PHYS 202

Lecture 3Professor Stephen Thornton

January 26, 2005

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

Problem 19-75

See next two pages where I have worked out solution.

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 =

Chapter 20Electric Potential and Electric

Potential Energy

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.

Change in Electric Potential Energy

Who (or what) is doing work here?

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

+ = +

∆∆ = ∆ = ∆

=− = − = −

We can work problems to find the increased speed of charged particles in an electric field.

A 0v =

−

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.

Work Problem 20-13

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

Xerography

Electrocardiogram

Electroencephalogram

Work Problem 20-35

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.

Van de Graaff

Accelerator

Do demos

Lightning rodVan de Graaff generator