PHYS 202

Lecture 2Professor Stephen Thornton

January 24, 2005

Reading QuizLook carefully at theelectric field lines for thefour charges. Which viewis correct for the electricfield lines?

1. Top2. Bottom3. Neither

Answer: 2The top view cannot be correct, because two of the electric field lines cross. More lines should go to –2qthan to +q. Place a test charge q0 at various points, and the bottom view does seem to represent the electric field lines.

Scheduling PHYS 201-2Discuss problem with late afternoon lecture. Discuss possible lecture times. No conflict with required chemistry and biology courses for pre-health careers.Consider moving to TTh morning next year.

I am taking PHYS202 because1) It is required for my major.2) It has been advised to take for my

major.3) I wanted to know some more

science.4) Seemed like a good idea at the time.

The following best describes my situation:1) Premed2) Prevet3) Predental4) Chemistry major, but not pre-health5) Biology major, but not pre-health6) Other science major, but not pre-health7) Other

I might have to do some rearranging (even change years), but I could take PHYS 202 at these times (TTh):1) 9:30-10:45, 11:00-12:15, or 12:30-1:452) Only 9:30-10:45 or 11:00-12:153) Only 9:30-10:45 or 12:30-1:454) Only 11:00-12:15 or 12:30-1:455) Only 9:30-10:456) Only 11:00-12:157) Only 12:30-1:458) None of these times

If you are not listed on WebAssign, please see me after class, and I will add you right here. This applies especially to Continuing Ed students.

I increased the authorized enrollment in the problem sections today from 27 to 28.

Last Time1) Organization of course, grades, etc.2) Electric charge.3) Coulomb force law.

Show movie on what can happen with electrostatics.

Today1) Learn about electric field.2) Learn how to obtain electric fields

for various charge configurations.3) Study effects of electric field.4) Charge induction5) Learn about electric flux, Gauss’

law.

Electric field

What is a field? Why do we want to learn about it.

Discuss fields in general temperature gravitation

Force Between 2 Point Charges

20qqF k r=

An Electrostatic Force Field

0q

Definition of Electric Field

1 02

qqF k r= 10

is force between charge and test charge (small).F q

q

1r2

0

1

ˆ= e

The test charge is used to map out the electric field due to charge ( in this case).

F kqEq r

q q

=1 0

Electric field due to a charge (not ). Unit: N/Cq q

Electric Field of a Point Charge

The Direction of the Electric Field

Superposition of the Electric Field

We have to make sure that the test charge q0 does not affect the electric field that we are testing. It must be a small point charge.

Now we have an electric field. What can we do with it?

Relation between F and E

If we put a charge in an electric field , then the charge feels a force of value

***

q Eq

F qE= This is the really useful part.

Do electric field demos.Felt and oil (electric field)Electric lines of force (capacitor,

rotating needle, Wimshurstmachine

Electric wind (capacitor, candle,Wimshurst machine

Determining electric fields

***Rules and hints:1) E lines start on + charges, end on – charges.

Can start and stop at infinity.2) Place test charge q0 at any point and find

direction of force on q0 to determine E line.3) E lines can never intersect!4) E lines are more dense when magnitude is

greater.

Let’s draw some E lines

1) Something simple, points -2q and +q.2) Two point charges together, point

charges of q and –q. 2q and –q. +q and +q.

3) Charged plate. (charge must be equally spread on plate).

4) Two oppositely charged plates.5) Positively charged plate (+Q) and

negative point charge (-Q).

Figure 19-14Electric Field Lines for a Point Charge

Figure 19-15aElectric Field Lines for Systems of Charges

We call this a dipole. It is a dipole field.

Figure 19-15bcElectric Field Lines for Systems of Charges

Figure 19-16The Electric Field of a Charged Plate

Figure 19-17A Parallel-Plate Capacitor

Conceptual QuizA negatively charged object is placed in an electric field as shown below.The direction of

the electrostatic force on the object is

1. to the right 2. to the left

3. neither to the left nor to the right4. depends on whether the field is created by a

positively or negatively charged object5. There is no force on the object at the

location shown in the figure

E

Answer: 2

Because the charge is negative, the force is opposite to the electric field.

F qE q E= = −

Conceptual QuizA dipole is placed as illustrated. The electric field at point P is

1. along x.2. along -x.3. along y.4. along -y.5. in another direction.6. The electric field at P is zero.

Answer: 1Put a test charge q0 at point P and see in what direction the force on q0 will be. If we add the two forces, we will see the net force is to the right along +x.

Figure 19-18Charge Distribution on a Conducting Sphere

Wrong

Correct

If charges were inside thesphere, they would repeleach other.

Charges placed on ametal conductor must reside on the surface.

The electric field near a conducting surface must be perpendicular to the surface when in equilibrium.

If we place conductor in electric field,the E lines must be to surface. If not,charges would move. must be zero inside.E

⊥

Do demos to show electric field is high near sharp corners.

Lightning rodIonic drive

Figure 19-20Intense Electric Field Near a Sharp Point

Conductor placed around a charge +Q

Conductor

Charging by Induction

Conceptual QuizIf, during charging by induction, the near side instead of the far side of the sphere is grounded, the charge left on the sphere after the grounding is

1. positive2. negative3. neither - the sphere remains neutral4. it depends

Answer: 1With the plus charge on the left, the left side of the metal sphere will be negative, and the right side will be positive. The negative charge will be drawn off by the grounding wire. When the wire is removed, there will be a net positive charge on the sphere.

Electric Flux

Electric fluxEAΦ =

0Φ =

Electric Flux – surface at an angle

cos Flux is a scaler.We want component of electricfield perpendicular to surface.

EA θΦ =

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 permittivityof free space (a constant).

o

qεε

Φ =

Figure 19-24Electric Flux for a Point Charge

Two Gaussian surfaces

Figure 19-25Gauss’s Law Applied to a Spherical Shell

0E =

0E ≠

0E ≠Conductor

Figure 19-26Gauss’s Law Applied to a Sheet of Charge

ImaginaryGaussianSurface

Electric field of charged sheet

0 0

0

0

(2 )

where is charge/area on the sheet.

2

2

q AE A

AE A

E

σε ε

σσε

σε

Φ = = =

=

=

Work Problems19-5219-75

PHYS 202Reading QuizLook carefully at theelectric field lines for thefour charges. Which viewis correct for the electricfield liAnswer: 2Scheduling PHYS 201-2I am taking PHYS202 becauseThe following best describes my situation:I might have to do some rearranging (even change years), but I could take PHYS 202 at these times (TTh):If you are not listed on WebAssign, please see me after class, and I will add you right here. This applies especially to ContLast TimeTodayElectric fieldWhat is a field? Why do we want to learn about it. Discuss fields in general temperature gravitationForce Between 2 Point ChargesAn Electrostatic Force FieldDefinition of Electric FieldElectric Field of a Point ChargeThe Direction of the Electric FieldSuperposition of the Electric FieldWe have to make sure that the test charge q0 does not affect the electric field that we are testing. It must be a small pointRelation between F and EDo electric field demos.Felt and oil (electric field)Electric lines of force (capacitor, rotating needle, WimshurstDetermining electric fieldsLet’s draw some E linesFigure 19-14Electric Field Lines for a Point ChargeFigure 19-15aElectric Field Lines for Systems of ChargesFigure 19-15bcElectric Field Lines for Systems of ChargesFigure 19-16The Electric Field of a Charged PlateFigure 19-17A Parallel-Plate CapacitorConceptual QuizA negatively charged object is placed in an electric field as shown below.The direction ofAnswer: 2 Because the charge is negative, the force is opposite to the electric field.Conceptual QuizA dipole is placed as illustrated. The electric field at point P is 1. along x.2. along -x.3. along y.Answer: 1Figure 19-18Charge Distribution on a Conducting SphereThe electric field near a conducting surface must be perpendicular to the surface when in equilibrium.Do demos to show electric field is high near sharp corners.Lightning rodIonic driveFigure 19-20Intense Electric Field Near a Sharp PointConductor placed around a charge +QCharging by InductionConceptual QuizIf, during charging by induction, the near side instead of the far side of the sphere is grounded, the chargeAnswer: 1Electric FluxElectric Flux – surface at an angleElectric FluxUse an imaginary surface, called a Gaussian surface, to surround any area you choose. The electric flux througFigure 19-24Electric Flux for a Point ChargeFigure 19-25Gauss’s Law Applied to a Spherical ShellFigure 19-26Gauss’s Law Applied to a Sheet of ChargeElectric field of charged sheetWork Problems19-5219-75