆= −
∆
High potential Low potential
E = constant = 0/σ ε
Energy conversation
Energy conservation relations are still valid.
0
If we look at definition of ,
we have , so
or ( ) ***
A A B B
B A A B A B
K U K UV
UV U q Vq
U qVK K U U q V V
+ = +
∆∆ = ∆ = ∆
=− = − = −
−
Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the –plate. Which particle has the greatest kinetic energy when it reaches the other plate?
1. proton2. electron3. the kinetic energies are the same.
Answer: 3The particles experience the same electric field and have the same charge. The kinetic energy increase is equal to the work done by the electric field. W = Fd = qEd
−−
Conceptual Quiz. A proton is released from the + plate as shown, and an electron is released from the –plate. Which particle has the greatest speed when it reaches the other plate?
1. proton2. electron3. the kinetic energies are the same.
Answer: 2We just saw that the proton and electron will have the same kinetic energy increase. But K = mv2/2, and because the electron has such a smaller mass, its velocity must be much greater than that of the proton.
Energy Conservation in an Electrical System
002
At point A,
The test charge feelsforce and speeds up;Gains K.E., loses P.E.
A
A B
qqF k q Er
U U
= =
>
0 doesn't work here, because changes with distance, so we must
use integral calculus to find and .
W F s q E sE
W U
= ∆ = ∆
∆
Electric potential for a point charge0 0
0
0
Earlier, we found ( )
We can define zero to be anywhere we want, say .
*** without subscripts
A BA B A b
A B A B
A BA B
qq qq kq kqU U k k qr r r r
U U q V Vkq kqV Vr r
BkqVr
⎛ ⎞− = − = −⎜ ⎟
⎝ ⎠
− = −
− = −
=
Notes on electric potential
Point charge ***
Scalar quantity, not vector like electric field.For multiple charges, we simply add numerical values for simple superposition!In practice, we use potential concept much more than electric field. We can measure potential easily, but not electric field.
kqVr
=
The Electric Potential of a Point Charge
0 as far away from charge as 0 close to charge
V rV r→ →∞→∞ →
kqVr
=
+ charge
- charge
Electric Potential Energy
Electric potential energy for two point charges, q and q0, separated by a distance r, is simply
00
q qU q V kr
= =
ApplicationsElectrostatic precipitatorsXerographyElectrocardiogram EKGElectroencephalogram EEGNeurons - nerve cells
Conceptual QuizConsider a rectangular Gaussian surface surrounding a dipole that has 16 field lines emanating from its positively charged end.
If you move the Gaussian rectangle around (anywhere in the plane), the field line flux through the rectangle: 1. always remains zero.2. varies between -32 and 32.3. varies between -16 and 16.4. is -16, zero, or 16.5. Other.
Answer: 4Remember that the actual picture is much larger than shown. If we move the rectangle over the + charge and exclude the -, we have 16. Similarly over the -, but exclude the +, we have –16. If we exclude both + and -, we have zero. If we include neither charge, we have zero. For point charges, that is all the possibilities. See next slide.
Conceptual QuizConsider a rectangular Gaussian surface surrounding a dipole that has 16 field lines emanating from its positively charged end.
If you move the Gaussian rectangle around (anywhere in the plane), the field line flux through the rectangle: 1. always remains zero.2. varies between -32 and 32.3. varies between -16 and 16.4. is -16, zero, or 16.5. Other.
Conceptual Quiz. A positively charged rod is held near a grounded surface as illustrated below.
Compared to ground, the potential at point A is 1. higher2. the same3. lower4. undefined
Answer: 1
The potential will be zero at the ground. If we place our test charge near the positive rod, it will be repelled. Therefore, it has higher potential energy near the rod.