t¸c gi¶: pgs. ts §ç ngäc uÊn viÖn vËt lý kü thuËt tr êng
TRANSCRIPT
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Bμi gi¶ng VËt lý ®¹i c−¬ng
T¸c gi¶: PGS. TS §ç Ngäc UÊn
ViÖn VËt lý kü thuËt
Tr−êng §H B¸ch khoa Hμ néi
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Tμi liÖu tham khaá:1. Physics Classical and modernFrederick J. Keller, W. Edward Gettys, Malcolm J. SkoveMcGraw-Hill, Inc. International Edition 1993.2. R. P. FeymannLectures on introductory Physics3. I. V. SavelyevPhysics. A general course, Mir Publishers 19814. VËt lý ®¹i c−¬ng c¸c nguyªn lý vμ øng dông, tËp I, II, III. Do TrÇn ngäc Hîi chñ biªn
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C¸c trang Web cã liªn quan:http://ocw.mit.edu/OcwWeb/Physics/http://nsdl.exploratorium.edu/
Bμi gi¶ng cã trong trang:http://iep.hut.edu.vnVμo §μo t¹o ->Bμi gi¶ng VL§CIIload bμi gi¶ng vÒ in thμnh tμi liÖu cÇm tay, khi nghe gi¶ng ghi thªm vμo!
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• Tμi liÖu häc : VËt lý ®¹i c−¬ng: Dïng cho khèic¸c tr−êng §H kü thuËt c«ng nghiÖp (LT&BT)TËp II: §iÖn, Tõ, Dao ®éng & sãng.
C¸ch häc: Lªn líp LT; mang theo tμi liÖu cÇmtay, nghe gi¶ng, ghi thªm vμo tμi liÖu. • VÒ nhμ: Xem l¹i bμi ghi, hiÖu chØnh l¹i cïng tμiliÖu -> Lμm bμi tËp. • Lªn líp BT b¾t ®Çu tõ tuÇn 2: SV lªn b¶ng, thÇy kiÓm tra vë lμm bμi ë nhμ.• §iÓm QT hÖ sè 0,3 gåm ®iÓm kiÓm tra gi÷a kú+ §iÓm chuyªn cÇn; NÕu nghØ 2,3 buæi trõ 1 ®iÓm, nghØ 4,5 buæi trõ 2 ®iÓm.
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� Hoμn chØnh bμi nμy míi ®−îc lμm tiÕp bμi sauCuèi cïng ph¶i b¶o vÖ TN� NÕu SV kh«ng qua ®−îc TN, kh«ng ®−îc dùthi. • Thi: 15 c©u tr¾c nghiÖm (m¸y tÝnh chÊm) + 2 c©u tù luËn, räc ph¸ch (thÇy ngÉu nhiªn chÊm)Mçi ng−êi 1 ®Ò . §iÓm thi hs 0,7• §iÓm qu¸ tr×nh hÖ sè 0,3.
• ThÝ nghiÖm: §äc tμi liÖu TN tr−íc, kiÓm traxong míi ®−îc vμo phßng TN, Sau khi ®o ®−îcsè liÖu ph¶i tr×nh thÇy vμ ®−îc thÇy chÊp nhËn.• §ît 1: tõ tuÇn 3 (22/2/10)• Tμi liÖu: Liªn hÖ BM VLDC tÇng 2 nhμ D3.
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Ch−¬ng 1
Tr−êng tÜnh ®iÖn
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1. Nh÷ng kh¸i niÖm më ®Çu:• HiÖn t−îng nhiÔm ®iÖn do cä x¸t• §iÖn tÝch nguyªn tè: ®iÖn tö -e=-1,6.10-19C, me=9,1.10-31kg; Proton: +e, mp=1,67.10-27kg• MÊt ®iÖn tö nhiÔm ®iÖn d−¬ng: thuû tinh• NhËn ®iÖn tö nhiÔm ®iÖn ©m: lôa• §Þnh luËt b¶o toμn ®iÖn tÝch: Tæng ®¹i sè ®iÖntÝch cña hÖ c« lËp lμ kh«ng ®æi.• Ph©n lo¹i vËt: DÉn ®iÖn, ®iÖn m«i, B¸n dÉn -> c¸c thuyÕt:KhÝ ®iÖn tö tù do ¸p dông cho kim lo¹iLý thuyÕt vïng n¨ng l−îng ¸p dông cho TThÓ
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2. §Þnh luËt Cul«ng2
21
021 r
|qq|4
1FFεπε
==
3. Kh¸i niÖm vÒ ®iÖn tr−êng, VÐc t¬ c−êng ®é ®iÖn tr−êng r
rr4
qE 20
rr
πε=
∑=
=n
1iiEErrNguyªn lý chång chÊt
®iÖn tr−êng•L−ìng cùc ®iÖn lqpe
rr=
30
eM r4
pEεπε
−=rr
30
eN r4
p2Eεπε
=rr
4.1. §−êng søc ®iÖn tr−êng
§Æc ®iÓm: §−êng søc cña tr−êng tÜnh ®iÖn lμ c¸c®−êng hë
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2. §Þnh luËt Cul«ng
q1 q2
21rr20Fr
10Fr
q1 q2
12rr20Fr
10Fr q1q2>0
q1 q2
r
20Fr
10Fr
q1q2<0
rr
rqqkF 212
2110
rr=
rr
rqqkF 122
2120
rr=
221
2010 rqqkFF ==
2
29
0 CNm10.9
41k =πε
=
2Nm
2C1210.86,80−=ε
221
02010 r
|qq|4
1FFπε
==H»ng sè ®iÖn m«i
2.1. §Þnh luËt Cul«ngtrong ch©n kh«ng
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� §L Cul«ng: Lùc t−¬ng t¸c gi÷a hai ®iÖn tÝchcã ph−¬ng n»m trªn ®−êng nèi hai ®iÖn tÝch, lμlùc hót nhau nÕu hai ®iÖn tÝch tr¸i dÊu vμ ®Èynhau nÕu cïng dÊu, cã ®é lín tû lÖ víi ®é líntÝch gi÷a hai ®iÖn tÝch ®ã vμ tû lÖ nghÞch víi b×nhph−¬ng kho¶ng c¸ch gi÷a hai ®iÖn tÝch ®ã
221
021 r
|qq|4
1FFεπε
==
2.2. §Þnh luËt Cul«ng trong m«i tr−êng
ε- §é ®iÖn thÈm hay h»ng sè ®iÖn m«i tû ®èi
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Ch©n kh«ng 1Kh«ng khÝ 1,0006Thuû tinh 5 ÷ 10H2O 81DÇu c¸ch ®iÖn 1000
� §é ®iÖn thÈm hay h»ng sè ®iÖn m«i tû ®èi εcña mét sè chÊt:
� Lùc Cul«ng do hÖ ®iÖn tÝch ®iÓm q1, q2, ..., qn
t¸c dông lªn ®iÖn tÝch ®iÓm q0 :
∑=
=+++=n
1iin21 FF...FFFrrrrr
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3. Kh¸i niÖm vÒ ®iÖn tr−êng, VÐc t¬ c−êng ®é®iÖn tr−êng3.1. Kh¸i niÖm vÒ ®iÖn tr−êng:T−¬ng t¸c gi÷a hai ®iÖn tÝch ®iÓm x¶y ra nh−thÕ nμo?• ThuyÕt t¸c dông xa: Tøc thêi, kh«ng th«ngqua m«i tr−êng nμo c¶ ->Sai• ThuyÕt t¸c dông gÇn: Quanh ®iÖn tÝch cã m«itr−êng ®Æc biÖt->®iÖn tr−êng lan truyÒn víi c-> vËn tèc t−¬ng t¸c giíi h¹n->®iÖn tr−êng cña ®iÖn tÝch nμy t¸c dông lùclªn ®iªn tÝch kia
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3.2. VÐc t¬ c−êng ®é ®iÖn tr−êng§Þnh nghÜa:VÐc t¬ c−êng ®é ®iÖntr−êng t¹i mét ®iÓm lμ ®¹i l−îngcã gi¸ trÞ b»ng lùc t¸c dông cña®iÖn tr−êng lªn mét ®¬n vÞ ®iÖntÝch d−¬ng ®Æt t¹i ®iÓm ®ã
0qFEr
r=
Thø nguyªn:
q0
⊕q
⊕
Fr
)mV(
VÐc t¬ c−êng ®é ®iÖn tr−êngg©y ra bëi ®iÖn tÝch ®iÓm
MEr
rr
r4qqF 2
0
0rr
πε=
rr
rr
r4qE 2
0
rr
πε=
20r4|q|E
πε=
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VÐc t¬ c−êng ®é ®iÖn tr−êng g©y ra bëi hÖ®iÖn tÝch ®iÓm
⊕
⊕1q
1Fr
⊕iq
iFr
-2Fr
q2
∑=
=+++=n
1iin21 FF...FFFrrrrr
∑ ∑∑
= =
= ====n
1i
n
1ii
0
i
0
n
1ii
0E
qF
q
F
qFE
rr
rr
r ∑=
=n
1iiEErr
q0
M
...t¹i M b»ng tæng c¸c vÐc t¬ c−êng ®é ®iÖntr−êng g©y ra bëi c¸c ®iÖn tÝch ®iÓm t¹i ®iÓm®ã-> nguyªn lý chång chÊt ®iÖn tr−êng
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VÐc t¬ c−êng ®é ®iÖn tr−êng g©y ra bëi vËtmang ®iÖn tÝch dq
Mrrrr
r4dqEdE
tbv2
0
rrr∫∫ επε
==vËt bé Toμn
Edr
Trong tr−êng hîp cô thÓ ph¶i x¸c ®Þnh ph−¬ngvμ chiÒu b»ng h×nh vÏ, tÝch ph©n chØ x¸c ®Þnhgi¸ trÞ cña E
rr
r4dlE
tbv2
0
rr∫ επε
λ=
D©y:λ(C/m)dq= λdl
MÆt:σ(C/m2)dq= σdS
Khèi:ρ(C/m3)dq= ρdV
rr
r4dSE
tbv2
0
rr∫ επε
σ=
rr
r4dVE
tbv2
0
rr∫ επε
ρ=
dqi
irr iEd
r
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3.3. ThÝ dô•L−ìng cùc ®iÖn
⊕lr
--q q
lqpe
rr=
α
α
r1 r r21Er2Er
Er
M
21 EEErrr
+= E=2E1cosα
3101
210 r4
qlr2l
r4q2E
επε=
επε=
r4lrrlr2
21 ≈+=⇒>> qlpe =
30
e
r4pEεπε
=3
0
eM r4
pEεπε
−=rr
N•
30
eN r4
p2Eεπε
=rr
r
E ~ m«men l−ìng cùc ®iÖn pe
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•T¸c dông ®iÖn tr−êng ®Òu lªn l−ìng cùc ®iÖn+q
-ql
θ
0Er
'Fr
Fr
00 ElqEqlFlrrrrrrr
×=×=×=μ
0e Eprrr
×=μ μ=qlE0sinθ•VÐc t¬ c−êng ®é ®iÖn tr−êng g©y ra bëi d©y dÉnv« h¹n tÝch ®iÖn ®Òu
++++ Ed
r nEdr
//EdrM
rx α
α+επε
λ== ∫∫ cos
)rx(4dxdEE
tbd22
0tbdn
)rx/(rcos 2222 +=αα
α= 2cos
rddx
ααεπε
λ= ∫
π
π−
dcosr4
E2/
2/0 r2||E
0επελ
=
dq=λdx
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• VÐc t¬ c−êng ®é ®iÖn tr−êng g©y ra bëi ®Üatrßn ph¼ng tÝch ®iÖn ®Òu
dq=σdS=σxdxdϕ
αrh
2Edr
1Edr Ed
r
dE=2dE1cosα
2/322d 0 )xh(
xdxd2
hE+
ϕεπε
σ== ∫ ∫
tb tbd
dE
∫∫π
ϕ+επε
σ=
0
R
02/322
0d
)xh(xdx
2hE
dϕ
x dxϕ
R
))h/R1(
11(2
E 2/1220 +
−εε
σ=
®Üa ph¼ng v« h¹nR →∞
εεσ
=02
E
Er
2/122 )xh(hcos
+=α
xM
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4. §iÖn th«ng
4.1. §−êng søc ®iÖn tr−êng lμ ®−êng cong mμtiÕp tuyÕn t¹i mçi ®iÓm cña nã trïng víiph−¬ng cña vÐc t¬ c−êng ®é ®iÖn tr−êng t¹i ®iÓm ®ã chiÒu cña ®−êng søc ®iÖn tr−êng lμchiÒu cña vÐc t¬ c−êng ®é ®iÖn tr−êng
2Er1E
r
4Er3E
rTËp hîp ®−êng søc cña®iÖn tr−êng = ®iÖn phæ
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⊕
⊕⊕
§Æc ®iÓm: §−êng søc cña tr−êng tÜnh ®iÖn lμ c¸c®−êng hë
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4.2. Sù gi¸n ®o¹n ®−êng søccña ®iÖn tr−êng
⊕ε1ε2
NÕu 2ε1 = ε2 gi¸n ®o¹n t¹i biªn giíi hai m«i tr−êng=>VÐc t¬ c¶m øng ®iÖn
ED 0
rrεε= ED 0εε=
rr
r4qD 2
rr
π= 2r4
|q|Dπ
=
Thø nguyªnC/m2§iÖn tÝch ®iÓm
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dS
Dr
n.dSSd rr=nrα
dSn
4.3. Th«ng l−îng c¶m øng ®iÖn/®iÖn th«nglμ ®¹i l−îng cã ®é lín b»ng sè®−êng søc vÏ vu«ng gãc qua diÖn tÝch
nne DdSdSDcosDdSSdDd ==α==Φrr
qua diÖn tÝch S
SdDdS
eS
e
rr∫∫ =Φ=Φ
nr
nrnr
mÆt kÝn
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5. §Þnh lý «xtr«gratxki-Gauox (¤-G)5.1. Gãc khèi: gãc nh×n mét diÖn tÝch tõ mét®iÓm
dS n.dSSd rr=
dΩO
nr 2rcosdSd α
=Ωαrr
dScosα=dSnGãc nh×n mÆt cÇu (ph¸p tuyÕn ra):
π==α
=Ω ∫∫ 4r
dSrcosdS
S2n
S2
O
nr
nr
nrGãc nh×n mÆt cÇu(ph¸p tuyÕn vμo): Ω’=-4π
'nr' nr'nr
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5.2. §iÖn th«ng xuÊt ph¸t tõ ®iÖn tÝch ®iÓm q
2r4|q|D
π=
§iÖn th«ng qua dS α==Φ cosDdSSdDd e
rr
Ωπ
=απ
=Φ d4qcosdS
r4qd 2e
§iÖn tÝch ®iÓm q trong mÆt kÝn S
qd4qd
SSee =Ω
π=Φ=Φ ∫∫
§iÖn tÝch ®iÓm q ngoμi mÆt kÝn S
S2 S1
)dd(4q
1 2S Se ∫ ∫ Ω+Ω
π=Φ
0)(4q
=ΔΣ−ΔΣπ
= q
q
Sdr
nr
nr nr
ΔΣ
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5.3.§Þnh lý «xtr«gratxki-Gauox (¤-G)
§iÖn th«ng qua mÆt kÝn bÊt kú b»ng tæng ®¹i sèc¸c ®iÖn tÝch chøa trong mÆt kÝn Êy:
∑∫∫ ==Φi
iS
e qSdDrr Σqi Tæng ®¹i sè (dÊu
cña ®iÖn tÝch)
5.4. D¹ng vi ph©n ®Þnh lý «xtr«gratxki-Gauox
∫∫∫∫∫ =VS
dVDdivSdDrrr
zD
yD
xDDdiv zyx
∂∂
+∂
∂+
∂∂
=r
∫∫∫∑ ρ=Vi
i dVq Ddivr
=ρPh−¬ng tr×nh Poisson (Po¸t X«ng)
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5.5. øng dông: TÝnh D & E5.5.1 CÇu b¸n kÝnh R tÝch ®iÖnmÆt q
X¸c ®Þnh ®iÖn tr−êng t¹i ®iÓm:• Ngoμi cÇu(r>R):
• Trong cÇu (r’<R):
∑∫∫ ===Φi
iS
e qqSdD1
rr
D4πr2=q 2r4qDπ
=2
00 r4qDEεπε
=εε
=
∑∫∫ ===Φi
iS
e 0qSdD2
rrD=0, E=0
• Trªn mÆt cÇu (R):2R4
qDπ
= 20 R4qEεπε
=
Rqr’
S2
S1
r
![Page 27: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/27.jpg)
5.5.2 MÆt ph¼ng v« h¹n tÝch ®iÖn ®Òunr
Dr
σ>0
∫∫∫∫∫∫ +==Φ2d¸ynbªmÆt trômÆt
SdDSdDSdDe
rrrrrr
0SdD =∫∫nbªmÆt
rrS2DSdD Δ=∫∫
2day
rr
ΔS
σΔ==Φ ∫∫ SSdDe2d¸y
rr 2D σ=
εεσ
=02
E
5.5.3 Gi÷a 2 mÆt ph¼ng v« h¹n tÝch ®iÖn ®Òuσ<0 σ>0
D=0 D= σ D=0
Gi÷a: E ®Òuεεσ
=0
E
Ngoμi: E=0
![Page 28: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/28.jpg)
5.5.4 MÆt trô v« h¹n tÝch ®iÖn ®Òu
l rR
Dr
ΔVÏ mÆt trô: qua M, b¸n kÝnh r, cao l
∫∫∫∫∫∫ +==Φ2d¸ynbªmÆt trômÆt
SdDSdDSdDe
rrrrrr
rl2DSdD π=∫∫nbªmÆt
rr0SdD =∫∫
2d¸y
rr
lRl2QSdDe λ=σπ===Φ ∫∫nbªmÆt
rr
r2rR
rl2QD
πλ
=σ
=π
=
r2rR
rl2QE
000 επελ
=εε
σ=
επε=
nr
M
Q - §iÖn tÝch trªn mÆt trôtrong, cao l
r
σ -MËt ®é ®iÖn mÆtλ - MËt ®é ®iÖn dμi
![Page 29: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/29.jpg)
6. §iÖn thÕ
6.1 C«ng cña lùc tÜnh ®iÖn. TÝnhchÊt thÕ cña tr−êng tÜnh ®iÖn
q
q0
Nrr
Mrr
sdrαFr
sdEqsdFdA 0rrrr
==
sdrr4
qqdA 30
0rr
επε=
20
02
0
0
r4qdrqcosds
r4qq
επε=α
επε= ds.cosα=dr
N
M
N
M
rr
0
0r
r2
0
0MN |)
r1(
4qq
rdr
4qqA −
επε=
επε= ∫
N0
0
M0
0MN r4
qqr4
qqAεπε
−επε
=C«ng cña lùc tÜnh ®iÖn
Trong ®iÖntr−êng cña q
=> TÝnh chÊt thÕ
rrM
N
![Page 30: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/30.jpg)
Trong ®iÖn tr−êng bÊt k×q0 ch ®éng trong ®iÖn tr−êng cña hÖ q1,q2,...qn
∑∑==
==n
1ii0
n
1ii EqFF
rrr
∑∑== επε
−επε
=n
1i iN0
i0n
1i iM0
i0MN r4
qqr4
qqA
C«ng cña lùc tÜnh ®iÖn trong sù dÞch chuyÓn®iÖn tÝch q0 trong ®iÖn tr−êng bÊt k×:• Kh«ng phô thuéc vμo d¹ng cña ®−êng cong dÞch chuyÓn
0sdEqsdFA 0 === ∫∫rrrr
•ChØ phô thuéc vμo ®iÓm ®Çuvμ cuèi cña chuyÓn dêi•=> TÝnh chÊt thÕ:
![Page 31: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/31.jpg)
� L−u sè vÐc t¬ c−êng ®é ®tr−êngdäc theo mét ®−êng cong kÝn b»ngkh«ng:
0sdE =∫rr
6.2 ThÕ n¨ng cña mét ®iÖn tÝch trong ®iÖntr−êng
N0
0
M0
0MN r4
qqr4
qqAεπε
−επε
=
C«ng b»ng ®é gi¶m thÕ n¨ng dA=-dW
N
N
M
N
MMMN WWdWdAA ∫ ∫ −=−==
M0
0M r4
qqWεπε
=
N0
0N r4
qqWεπε
=
![Page 32: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/32.jpg)
Cr4
qqW0
0 +επε
= W∞ = 0 =>C=0
r4qqW0
0
επε=
r
W
0
q0q>0
q0q<0
∫∞
=M
0M sdEqW rr
� ThÕ n¨ng q0 t¹i M trong ®iÖntr−êng lμ ®¹i l−îng vÒ trÞ sèb»ng c«ng cña lùc tÜnh ®iÖntrong sù dÞch chuyÓn q0 tõ M raxa v« cïng
6.3. §iÖn thÕ
6.3.1 §Þnh nghÜa: W/q0 kh«ng phô thuéc vμo®iÖn tÝch q0 mμ chØ phô thuéc vμo vÞ trÝ trong®iÖn tr−êng vμ ®iÖn tÝch g©y ra ®iÖn tr−êng
![Page 33: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/33.jpg)
§iÖn thÕ t¹i ®iÓm ®ang xÐt cña ®t0q
WV =
r4qV
0επε=§iÖn thÕ q g©y ra t¹i r
§iÖn thÕ hÖ qi
g©y ra t¹i r ∑∑ επε==
i i0
i
ii r4
qVV
∫∞
=M
M sdEV rr
AMN=WM-WN=q0(VM-VN)
� §iÖn thÕ t¹i M trong ®iÖn tr−êng lμ ®¹i l−îng vÒ trÞ sè b»ng C«ng cña lùc tÜnh ®iÖntrong sù dÞch chuyÓn ®¬n vÞ ®iÖn tÝch d−¬ng tõM ra ∞
C«ng dÞch chuyÓn q0 tõ M ->N:
![Page 34: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/34.jpg)
6.3.2 ý nghÜa
0
MNNM q
AVV =−q0=+1 => VM-VN=AMN
� HiÖu ®iÖn thÕ gi÷a 2 ®iÓm M,N = C«ng cñalùc ®iÖn tr−êng dÞch chuyÓn ®¬n vÞ ®iÖn tÝchd−¬ng tõ M->N.
VM-V∞=AM∞ -> VM = AM∞� §iÖn thÕ t¹i ®iÓm M = C«ng dÞch chuyÓn ®¬n vÞ ®iÖn tÝch d−¬ng tõ M-> ∞.• §iÖn thÕ t¹i 1 ®iÓm trong ®iÖn tr−êng cña hÖ®iÖn tÝch: dq
Mrr
dV
∫∫ επε==
t hÖ C¶t hÖ C¶ d 0d rdq
41dVV
thø nguyªn V lμ v«n
![Page 35: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/35.jpg)
7. MÆt ®¼ng thÕ7.1. §Þnh nghÜa: Quü tÝch cña nh÷ng ®iÓm cãcïng ®iÖn thÕ. V = C =const§iÖn tÝch ®iÓm: r = const
7.2. TÝnh chÊt mÆt ®¼ng thÕ:� C«ng cña lùc ®iÖn tr−êng dÞch chuyÓn q0:
AMN=q0(VM-VN)=0 (M,N trªn mÆt ®t)� VÐc t¬ c−êng ®é ®iÖn tr−êng t¹i mét ®iÓm trªnmÆt ®t lu«n vu«ng gãc víi mÆt ®t t¹i ®iÓm ®ã
0sdEqdA 0 ==rr
0sdE =rr
Er
sdr
⊕
� C¸c mÆt ®¼ng thÕ kh«ng c¾t nhau
![Page 36: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/36.jpg)
sdEqdA 0rr
=
8. Liªn hÖ gi÷a vÐc t¬ c−êng ®é®iÖn tr−êng vμ ®iÖn thÕ
V V+dVnr
sdrEr
sEdA=q0[V-(V+dV )]=-q0dV
dVsdE −=rr
2 0cos
π>α→<α
α
VÐc t¬ c−êng ®é ®iÖn tr−êngtheo chiÒu gi¶m ®iÖn thÕ
dVdsEs −==αEdscos
� H×nh chiÕu vÐc t¬ c−êng ®é ®iÖn tr−êng trªnmét ph−¬ng nμo ®ã cã trÞ sè b»ng ®é gi¶m ®iÖnthÕ trªn ®¬n vÞ dμi cña ph−¬ng ®ã
0Edscos 0dV <α→>
dsdVEs −=→
![Page 37: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/37.jpg)
zVE;
yVE;
xVE zyx ∂
∂−=
∂∂
−=∂∂
−=
zyx EkEjEiErrrr
++=)
zVk
yVj
xVi(E
∂∂
+∂∂
+∂∂
−=rrrr
VgradE −=r
HÖ thøc
� VÐc t¬ c−êng ®é ®iÖn tr−êng t¹i mét ®iÓmb»ng vÒ gi¸ trÞ nh−ng ng−îc chiÒu víi gradiencña ®iÖn thÕ t¹i ®iÓm ®ã
En lμ h×nh chiÕu cña trªn ph¸p tuyÕnEr
EdndVEn =−=
®èi víi mÆt®¼ng thÕ:
|dndV||
dsdV| ≤� §iÖn thÕ biÕn thiªn nhiÒu nhÊt
theo ph¸p tuyÕn víi mÆt ®¼ng thÕ
α=−= cos.EdsdV
sE
![Page 38: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/38.jpg)
øng dônga, HiÖu ®iÖn thÕ gi÷a hai mÆtph¼ng song song tÝch ®iÖn ®Òu
V1
+++
V2
---
ddVVE 21 −=
εεσ
=0
Eεε
σ=−
021
dVV
d=1m, V1-V2=1v«n ->E=1V/mV/m lμ c−êng ®é ®iÖn tr−êng trong §T ®ång tÝnhmμ hiÖu ®iÖn thÕ trªn mçi m lμ 1v«nb,HiÖu ®iÖn thÕ gi÷a hai mÆt cÇu mang ®iÖn ®Òu
20 r4
qdrEdrdVεπε
==−R1 R2
r)R1
R1(
4q
r4qdrVV
210
R
R2
021
2
1
−επε
=επε
=− ∫
![Page 39: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/39.jpg)
c, HiÖu ®iÖn thÕ gi÷a hai ®iÓm trong ®iÖntr−êng cña mÆt trô tÝch ®iÖn ®Òu
1
2
0
R
R21 R
Rlnl2
QEdrVV2
1επε
==− ∫
r2rR
lr2QE
000 επελ
=εε
σ=
επε=
1
2
01
2
0 RRln
2RRlnR
επελ
=εε
σ=
![Page 40: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/40.jpg)
21
21
02010 rrrr
4q
r4q
r4qV −
επε=
επε+
επε−
=
d, VÐc t¬ c−êng ®é ®iÖn tr−êngg©y bëi l−ìng cùc ®iÖn
⊕lr
--q q
αrdsd =α
r1 r r2
αEr
rErEr
MLÊy -q lμm gèc
α+= EEE r
rrr
r1 -r2=lcosα vμ r1r2≈r2
20
e2
0 r4cosp
rcosl
4qV
επεα
=α
επε=
ds
⊕lr
--q q
rr
α
To¹ ®é cùc
ph©n tÝch
![Page 41: T¸c gi¶: PGS. TS §ç Ngäc UÊn ViÖn VËt lý kü thuËt Tr êng](https://reader031.vdocuments.pub/reader031/viewer/2022030201/621d6807f9284c1f057c6d9c/html5/thumbnails/41.jpg)
12cos33r04ep2E2
rEE +αεπε
=α+=
30
er r4
cosp2rVE
επεα
=∂∂
−=
30
e
r4sinp
rVE
επεα
=α∂
∂−=α