Lecture 5 was cancelled due to weather.

Example 1: Electric field of a point charge is directly radially away from or toward the charge.

rr

qE ˆ

4

12

0

Example 2: Electric field of a dipole

Example 3: Electric field at the center of a charged ring

Think first!(before you start doing calculations)

0E

Example 4: Find the electric field at the center of a semi-circle of radius R, if a charge Q is uniformly spread over the semi-circle.

OxiR

QE

2

022

Example 5: Electric field on ring’s axis

ziRz

QzE

2322

0 )(4

1

z

Example 6: Electric field on disk’s axis

2

122

32 )(

1

)( cxcx

xdx

ziRz

z

z

zE

22202

ziz

QEzRz

2

04

10,

z

z

z

iEz

iEz

iz

zERz

0

0

0

20

20

2

z

Exercise 5 page 33

In a famous experiment Millikan measured the size of the electron’s charge by adjusting an field so that the force of gravity pulling down on a small, charged oil drop was cancelled by the electric force pushing up. If the mass of the drop was kg and it contained 10 electronic charges, what size field was necessary to keep the drop in equilibrium?

E

13100.2 E

Robert Millikan’s oil-drop experiment (1909)

Robert Andrews Millikan1868-1953

American experimental physicist 1923 Nobel Prize

Millikan received a Bachelor’s degree in the classics from Oberlin College in 1891 and his doctorate in physics from Columbia University in 1895 – he was the first to earn a Ph.D. from that department.

"At the close of my sophomore year [...] my Greek professor [...] asked me to teach the course in elementary physics in the preparatory department during the next year. To my reply that I did not know any physics at all, his answer was, 'Anyone who can do well in my Greek can teach physics.' 'All right,' said I, 'you will have to take the consequences, but I will try and see what I can do with it.' I at once purchased an Avery’s Elements of Physics, and spent the greater part of my summer vacation of 1889 at home – trying to master the subject. [...] I doubt if I have ever taught better in my life than in my first course in physics in 1889. I was so intensely interested in keeping my knowledge ahead of that of the class that they may have caught some of my own interest and enthusiasm."

Exercise 5 page 33

In a famous experiment Millikan measured the size of the electron’s charge by adjusting an field so that the force of gravity pulling down on a small, charged oil drop was cancelled by the electric force pushing up. If the mass of the drop was kg and it contained 10 electronic charges, what size field was necessary to keep the drop in equilibrium?

E

13100.2 E

Motion in an electric field

A positively charged object, with mass m, is placed at rest in a constant field. How fast will the object be moving after it has traveled a distance L?

E

Example 2

Consider a constant, vertical electric field somehow created in a limited region of space. An electron enters the region traveling horizontally with speed . If the region has a length L, how much will the electron be deflected at the end of the region?

0v

Example 3A particle with mass m and charge q is ejected from the lower of two parallel plates with velocity of magnitude as shown. If a constant electric field exists between the plates, magnitude E, where will the particle return to the lower plate? How large must L be so that the particle doesn’t strike the upper plate? (Neglect gravity.)

0v

E

0v

L

x

y

One-dimensional problem:

dxxFWx

x

)(2

1

dx

dUxF )(

dxdx

dUx

x

2

1

)]()([ 12 xUxU

P218 Review: Conservative forces

Two-dimensional problem:

dyFdxFrdFWr

r

y

r

r

x

r

r 2

1

2

1

2

1

)]()([ 12 rUrU

y

UF

x

UF yx

;

veconservatiW does NOT depend on path!

veconservatiW around the closed path is zero!

Chapter 3. Electric Potential

• Constant electric field

• The Electric Potential: V

- Single Charge

- Dipole

EqF

- conservative? potential energy function?

€

rE • d

r r

r r 1

r r 2

∫ = − limq0 → 0

1

q0

[U(r r 2) −U(

r r 1)] = −[V (

r r 2) −V (

r r 1)]

ExxVConstE )(

For a point charge at the origin:

r

qrV

04

1)(

Have a great day!

Hw: All Chapter 3 problems and exercisesReading: Chapter 3