1

TM TT L THUYT N TP MN IN HC

1. nh lut Coulomb

Pht biu: Lc tng tc gia hai in tch im t trong chn khng c phng trng vi

ng thng ni hai in tch im, chiu ca lc y nu hai in tch cng du, chiu ca lc ht

nu hai in tch tri du, c ln t l thun vi tch ca cc in tch, t l nghch vi bnh phng

khong cch gia chng.

Biu thc vect: 0

1 2

2

1. .

4

q q rF

r r

Biu thc ln: 0

1 2

2

1.

4

q qF

r vi 0 = 8,85.10

-12 C

2/Nm

2

2. in trng. Cng in trng

Khi nim in trng: in trng l mt mi trng vt cht c bit bao quanh cc in tch,

s to ra lc tc dng ln bt c in tch no t trong n. in trng lan truyn trong khng gian

vi vn tc hu hn v gn bng vn tc nh sng.

nh ngha cng in trng: Cng in trng ti mt im trong in trng l i

lng c trng cho in trng v tc dng lc, c gi tr bng lc tc dng ln mt n v in tch

dng c ti im v c phng chiu ca lc ny.

Cng thc vect: F

Eq

Cng thc ln:F

Eq

3. Cng ca lc tnh in. Lu s in trng

a) Cng ca lc tnh in

i vi in trng gy ra bi 1 in tch im:

Gi s, ta c in tch im q trong khng gian gy ra in trng. Trong in trng , ta cho

in tch im th q0 dch chuyn t M n N theo ng cong l.

Gi s ti mt im bt k trn ng cong l, ta cho q0 dch chuyn mt vi phn dl.

dA=Fdlcos

0

02

1.

4

qqF

r

dlcosMHdr

T

2

0

0

2

1. .cos .

4

4 . 4 .

N

M

M N

r

l l r

qqA dA F dl dr

r

q qA q

r r

i vi in trng gy ra bi n in tch im:

Theo nguyn l chng cht in trng th cng ca in trng do n in tch im gy ra cho

in tch q0 l: 001 0

.4 4

i i

iM iN

n

i

q qA q

r r

i vi in trng gy ra bi vt mang in: ta chia nh vt mang in thnh n in tch im ri p

dng cng thc i vi in trng gy ra bi n in tch im.

Nhn xt: Cng ca trng tnh in khng ph thuc vo dng ng i m ch ph thuc vo im

u v im cui ca ng i. Cng ca trng tnh in dch chuyn in tch q0 dc theo ng

cong kn bng 0 nn trng tnh in l trng th.

b) Lu s in trng

Gi s ta c in trng tnh bt k, cho in tch th q0 dch chuyn t M n N, cng A ca

lc in trng xc nh nh sau:

0l

A dA q Edl . T y suy ra 0

.l

AE dl

q

nh ngha: Lu s in trng l cng lm dch chuyn mt n v in tch dng dc theo

ng cong l.

Biu thc: 0

.l

AE dl

q

Tnh cht: c tnh cht ging cng ca lc in trng:

- Lu s ca in trng tnh khng ph thuc vo dng ng i m ch ph thuc vo im

u v im cui ca ng i

- Lu s in trng tnh dc theo ng cong kn bng 0

4. in th, hiu in th, ngha, n v o

a) in th:

Gi s ta c 1 in trng tnh bt k, ti im M trong in trng , ta cho in tch im th

q0 di chuyn t M ra xa v cng th 0MM

A q Edl

Ta thy 0

M

M

M

AV Edl

q

khng ph thuc vo dng ng i, khng ph thuc vo in tch

th q0 m ch ph thuc vo in trng v v tr ca im M. Do , in th c trng cho in

trng v kh nng sinh cng.

3

nh ngha: in th ti mt im trong in trng l i lng c trng cho in trng v kh

nng sinh cng, c gi tr bng cng ca lc in trng lm dch chuyn mt n v in tch dng

t im ra xa v cng.

Biu thc: 0

M

M

AV

q

n v: V

Nhn xt: in th ti mt im trong in trng c gi tr ph thuc vo gc in th m ta chn.

chn gc in th xc nh th in th ti mt im trong in trng l i lng xc nh.

in th trong in trng ca in tch im:

0 0 0

M MN

MN M

MN M N

M N MN

N

N

A A A

A A A

A A AV V U

q q q

in th trong in trng ca vt mang in: Theo nguyn l chng cht in trng, ta ly mt

phn t dq bt k gy ra ti M mt in th dV

0

1.

4

dqdV

r

Suy ra:

0

1.

4vatmangdien

dqV

r

b) Hiu in th

Gi s ta c mt in trng, ti im M trong in trng, ta cho in tch th q0 di chuyn ra

xa v cng. Do cng ca lc in trng khng ph thuc vo ng i nn:

0 0 0

M MN

MN M

MN M N

M N MN

N

N

N

M

A A A

A A A

A A AV V U Edl

q q q

nh ngha: Hiu in th gia hai im trong in trng c gi tr bng cng ca lc in trng

lm dch chuyn mt n v in tch dng t im ny n im kia.

Biu thc: 0

MN

MN

N

M

AU Edl

q

n v: V

c) ngha

(Nm trong phn nh ngha)

d) n v o

Vn l hiu in th gia hai im trong in trng m cng ca lc in trng lm dch

chuyn 1C t im ny n im kia bng 1J.

4

5. Gradien in th

Gi s ta c mt in trng tng hp bt k, trong in trng , ta ly hai mt ng th st

nhau, cch nhau mt vi phn dn. Mt mt c in th l V, mt kia c in th l V+dV (dV>0). Cho

in tch th q0 dch chuyn t im M thuc mt ng th V n im N thuc mt ng th V+dV.

Cng dA=F.dn.cos=q0.E.dn.cos (1) 0

0

0 cos 1( , )

180 co 1sE dn

dA=q0UMN=q0(VM-VN)=q0[V-(V+dV)]=-q0.dV (2)

T (1) v (2), ta c cos=1=>=1800

Kt lun: Cng in trng E hng t ni c in th cao v ni c in th thp.

.dV dV dn

E Edn dn dn

V V VE i j k

x y z

E gradV

Cng in trng ti mt im trong in trng:

- C phng vung c vi mt ng th ti

- C chiu hng theo chiu gim ca in th

- C ln bng gradV ti .

nh ngha V/m: V/m l cng in trng ca mt in trng u m hiu in th dc

theo 1m ca ng sc in bng 1V.

6. Tnh cht ca vt dn mang in

a) TC1: iu kin cn bng ca vt dn mang in: khi vt dn mang in th in trng trong

lng vt dn lun bng 0.

Chng minh phn chng: Gi s vt dn mang in v E0. Khi trong lng vt dn lun c

cc in tch t do, xut hin lc in trng tc dng ln cc in tch t do, lm chng chuyn ng

c hng trong vt dn to thnh dng in, ph v trng thi cn bng tnh in ca vt dn nn tri

vi gi thuyt ban u

Nh vy, in trng trong lng vt dn mang in bng 0. Thc nghim chng t rng, khi ta

tch in q cho vt dn th cc in tch x y nhau, sp xp trng thi cn bng sao cho in trng

trong lng vt dn bng 0, qu trnh trn xy ra vi tc nh sng.

5

b) TC2: Khi vt dn mang in th in tch ch phn b mt ngoi ca vt dn , trong lng vt

dn khng c in tch

Ta ly mt kn Gauss trong lng vt dn th thng lng in cm gi qua mt Gauss bng 0.

Chn mt Gauss trng vi mt ngoi ca vt dn => 0Q Thc nghim cho thy nu vt dn mang in dng th cc electron phn b lp ion dng

ngoi cng ca vt dn. Nu vt dn tch in m th cc electron ch bm st mt ngoi ca vt dn

mang in to thnh mt lp my in t.

c) TC3: Khi vt dn mang in th ton b vt dn mt in th duy nht.

Chng minh: gi s ta cho in tch th q0 dch chuyn t M n N trn vt dn th

0

0MN

MN M N

M N

N

M

AU V V Edl

q

V V

(do 0E )

H qu:

- Mt ngoi ca vt dn l mt ng th

- Cc ng sc in lun vung gc vi mt ngoi ca vt dn mang in.

d) TC4: S phn b in tch trn mt ngoi vt dn l khng u (tr hnh cu). Ni no lm th

in tch t, ni no li th in tch nhiu. in tch phn b nhiu nht mi nhn v gy ra

hiu ng mi nhn.

Nu in tch phn b mi nhn nhiu, gy ra in trng mnh lm ion ha khng kh, cc

in tch cng du b y ra xa v to thnh lung gi in, cc in tch tri du b ht vo mi nhn,

lm trung ha cc in tch tri du y, lm mi nhm mt bt in tch. Nhng E=0 th in

tch cc ni khc dn v mi nhn. Qu trnh trn tip tc tip din lm cho in tch mt dn mi

nhn, ta ni vt dn phng in qua mi nhn.

7. in dung ca vt dn c lp. in dung ca t in. Nng lng in trng.

a) in dung ca vt dn c lp

Nghin cu kh nng tch in ca vt dn, c l thuyt v thc nghim u khng nh in

tch m vt dn tch in t l thun vi in th ca n.

Trong h SI: q=C.V

C ph thuc vo hnh dng, kch thc vt dn, c trng cho kh nng tch in ca vt dn,

c gi l in dung vt dn c lp q

CV

nh ngha: in dung ca vt dn c lp l i lng c trng cho kh nng tch in ca vt dn,

c gi tr bng in lng m vt dn tch c khi ta nng in th ca n t 0 ln 1 n v.

Biu thc: q

CV

n v: F l in dung ca vt dn c lp nu n tch c 1C khi ta nng in th ca n t 0 ln 1V

b) in dung ca t in

L thuyt v thc nghim chng minh, in tch q m t tch c t l thun vi hiu in th

U gia hai bn.

q=C.U

6

H s t l C ph thuc vo hnh dng, kch thc ca t in v bn cht ca mi trng in

mi gia hai bn t in, c gi l in dung ca t in.

nh ngha: in dung ca t in l i lng c trng cho kh nng tch in ca t in, c gi tr

bng in tch Q m t tch c khi ta nng hiu in th gia hai bn t t 0 ln 1 n v.

Biu thc: Q

CU

c) Nng lng in trng

Nng lng ca h in tch

???????????????????????????????????????????????

Nng lng ca in trng u

Tch in cho t l q th 201 1

2 2EU VW q l nng lng in trng gia hai bn t in

vi V l th tch in trng u.

Ni no c in trng th ni nng lng in trng v ngc li

Mt nng lng in trng l nng lng in trng c trong mt n v th tch:

2

0

1

2E

Ww

V

Nng lng in trng bt k

Ly mt vi phn th tch dV nh sao cho n l in trng u.

Mt nng lng in trng trong dV l 201

2Ew

Nng lng in trng trong th tch dV l d 201

2dVW E

Nng lng in trng ca ton b khng gian l: 201

2V V

W dW E dV

8. Tng tc t ca dng in. nh lut Ampere

a) Tng tc t ca dng in

Mt s v d v tng tc t: nam chm ht y nhau, nam chm ht kim loi, dng in tc

dng ln kim nam chm, nam chm tc dng ln dng in,.

Tt c cc tng tc trn u c chung mt bn cht, l tng tc gia cc dng in vi

nhau, gi l tng tc t.

Nam chm tc dng ln nam chm th l tng tc ca cc dng in phn t.

b) nh lut Ampere

Phn t dng in: trn dng in, ta ly mt vi phn dl th tch Idl c gi l phn t ca

dng in, c phng chiu trng vi phng chiu ca dng in ti , ln l Idl.

7

Lc tng tc dF gia phn t dng in Idl ln phn t dng in 1 1I dl cch n mt khong

r c ln t l thun vi I1dl1.Idl, vi sin.sin1 v t l nghch vi r2

Idl r n lp thnh tam din thun theo quy tc nm tay phi: cho nm tay phi quay theo

chiu t Idl sang r th ngn tay ci choi ra ch chiu php tuyn n

Trong h SI: 1 1 1

2

sin sin.

4

I dldF

r

vi 0=4.10

-7H/m

1 1dF I dl n lp thnh tam din thun

Kt hp c phng, chiu, ln th cng thc ca Ampere:

1 1

3

, ,.

4

I dl Idl rdF

r

Ch : nh lut Ampere v tng tc t l nh lut l thuyt nhng cc h qu ca n li c

kim chng bng thc nghim.

Trong mi trng t mi, lc tng tc tng ln ln, l t thm ca mi trng

9. Vect cm ng t, nh lut Bio Savart Laplace. Vect cng t trng

a) nh lut Bio Savart Laplace (vect cm ng t)

Gi s trong khng gian, ta c phn t dng in Idl gy ra xung quanh mt t trng, ti im

M trong t trng , cch Idl mt on r, t phn t dng in th 1 1I dl

Nh vy, t trng s tc dng ln phn t dng in mt lc t dF , theo nh lut Ampere:

1 1

3

, ,.

4

I dl Idl rdF

r

V 1 1I dl l dng in th nn 0

3

[ , ].

4

Idl rdB

r

khng ph thuc vo 1 1I dl , m ch ph thuc

vo phn t dng in Idl gy ra t trng. V vy, n c trng cho t trng v phng din tc

dng lc, c gi l cm ng t dB ti im M trong t trng.

[B]=T

Trong mi trng t mi, cm ng t dB tng ln ln, l t thm ca mi trng.

V ln: 0

2

sin.

4

IdldB

r

vi l gc gia Idl v r

dB c phng vung gc vi mt phng cha Idl v r

Chiu xc nh theo quy tc nm tay phi 1: cho 4 ngn tay quay t 1 1I dl n r , ngn tay ci

choi ra ch chiu ca chiu ca dB

8

b) Vect cng t trng

nh ngha: Vect cng t trng H ti mt im M trong t trng l mt vect bng t

s gia vect cm ng t B ti im v tch 0 .

Biu thc: 0

dBdH

, n v [dH]=A/m

10. Lu s ca vect cng t trng (nh l Ampere v dng in ton phn)

Lu s ca in trng tnh dc theo ng con kn bng 0, v vy in trng tnh l trng th

nng. . 0E dl a) Dng in thng di v hn

ng lu thng kn, phng, vung gc vi dng in

Dng in xuyn qua trong lng ng lu thng

cos

c

2

.

os

2

H dl Hdl

d MH rd

I

r

Ird I

r

l

H dl

H dl I

( ) ( )

. . .cos( , )C C

H dl H dl H dl

Dng in nm ngoi ng lu thng

Tng t cch CM trn:

02 2

l l abc cba

I IH dl d d d

ng lu thng kn, khng phng

Ngi ta chng minh c rng khi ng lu thng kn, khng phng th kt qu nh trn.

b) Dng in bt k

i vi dng in bt k th cng ging nh trng hp trn. Trong trng hp c nhiu dng

in th theo nguyn l chng cht t trng th lu s ca H dc theo ng cong kn bng tng i

s ca cc cng dng in

1( )

. in

iC

H dl I

vi Ii l dng in xuyn qua lng ng lu thng.

Lu s ca H dc theo ng cong kn bt k bng tng i s ca cc cng dng in xuyn

qua trong lng ng cong vi quy c:

- Ii s mang du dng nu n nhn ng lu thng theo chiu thun ca quy tc nm tay phi

- Ii s mang du m nu n nhn ng lu thng theo chiu ngc ca quy tc nm tay phi

11. Tc dng ca hai dng in thng, song song, di v hn. nh ngha n v o cng

dng in.

9

a) Tc dng ca hai dng in thng, song song, di v hn

Gi s ta c 2 dng in thng, song song, di v hn t cch nhau mt khong d.

I1 s gy ra ti dng in I2 mt cm ng t 1B , c chiu theo quy tc nm tay phi, ln 1

1

0

2B

d

I

Dng in I2 t trong t trng c cm ng t 1B , lc t tc dng ln I2 2 2 2 1[ , ]F I l B c

phng vung gc vi mt phng cha 2 2I l v 1B , chiu xc nh theo quy tc bn tay tri.

Tng t, dng in I1 t trong t trng c cm ng t 2B , lc t tc dng ln I1

1 1 1 2[ , ]F I l B c phng vung gc vi mt phng cha 1 1I l v 2B , chiu xc nh theo quy tc

bn tay tri.

Theo hnh v, nu hai dng in cng chiu th ht nhau, ngc chiu th y nhau

1 2 2 2 sinF F F I l B

Nu =900 th 20 1

2

2

IF I l

d

vi 0 l hng s t bng 4.10-7 H/m

b) nh ngha n v o cng dng in

A l cng dng in ca hai dng in bng nhau chy trn hai dy dn thng, song song,

di v hn, t cch nhau 1m trong chn khng th lc t tc dng ln mi m chiu di ca dng in

bng 2.10-7N.

12. Lc Lorentz. Hiu ng Hall. Cng ca lc t

a) Lc Lorentz

Gi s ta c 1 dng in cng I t trong t trng th lc t tc dng ln 1 phn t dng

in Idl bng: ,dF Idl B

Cng dng in: I=JdS

Mt : J=n0evdS

0 ,dF n evdsdl B

Do v cng phng cng chiu vi Idl 0 0, ,dF n edsdlv B n edsdl v B

t ds.dl=dV: th tch phn t dng in

t N=n0dV: s ht mang in trong th tch V

Lc tc dng ln 1 ht mang in chuyn ng trong t trng c gi l lc Lorentz.

,ldF

f e v BN

10

Nu ht mang in c in tch q th: ,lf q v B

,lf v B , chiu xc nh theo quy tc bn tay tri. ln sinlf qvB vi l gc gia v v B

b) Hiu ng Hall:

Khi cho dng in c cng I chy qua bn kim loi t trong t trng cm ng t B

vung gc vi bng th trn b mt ca 2 bng xut hin mt hiu in th xc nh gi l hiu in

th Hall Uh, hiu ng trn gi l Hiu ng Hall.

Thc nghim chng t Uh t l thun vi cng dng in I v cm ng t B , t l nghch

vi b dy ca bng b

Trong h SI: Uh =k IB

b , k ph thuc bn cht kim loi v c gi l h s Hall

Gii thch:

- nh tnh:

Xut hin lc Lorentz ,lf e v B lm in tch dng dch chuyn ln mt trn ca bng,

pha trn bng mang in dng, pha di mang in m, xut hin in trng nn c lc in

trng tc dng ln ht mang in ef eE , lf v ef cng phng ngc chiu.

n mt lc no , hai lc ny cn bng nhau, ht chuyn ng thng. Khi , in tch gia

mt trn v mt di l xc nh, xut hin mt hiu in th xc nh, y l hiu in th Hall

- nh lng: fl=fe

qvB=qE

vB=E=hU

d

Uh=dvB

I=Jds=n0evdb

v = 0

I

n edb

0 0

1.

IB IBUh d

edb n e bn

0

1k

en , tuy nhin hng s k khng ph hp vi thc nghim

Thc nghim cho thy: 0

2 1.

3k

n e => h

IBU k

b

11

Thc t, theo thuyt lng t, mt phn t in tun theo phn b Fecmi.

ng dng: dng o cm ng t, gi l u d t trng

c) Cng ca lc t:

Ta xt 1 th nghim l tng nh hnh v, trong mch c dng in cng I, mch in t

trong t trng u c B vung gc vi mch in, thanh MN c chiu di l c th trt khng ma

st trn 2 thanh ray. Dng in t trong t trng th s xut hin lc t tc dng ln thanh MN,

phng chiu ca lc ny xc nh theo quy tc bn tay tri, c ln F=IBlsin, ( =900) => F=IBl

Gi s trong 1 thi gian dt rt nh thanh MN trt 1 khong dx

dA=Fdx=IBldx =IBdS

m d= BdS

dA= Id

A=dA =Id= I(2-1)

A =I

Ngi ta chng minh c rng trong mi trng hp (dng in I bt k v t trng bt k)

th cng thc tnh cng ca lc t vn ng nh trn.

T kt lun, cng ca lc t bng tch ca cng dng in trong mch vi bin thin

ca t thng gi qua mch in .

13. Chuyn ng ca ht mang in trog t trng u:

a) T trng u

v B

Cho ht mang in +q chuyn ng vo t trng u vi vn tc v , t trng c cm ng t

B vung gc vi v , s xut hin lc Lorentz tc dng ln ht mang in

,

,

l

l

f q v B

f v B

y gi l lc hng tm lm vt chuyn ng trn qu o trn, chiu theo quy tc bn tay

tri: fl=qvBsin, (=900)

Fl=qvB=const

Chuyn ng trn u vi bn knh r no :

12

fl=fht

2m

qvBR

v

.

vR

qB

m

q/m ch ph thuc vo c tnh ca ht gi l in tch ring ca ht

.q

Bm

khng ph thuc vo vn tc ca ht nn c gi l tn s Xyclotron

Chu k quay ca ht: 2

.

Tq

Bm

T khng ph thuc vo v

Nhn xt: Nu bn mt chm ht c vn tc khc nhau th chng c chu k bng nhau, c ngha

l sau mt chu k, tt c cc ht tr v ng im xut pht. ng dng ch to my gia tc ht.

v hp vi B mt gc bt k

Cho ht mang in bay vo t trng u vi vn tc v hp vi cm ng t B mt gc

Ta chiu v ln 2 phng :

vn =vsin

vt = vcos

nv B : thnh phn ny lm ht chuyn ng trn u trn ng trn vung gc vi cm ng t B

vi

sin

.

.

2

.

vR

qB

m

qB

m

Tq

Bm

,l tf q v B

Thnh phn ny lm ht chuyn ng thng u dc theo ng sc t vi vn tc vt =vcos

Kt lun: Ht ng thi tham gia 2 chuyn ng: chuyn ng trn u trn ng trn vung

gc vi ng sc t, chuyn ng thng dc theo cc ng sc t

13

Vy ht chuyn ng trn qu o xon c, gi l ng xyclotron, bc c l qung ng ht

tnh tin sau 1 chu k 2

. cos .

.

tl v T vq

Bm

b) T trng bt k

Ht vn chuyn ng theo hnh xon c dc theo ng sc t nhng bn knh ng xon c ph

thuc vo ln ca B

14. Cc nh lut Cm ng in t

a) nh lut Lenzt v chiu ca dng in cm ng:

y l nh lut thc nghim

nh lut: Dng in cm ng xut hin trong khung dy c chiu sao cho t trng m n sinh ra

chng li nguyn nhn sinh ra n.

Gi s, ta c B qua 2 khung dy hng ln. hnh 1 B tng theo thi gian, nh vy dng in cm

ng phi c chiu sao cho n sinh ra t trng ph 'B sao cho chng li s tng ca cm ng t B .

Tng t cho hnh 2

b) nh lut Faraday v sut in ng cm ng

y l nh lut thc nghim, Faraday pht hin sut in ng cm ng xut hin trong khung dy t

l thun vi tc bin i ca t thng trong khung dy

Maxwell kt hp vi nh lut Lenzt

c

d

dt

Chng minh: Gi s ta dng cng ca ngoi lc di chuyn khung dy trong t trng trong thi gian

dt, t thng qua khung dy bin thin l d th trong khung dy xut hin dng in cm ng ic , sut

in ng cm ng c, sinh ra cng dA= iccdt

Ta xt cng ca t lc: dAtl= icd

Cng ca ngoi lc lm di chuyn khung dy trong t trng: dAngl=-dAtl= - icd

Theo nh lut bo ton nng lng, ton b cng ca ngoi lc s chuyn thnh cng ca dng in:

dAngl=dAdd

- icd= iccdt

14

c

d

dt

Pht biu nh lut: sut in ng cm ng xut hin trong khung dy bng v ln nhng tri v

du vi tc ca t thng gi qua khung dy.

nh ngha Wb

1Wb= 1V.1s

1Wb l t thng gi qua khung dy m nu gim v 0 trong thi gian 1s th sinh ra 1 sut in ng

cm ng bng 1V

15. Hin tng t cm. Nng lng t trng

a) Hin tng t cm:

Cho s th nghim nh hnh v:

Lc u kha K ng, bng n sng bnh thng, ta ngt K thy bng n khng tt ngay m

sng 1 lc lu sau mi tt.

Gii thch:

Khi cha ngt K, dng in qua dy I t trng qua cun dy B= 0In, ngt K I gim v 0

nn B cng gim v 0. T thng qua dy gim v 0 , trong cun dy xut hin dng in cm ng Ic,

sut in ng c. Dng in ny cng chiu vi dng in I ban u chy qua bng n. V vy, khi

ngt K, n sng 1 lc ri mi tt.

Hin tng cm ng in t do chnh dng in trong mch gy ra th gi l t cm.

b) Nng lng t trng

NL t trng u:

Xt th nghim ca hin tng t cm khi ngt mch vi cun dy l tng.

nh tnh:

Khi ngt K, bng n khng tt ngay m sng 1 lc lu ri mi tt, ta tnh cng ca dng in

sau khi ngt K. Trong thi gian dt, cng dA ca dng in l:

dA = iccdt = -Lidi 0

2

0

1

2I

A dA Lidi LI

Sau khi ngt K, ngun in khng cn cung cp nng lng cho mch nhng lc trong mch

vn xut hin cng ca dng in. Gi thuyt rng t trng trong ng dy c nng lng v mt phn

nng lng t trng ny chuyn thnh nng lng dng in nn mi c cng dng in. Khi dng

in tt, theo nh lut bo ton nng lng, ton b nng lng t trung bin i thnh cng ca

dng in, c ngha l nng lng t trng u ng bng cng A ca dng in.

nh lng:

15

Theo nh lut bo ton nng lng, ton b nng lng ca t trng bin thnh cng ca

dng in:

22 2 2

2

1 1 1.

2 2 2

1

2

S BA W I n lSI lS

l

BW V

ngha: ni no c t trng th ni c nng lng t trng v ngc li.

Mt nng lng t trng w=21

2

B

Nng lng t trng bt k:

Gi s ta c 1 t trng bt k, tm nng lng ca t trng ta ly 1 phn t th tch dV

trong t trng, dV nh sao cho t trng c coi l t trng u th mt nng lng t

trng trong dV l: 21

.2

BdW w dV dV

Nng lng t trng trong ton b khng gian ca t trng: 21

2V V

BW dW dV

16. Lun im th nht ca Maxwell. Phng trnh Maxwell- Faraday

a) Lun im th nht ca Maxwell (in trng xoy)

Ta cho t trng cm ng t B qua vng dy bin thin th trong vng dy xut hin dng

in cm ng v sut in ng cm ng. cc in tch t do c trong dy dn chuyn ng c

hng chuyn thnh dng in cm ng th trong dy dn phi c mt in trng l to ra lc tc

dng ln cc in tch t do, Mt khc, c sut in ng cm ng trong vng dy th cng cn c

mt in trng l. in trng l trong vng dy c gi l in trng xoy

Maxwell t nhiu vng dy c kch thc khc nhau, cht liu khc nhau cc v tr khc nhau

th thy ti bt k ni no c vng dy u thy trong vng dy xut hin dng in cm ng v sut

in ng cm ng, chng t bt c ni no t vng dy th trong vng dy u c in trng xoy

Kt lun: in trng xoy c mi ni trong khng gian cn cc vng dy ch l phng tin

(ng h o) ta nhn bit s c mt ca in trng xoy.

T , Maxwell rt ra lun im th 1:

- Mi khi trong khng gian c t trng bin thin theo thi gian th trong khng gian xut hin

1 in trng xoy.

- in trng xoy c cc ng sc in l nhng ng cong kn bao quanh cc ng sc t

(tnh cht xoy).

16

b) Phng trnh Maxwell- Faraday:

Gi s trong khng gian c t trng bin i theo thi gian, ta t mt vng dy kn c chiu

di l bt k th trong vng dy xut hin sut in ng cm ng.

Theo nh lut Faraday v sut in ng cm ng:

.S

c

d B dsd

dt dt

.S

c B dst

(1)

Theo nh ngha ca sut in ng

.cl

AE dl

q (2)

T (1) v (2) =>Phng trnh Maxwell- Faraday: . .l S

E dl B dst

ngha: Lu s ca vect cng in trng dc theo ng cong kn bt k bng v ln

nhng tri v du vi tc bin i ca t thng gi qua din tch gii hn bi ng cong kn .

17. Dng in dch. Lun im th 2 ca Maxwell. Phng trnh Maxwell- Ampere

a) Lun im th 2 ca Maxwell (Dng in dch)

Xt cc hin tng vt l Maxwell nhn thy iu ngc li vi lun im 1 vn ng, t

pht biu lun im 2: Mi khi trong khng gian c in trng bin i theo thi gian th trong

khng gian xut hin mt t trng xoy.

T trng xoy c cc ng sc t l nhng ng cong kn bao quanh cc ng sc in.

Ta xt mt mch dao ng in t, gi s mch ang dao ng in t, dng in trong mch c chiu

nh hnh v, gi l dng in dn.

in tch gia hai bn t gim (bin thin theo thi gian) th theo lun im th hai ca Maxwell

lm xut hin mt in trng xoy.

17

Ta thy dng in sinh ra t trng, in trng bin i theo thi gian cng sinh ra t trng

nn v phng din to ra t trng th in trng bin i theo thi gian cng ging nh dng in

nn gi l dng in dch.

**So snh dng in dn v dng in dch

Ging: u sinh ra t trng

Khc: Dng in dn do cc in tch chuyn ng c hng nn gy ra hiu ng ta nhit

Jun-Lenx. Dng in dch do in trng bin i theo thi gian nnkhng gy ra hiu ng

ta nhit Jun-Lenx.

**Ta xt v mt nh lng ca dng in dch

Xt cc mch dao ng in t c t l tng, vo thi im t, in tch ca t l q, mt in

tch mt l th D=

1.

qd

dD d dq iSJ

dt dt dt S dt S

y chnh l mt dng in dch

dichdD

Jdt

Xt trng hp ni trn th vo thi im t, in tch q trn t in gim nn E gim, D gim.

J dch cng phng cng chiu E v D

Dng in dch cng chiu vi dng in dn, ln ca mt dng in dn bng ln mt

dng in dch.

Dng in dch chy qua t in khp kn dng in dn ca mch.

b) Phng trnh Maxwell-Ampere

Theo nh lut Ampere v dng in ton phn

1

( ).n

k dich dan dan

kl

dDH dl I J J ds J ds

dt

Suy ra phng trnh Maxwell-Ampere: danl

dDH dl J ds

dt

ngha: Lu s ca vect cng t trng dc theo ng cong kn bt k bng tng cc cng

dng in (bao gm c dng in dch v dng in dn) xuyn qua din tch gii hn bi ng cong

kn .

(Ti liu ch mang tnh tham kho)