Elect Magnet 2

8/2/2019 Elect Magnet 2

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2 2


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1.1.

1.1. 1.1.

1.2. . 1.2. .

1.3. 1.3.

1.4. 1.4. 1.5. 1.5.

1.6. 1.6.

1.7. 1.7.

1.8. 1.8.


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1.5. 1.5.

? ?

DDqq

PP : :

!!

2

q

E k r r

D

D

ii2

i i

q E k r

r

D

i

2q 0i i

q E k lim r

rD

D

2

dqk r

r


4/21

, , [[//33

]]

, , [[//22]]

, , [[//]]

EE EExx, E, Eyy, E, Ezz (3(3 ))

Q

V Q

S

Q

l

dQ,

dV

2

dV E k ,

r

dQ,

dS

dQ

dl

2

dS E k ,

r

2

dlE k

r


5/21

20.7 20.7 The electric field dueThe electric field due

to a charged rod:to a charged rod: AArod of lengthrod of length llhas ahas auniform positive chargeuniform positive chargeper unit lengthper unit length and aand atotal chargetotal charge QQ..

Calculate the electricCalculate the electricfield at a pointfield at a point PPalongalongthe axis of the rod, athe axis of the rod, adistancedistance ddfrom one endfrom one end(Fig.).(Fig.).

..ll

QQ .. d

P .x

y

Pd l


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Solution:Solution: For thisFor this

calculation, the rod iscalculation, the rod is

taken to be along thetaken to be along the xxaxis.axis.

:: xx

..

The ratio ofDq, thecharge on the segment toDx, the length of the

segment, is equal to theratio of the total charge tothe total length of therod.

Dq Dx

.

q Q

x l

D

D

x

y

P

d l

xDx Dq=Dx


7/21

d>>ld>>l ll--

DDq=q=DDxx

PP x

y

Pd l

xDx Dq=Dx

2 2

q x E k k

x x

D DD

DE

l d

2

d

dxE k

x

2 2E k l / d kQ / d

l d

2d

dxE k x

l d

d

1 1 1k k

x d l d

lk

d( l d )


8/21

20.8 20.8 The electric field of a uniform ring of chargeThe electric field of a uniform ring of charge. A ring. A ring

of radiusof radius aa has a uniform positive charge per unithas a uniform positive charge per unitlength, with a total chargelength, with a total charge QQ. Calculate the electric. Calculate the electricfield along the axis of the ring at a pointfield along the axis of the ring at a point PP lying alying adistancedistance xx from the center of the ring (Fig.).from the center of the ring (Fig.).

..

aa

QQ..

xx PP . .

aP

x+

+

+

+

+

+

+

+

+

+

+

+


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DDqq

: :

xx

. . : :

(x>>a)(x>>a)

(x=0)(x=0)

Dq

a P

x+

+

+

+

+

+

+

+

+

+

+

+

DE

2

q

E k r

D

D

x E E cosD D ED ED

r

DEx

ED

Dq

122 2r ( x a ) , cos x / r

x E E cosD D 2q x

kr r

D

3

22 2

kxq

( x a )D

32

x 2 2

kxE q

( x a )D

3

22 2

kxQ

( x a )


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20.9 20.9 . . RR

. . xx . .

rr drdr 22pprdrrdr

dq=2dq=2pprdrrdr

20.8 20.8-- ((aa rr))

r=0r=0-- r=Rr=R

x 32 2 2

kxdE ( 2 rdr )

( x r )p

Q=pR2 P x 0,0, RR :: x 0 E 2 k / 2p

R

xPr

dr

dq

32

R

x 2 20

2rdr E kx

( x r )p

1

22 2

x... 2 k 1

( x R )p

32

R2 2 2

0kx ( x r ) d( r )p


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1.6. 1.6.

1. 1. EE

2. 2. N~EN~E

, ,

. .

+ -


12/21

, ,

, ,

2 2

N 1 E

4 r rp


13/21

, ,

((..))--

+ 2q q

!


14/21

1.7. 1.7.

EE qq qqEE

IIII FF=q=qEE=m=maa

(( ))

qEam


15/21

(x,y)

tt

t=x/vt=x/v00 y~xy~x22

YY EE

vv00ii

vvx0x0=v=v00, v, vy0y0=0=0

eEa j

m

x 0 y

eEv v const, v at t

m

2 2

0

1 1 eE

x v t , y at t 2 2 m

+ + + + + +

_ _ _ _ _ _

(0,0)

v

v0i

-


16/21

5,35,31010--1111

FFee/F/Fgg3310103939..

2 19 29 8

e 2 11 2

e ( 1,6 10 ) F k 9 10 8,2 10

r ( 5,3 10 )

31 27 e p 11 47

g 2 11 2

m m ( 9,11 10 )( 1,67 10 ) F G ( 6 ,7 10 ) 3,6 10

r ( 5,3 10 )


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20.10 20.10


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1.8. 1.8.

(())


19/21

. .

, ,

, ,

CC

AA


20/21


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Elect Magnet 2

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