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

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!

Have a great day!

Please don’t forget your pictures

Hw: All Chapter 3 problems and exercisesReading: Chapter 3