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CNG VT L A2

Cu 1: Khi nim tnh cht ca in trng. S ging v khc gia in trng v t trng.

1.1. Khi nim, tnh cht ca in trng:

in trng l trng vt cht tn ti xung quanh in tch ng yn. C tnh cht c bn l tc dng lc ln

cc in tch khc t trong in trng 1.2. S ging v khc nhau gia in trng v t trng

in trng T trng

Ging nhau

+ u c kh nng tc dng lc (ln cc in tch khc hoc t trng khc)+ u l biu hin ca mt trng thng nht l in - T trng++

Khc nhau

+ sinh ra quanh cc in tch ng yn + sinh ra quanh cc in tch chuyn ng hocdo s bin thin ca in trng hoc c ngungc t cc mment lng cc t

Cu 2: Thit lp nh l Gauss cho in trng (in thng), ng dng tnh:a. in trng ca mt cu tch in u.b. in trng ca mt phng v hn.c. in trng ca 2 mt phng song song v hn (cng hoc tri du).

2.1. Thit lp nh l Gauss cho in trng:Xt in tch im q>0 ti M. V mt cu (S) tm (M,r). Tnh thng lng gi qua (S). D u c phng

vung gc vi mt cu.

0 2

2

2

( ) ( ) ( )

1

44

4S S S

D E q

rr

Dd S DdS D dS q qr

= =

= = = = = ur ur

+ Nhn xt: in thng khng ph thc vo khong cch. in thng gi qua mi mt cu ng tm u bngnhau.

+ Kt lun: Nu trong mt cu (S) c nhiu in tch th theo nguyn l chng cht in trng suy ra in thngqua mt kn (S) bng tng in thng do trng in tch gy ra.

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http://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_t%C3%ADchhttp://vi.wikipedia.org/wiki/Chuy%E1%BB%83n_%C4%91%E1%BB%99nghttp://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_tr%C6%B0%E1%BB%9Dnghttp://vi.wikipedia.org/w/index.php?title=M%C3%B4ment_l%C6%B0%E1%BB%A1ng_c%E1%BB%B1c_t%E1%BB%AB&action=edit&redlink=1http://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_t%C3%ADchhttp://vi.wikipedia.org/wiki/Chuy%E1%BB%83n_%C4%91%E1%BB%99nghttp://vi.wikipedia.org/wiki/%C4%90i%E1%BB%87n_tr%C6%B0%E1%BB%9Dnghttp://vi.wikipedia.org/w/index.php?title=M%C3%B4ment_l%C6%B0%E1%BB%A1ng_c%E1%BB%B1c_t%E1%BB%AB&action=edit&redlink=1

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+ nh l Gauss: in thng qua mt kn bng tng i s cc in tch cha trong mt kn

e ii

S

DdS q = = 2.2. ng dng nh l Gauss tnh in trng ca mt cu tch in u:

Gi s mt cu mang in u c bn knh R; ln in tch trn mt cu bng q (trng hp mt cumang in tch dng). V in tch c phn b u trn mt cu nn in trng do n sinh ra c tnh chti xng cu. iu c ngha l vector cm ng in D (hay vector cng in trng E) ti mt imbt k phi hng qua tm mt cu; cm ng in D ch ph thuc khong cch r t im ang xt ti tm mtcu.

xc nh vector cm ng in D do mt cu mang in gy ra ti im M cch tm mt on r > R, tatng tng v qua M mt mt cu S cng tm vi mt cu mang in v tnh thng lng cm ng in quamt cu S .

Theo cng thc nh ngha: .e nS D dS = Trong trng hp ny Dn = D = const i vi mi im trn mt cu S nn:

( ) ( )

e n

S S

D dS D dS = = Hay 2.4e D r =

p dng nh l Gauss ta c: 2.4e D r q = =(q l in tch nm trong mt cu S, t l in tch ca mt cu mang in).

Suy ra:24

qD

r=

V cng in trng: 20 0

1.

4

D qE

r = =

D dng nhn thy D v E hng t tm mt cu ra pha ngoi nu mt cu mang in dng v hngvo tm mt cu nu n mang in m.Nu im M cch tm mt cu mang in mt khong r0 < R (M nm trong mt cu mang in) th bng phptnh tng t ta c:

2

0.4 0e D r = =Do D = E = 0

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V trong trng hp ny, mt cu S0 v qua M khng cha in tch no ( 0iq = )Nh vy bn trong mt cu mang in u in trng bng khng. ngoi mt cu in trng ging

in trng gy ra bi mt in tch im c cng i ln t tm ca mt cu mang in .

2.3. ng dng nh l Gauss tnh in trng ca mt phng v hn:

Gi s mt phng v hn mang in c mt in mt . V l do i xng, vector cm ng in D timt im bt k trong in trng s c phng vng gc vi mt phng mang in v cm ng in D ch cth ph thuc vo khong cch t im ang xt ti mt phng.

xc nh vector cm ng in do mt phng mang in gy ra ti mt im M, ta tng tng v qua Mmt mt tr kn ri p dng nh ly Gauss cho mt tr . Mt tr c cc ng sinh vung gc vi mt phng, chai y song song, bng nhau v cch u mt phng.

Theo nh ngha, thng lng cm ng in qua mt tr kn bng:

e n n n D dS D dS D dS = = +

mat tru hai ay mat ben

(Dn l hnh chiu ca D trn php tuyn n ).

Qua hnh v ta nhn thy: ti mi im ca mt bn D n = 0, do thng lng qua mt bn bng khng; timi im trn hai y Dn = D = const, v vy:

. .2n D dS D dS D S = = hai ay hai ay

Vi S

l din tch ca mi y. in tch nm trong mt tr bng: .q S

= . Vy theo nh l Gauss:.2 .e D S S = =

Suy ra:2

D

= (1)

V:0 02

DE

= = (2)

Cc biu thc (1) v (2) chng t D v E khng ph thuc vo v tr ca im M trong in trng ngha l ivi mi im trong in trng, D v do E khng i.

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Trong trng hp mt phng mang in dng, D v E hng ra pha ngoi mt phng; trng hp mt

phng mang in m D v E hng vo trong mt phng. Vy in trng gy ra bi mt phng v hn mangin u l mt in trng u. (xt trong mi na khng gian).

2.4. ng dng nh l Gauss tnh in trng ca 2 mt phng song song mang in tch i nhau

Xt trng hp 2 mt phng sng song v hn mang in u mt in mt bng nhau nhng tri du( , ) + . Vector cm ng in D do 2 mt phng mang in gy ra c xc nh bi nguyn l chng chtin trng, ta c:

1 2 D D D= +

Trong 1

D v2

D ln lt l cc vector cm ng in do tng mt phng gy ra ti im ang xt1

D v

2D u c phng vng gc vi 2 mt phng mang in v c ln bng nhau:

1 22

D D

= =

khong cch gia 2 mt phng1D v 2D cng chiu, do D cng cng chiu vi 1D (hoc 2D ), c

phng vung gc vi hai mt phng v c ln bng:

1 2 D D D = + =

Do : 0 0

D

E

= = ngoi hai mt phng mang in

1D v 2D trc i nhau, do : D =0

Vy: trong khong cch gia hai mt phng song song v hn mang in u c mt in mt bng nhaunhng tri du in trng l in trng u; ngoi hai mt phng c in trng c cng in trngbng khng.

2.5. ng dng nh l Gauss tnh in trng ca mt mt tr thng di mang in u:

Gi s mt tr thng di v hn c bn knh R, c mt in mt . V l do i xng tr, vector cm ngin D ti mt im bt k trong in trng ca mt tr c phng vung gc vi trc ca mt tr v c ln D ch c th ph thuc khong cch r t im ang xt ti trc ca mt tr .

xc nh vector cm ng in D do mt tr mang in gy ra ti mt im M cch trc ca mt tr mtkhong r (r > R), ta tng tng v qua im M mt mt tr kn (S) nh hnh v v p dng nh l Gauss chomt kn (S) . Mt tr kn (S) c cng trc vi mt tr mang in, c cc ng sinh song song vi trc, c haiy vung gc vi trc v cch nhau mt khong l

Theo nh ngha, thng lng cm ng in qua mt tr kn (S) bng:

e n n n D dS D dS D dS = = + mat tru mat ben hai ay

D dng thy rng, ti mi im ca mt bn Dn = D = const do :

n n D dS D dS D dS D2 rl = = =

mat ben mat ben mat ben

Ti mi im ca hai mt y, Dn = 0, do n D dS 0=

hai ay

p dng nh l Gauss ta c:

e D.2 rl Q = = (1)trong Q l in tch nm trong mt tr (S); nu gi l in tch trn mt n v chiu di ca mt tr (cn gil mt in di), ta c:

Q l 2 Rl = = (2)

T (1) v (2) ta thu c:4

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Q RD

2 lr 2 r r

= = =

(3)

Do :

0 0 0 0

D Q RE

2 lr 2 r r

= = = =

(4)

Vy: vector cm ng in D (hay vector cng in trng E) do mt tr thng di v hn mang inu gy ra ti mt im trong in trng c phng vung gc vi mt tr in, c chiu hng ra ngoi mt

tr nu mt tr mang in dng, hng vo trong mt tr nu mt tr mang in m v c ln c xcnh bi (3) hay (4) i vi E.

T (3) v (4), ta nhn thy D v E t l nghch vi khong cch r; gn mt tr ta c th thu c intrng rt mnh.

Nu mt tr thu li thnh mt dy mnh ( R 0 ) mt in di th D v E do dy gy ra c xc nhbi:

D2 r

=

v

0 0

DE

2 r

= =

Cu 3: Trnh by khi nim lng cc in. Tc dng ca in trng u ln lng cc in.

3.1. Khi nim lng cc in:

Lng cc in l mt h hai in tch im c ln bng nhau nhng tri du +q (q > 0) v q, cch nhaumt on l rt nh so vi khong cch t lng cc in ti nhng im ang xt ca trng. c trng chotnh cht in ca lng cc in ngi ta dng i lng vector momen lng cc in hay momen in ca

lng cc, k hiu le

P . Theo nh ngha: e P ql = . Vector momen in c trng cho tnh cht in ca lngcc in.

3.2. Tc dng ca in trng u ln lng cc in:

Gi s c lng cc ineP t trong in trng u 0E v nghing vi ng sc in trng mt gc

(hnh 1). Lng cc in s chu mt ngu lc1 0

F qE = v 2 0 F qE = c cnh tay n bng sinl . Momen

ca ngu lc c xc nh bi:

1 0 0l F l qE ql E = = = hay 0ep E= Di tc dng ca momen ngu lc , lng cc in b quay theo chiu sao cho ep trng vi hng ca

in trng0E . v tr ny cc lc 1F v 2F trc i nhau. Nu lng cc l cng ( l khng i), n s nm

cn bng. Nu lng cc n hi, n s b bin dng.

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Cu 4: Trnh by cc khi nim:+ Cng ca lc in trng.+ Th nng ca in tch trong in trng.+ in th, hiu in th.+ Khi nim, tnh cht mt ng th, mi lin h.

4.1. Cng ca lc in trng:

q0 > 0 chuyn ng trong in trng ca q (do q gy ra)

0

0 2

0

2

0 0

2 2

0 0

1. .

(1)

NN M

MNM M

M

MN

M N

q q

F q E k r

q qdA Fd l Fd r k dr

r

q q q qdr A dA k k

r r r

kq q kq qA

r r

= =

= = =

= = =

=

ur r ur r

Cng thc (1) chng t rng: cng ca lc tnh in trong s dch chuyn in tch q 0 trong in trng ca

mt in tch im khng ph thuc vo dng ca ng cong dch chuyn m ch ph thuc vo v tr im uv im cui ca chuyn di.

4.2. Th nng ca in tch trong in trng:

Th nng ca in tch im q0 ti mt im trong in trng l i lng c gi tr bng cng ca lc tnhin trong s dch chuyn in tch t im ang xt ra xa v cng.

0 .MM

W q E d s

= ur r

4.3. in th, hiu in th:

- in th: T cc cng thc ta c nhn xt t s0

W

q

khng ph thuc vo ln ca in tch q 0 m ch ph

thuc vo cc in tch gy ra in trng v v tr ca im ang xt trong in trng. V vy ta c th dng t

s c trng cho in trng ti im ang xt. Theo nh ngha t s0

WV

q= c gi l in th ca

in trng ti im ang xt. Vy in th ti mt im trong in trng l mt i lng v tr s bng cngca lc tnh in trong s dch chuyn mt n v in tch dng t im ra xa v cng.

- Hiu in th: hiu in th gia hai im M v N trong in trng l mt i lng v tr s bng cng calc tnh in trong s dch chuyn mt n v in tch dng t im M ti im N.

4.4. Khi nim, tnh cht ca mt ng th:6

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- Mt ng th: l tp hp tt c cc im trong khng gian c cng hiu in th:

( , , ) x y z

kq

r

= =

- Tnh cht:+ Cng ca lc tnh in trong s dch chuyn mt in tch q0 trn mt ng th lun bng khng.+ Vector cng in trng ti mt im trn mt ng th vung gc vi mt ng th ti im ..4.5. Lin h gia cng in trngEv in th

+ in trng c trng cho kh nng tc dng lc+ in th c trng cho kh nng sinh cng

C mt mi lin h gia in th v in trng.

Xt mt in tch chuyn ng trong mt in trng c mt ng th bt k.

( )1

1 2

2 2 1

( )

; ;

. . . .

x

x

x y z

dA Fdx qE dx qU q

E dx d

d d d Ex Ey Ez

dx dy dz

d d d

E E i E j E k i j k grad dx dy dz

= = = =

= = =

= = =

= = + = + + = =

ur uuur uuuur uuuur r r r uuuuur

Vy, vector cng in trng E ti mt im bt k trong in trng bng v ngc du vi grad cain th ti im .

Hai mt phng song song: 1 2 1 2( )U

Ed d

= = >

Cu 5: Khi nim, tnh cht ca vt dn cn bng tnh in. Hin tng in hng mt phn ton phn.

5.1. Khi nim vt dn cn bng tnh in:

Vt dn in l vt c cha cc in tch t do. Khi t trong in trng, cc in tch trong vt dn cphn b li.

iu kin cn bng ca vt dn:

+ Vector cng in trng ti mi im bn trong vt dn phi bng khng: 0trE =

+ Thnh phn tip tuyntE ca vector cng in trng ti mi im trn mt vt dn phi bng khng:

0,t n E E E = =

5.2. Tnh cht ca vt dn mang in:

- Vt dn cn bng tnh in l mt khi ng th. Mt vt dn l mt ng th.- Trong vt dn cn bng khng c in tch phn b theo th tch. in tch q ch c phn b trn b mt

vt dn; bn trong vt dn in tch bng khng.

5.3. Hin tng in hng.

Hin tng cc in tch cm ng xut hin trn vt dn (lc u khng mang in) khi t trong in trngngoi c gi l hin tng in hng.

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in hng mt phn: nu c mt s ng sc t vt A (nhim in ban u), mt s ng sc t t Akhng n B (vt dn cn bng tnh in) m ra . Lc ny ta c hin tng in hng mt phn. Trong hintng in hng mt phn, ln in tch hng ng (vt B) nh hn in tch trn vt mang in (vt A)

in hng ton phn: nu tt c ng sc t A u n B (trong trng hp A mang in tch dng, Bmang in tch m) gi l in hng ton phn. ln ca in tch hng ng bng ln ca in tch trn

vt mang in B Aq q=

Cu 6: in t trng, khi nim tnh cht ca ng cm ng t. T thng, vector cm ng t, vectorcng t trng.

6.1. in t trng:

in trng v t trng ng thi tn ti trong khng gian to thnh mt trng thng nht gi l trngin t. Trng in t l mt dng vt cht c trng cho tng tc gia cc ht mang in. Trng in t cnng lng.

6.2. Khi nim, tnh cht ca ng cm ng t:

ng cm ng t l ng v trong t trng sao cho tip tuyn ti mi im ca n trng vi phng cavector cm ng t B ti nhng im gn y. Chiu ca ng cm ng t l chiu ca vector cm ng t(chiu ca t trng)

Tnh cht:+ L nhng ng cong kn, khng c im bt u v im kt thc.+ T trng l t trng xoy.+ Mt ng sc t cho bit ln ca cm ng t. u mt ng sc t dy th cm ng t ln

v ngc li.

6.3. T thng, vector cm ng t, vector cng t trng:

T thng gi qua in tch dS l i lng v gi tr bng:

md Bd S =

- Trong B l vector cm ng t ti mt im bt k trn in tch y, d S l mt vector nm theo phng

ca php tuyn n vi din tch ang xt, c chiu l chiu dng ca php tuyn , v c ln bng chnh

ln in tch ( d S cn c gi l vector in tch)

- c trng cho t trng v mt nh lng (mt tc dng lc), ngi ta ua ra mt i lng vt l:

vector cm ng t. Vector cm ng t d B do mt phn t dng in Idl gy ra ti im M, cch phng t mt

on r l mt vector c:

+ Gc ti im M.

+ Phng vng gc vi mt phng cha phn t dng in Idl v im M

+ Chiu sao cho ba vector d l , r v d B theo th t ny hp thnh mt tam din thun+ ln (cn gi l cm ng t) dB c xc nh bi cng thc:

0

2

sin.

4

IdldB

r

=

- Vector cng t trng H ti mt im M trong t trng lag mt vector bng t s gia vector cm ng

t B ti im v tch 0 :

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0

BH

=

uur

7. Thit lp nh l Gauss cho t trng.

Da vo tnh cht xoy ca t trng (tc tnh khp kn ca cc ng cm ng t), ta tnh t thng gi qua

mt mt kn S bt k.

Theo quy c, i vi mt mt kn, ngi ta chn chiu dng ca php tuyn l chiu hng ra pha ngoi mt. V vy, t thng ng vi ng cm ng t i vo mt kn l m (trng hp im M1: 090 > , do ,

. .cos 0md B dS = < ); t thng ng vi ng cm ng t i ra khi mt kn l dng (trng hp im M2;090 < ; do , 0md > ). V cc ng cm ng t l khp kn nn s ng i vo mt kn bng s ng

i ra khi mt . Kt qu l, t thng ng vi cc ng cm ng t i vo mt kn v t thng ng vi ccng i ra khi mt bng nhau v tr s nhng tri du. V vy, t thng ton phn gi qua mt kn bt k thbng khng. l ni dung nh l Gauss i vi t trng. Cng thc biu din nh l l:

( )

. 0S

B d S =

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