Elect Magnet 5

8/2/2019 Elect Magnet 5

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3. 3. 3.1. 3.1.

3.2. 3.2.

3.3. 3.3.

3.4. 3.4.

3.5. 3.5. EE

3.6. 3.6. 3.7. 3.7.

......


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3.5. 3.5. EE

EE VV

VV EE

dsds 2 2

EE EExx (())

B

B AA

V V E ds

dV E ds

x E ds E dx

x xdVdV E dx E dx

E


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.. dV=dV= -- EErrdrdr..

V, EV, Err rr--

r E ds E dr

rdVEdr

+q

E


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55

3 : 3 :

-- , , y,zy,z :: V=3xV=3x22y+yy+y22+yz+yz

: :

--

: :

ds

dV E ds 0

x y z

V V V E ; E ; E

x y z

V / x V / x 6 xy

E V i j k V x y z


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22.8 22.8 Let us use the potential function for a point chargeLet us use the potential function for a point charge qq

to derive the electric field at a distanceto derive the electric field at a distance rr from thefrom the

charge.charge. qq

rr

:

r-

qV k

r

r

dV d q d 1 E k kq

dr dr r dr r

r 2

qE k

r


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22.9 22.9

The electric potential ofThe electric potential ofa dipole.a dipole.

An electric dipoleAn electric dipoleconsists of two equalconsists of two equaland opposite chargesand opposite chargesseparated by a distanceseparated by a distance2a2a, as in Fig., as in Fig.

Calculate the electricCalculate the electricpotential and the electricpotential and the electricfield at the pointfield at the point PPlocated a distancelocated a distance xx fromfromthe center of the dipole.the center of the dipole.

..

2a2a , ,

.. xx

PP . .

P+_

a ay

-q qx

x


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::

PP x>>ax>>a xx22--aa22

22--

PP

P+_

a a

y

-q qx

x

i

i

q

V k r

2

2kqa

V x

3

dV 2kqaE

dx x

2 2

q q 2kqa

k x a x a x a


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3.6. 3.6.

E=0E=0

A,BA,B 2 2

E ds

E ds 0

B AV V E ds 0


10/20 1010

, , 2 2

, ,

--

RR +Q+Q

: , : , kQ/rkQ/r22

: : kQ/RkQ/R,, kQ/rkQ/r

(( ))

, ,

+

+

+ +

+

+

+

+

R

E

rRV

2

kQ

r

kQr

kQR


11/20 1111

EE

E=0E=0 VVBB--VVAA=0=0

: :

, , A,BA,B VVAA--VVBB=0=0

B

B AA

V V E ds


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22.10 22.10 Two spherical conductorsTwo spherical conductors

of radiiof radii rr11 andand rr22 areare

separated by a distanceseparated by a distancemuch larger than themuch larger than theradius of either sphere.radius of either sphere.

The spheres areThe spheres areconnected by aconnected by aconducting wire as inconducting wire as inFig.Fig.

If the charges on theIf the charges on thespheres in equilibriumspheres in equilibrium

areare qq11 andand qq22,,,,respectively, find therespectively, find theratio of the fieldratio of the fieldstrengthes at thestrengthes at thesurfaces of the spheres.surfaces of the spheres.

rr11 rr22

..

. .

qq11,,,,qq22 . .


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:: VV

1 2

1 2

q qV k kr r

1 1

2 2

q r

q r

1 21 22 2

1 2

q q E k , E k

r r

1 2

2 1

E r

E r

q1

q2

r1

r2

3 7 3 7


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3.7. 3.7.

1929 1929

--

1 1 3 3101066

20 20

X hX h


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XerographyXerography 1940 1940 CarlsonCarlson, 1947 , 1947 XeroxXerox , ,

: : , ,


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, ,

, 99% , 99% 4040--100 100

, 2 , 2--

, , , , 22

E


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1. 1.

. . ?? ? ? ??

? ? 2. 2. . .

? ?

3. 3.

. . ? ? ? ? ? ? ? ?

4. 4.

, , ? ? 5. 5.

? . ? .


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6. 6. )) , , ))

..

7. 7. ? ?

8. 8. . . ? ?

9.9. . . ? ?

10.10.

. . 11.11.

, , ? ?

12. 12.

? ?


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2020

Elect Magnet 5

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