Tài liệu Bồi dưỡng học sinh giỏi vật lý 11 tập 1

Cty TNHH MTV DVVHKhnnn Vi?t LQI NOIDAU «B6I DlfONG HOC SINH GI61 VAT L I TRUNG HQC PHO THONG" la bo sach dung cho hoc sinh kha gioi, hoc sinh cac Idp chuyen Vat l i , cac thay c6 giao day Vat li d cac trUdng trung hoc pho thong. Bo sach gom 7 cuon: 1. Boi dUdng hQC sinh gioi Vat U10, tap I (Donf^ hoc, Dong lUc hoc, TTnh hoc) 2. Boi dUdng hpc sinh gioi Vqt li 10, tap I I (Cac dinh luat bcio loan, Nhiet hoc) 3. Boi dUdng hQC sinh gioi Vat li 11, t|ip I (D/pn va Dien til) • 4. Boi dUdng hgc sinh gioi Vat li 11, tap I I (Quang hinh) 5. Boi dUdng hgc sinh gioi Vat li 12, tap I {Dao dong va Song ai hoc) 6. Boi dUdng IIQC sinh gioi Vat li 12, tap I I {Dong dien xoay chieu va Dao don^ dien tCe) 7. Boi dUdng hgc sinh gioi Vat li 12, tap I I I {Quang li. Vat li hat nhdn) Ve cau true, moi cuon sach deu du'dc chia thanh cac phan Idn, trong moi phan gom nhieu chuyen de, moi chuyen de la mot noi dung kien thiJc tron ven. Moi chuyen de gom cac phan: A-T6m tat kien thrfc: Phan nay chiing toi trinh bay mot each c6 he thong nhi^ng kien thiJc trong tam cua chuyen de tiif cd ban den nang cao trong do chiing toi chu trong dao sau nhffng kien thiJc nang cao de lam cd sd cho viec giai cac bai tap cua chuyen de. B-Nhi?ng chu y khi giai bai tap: Trong phan nay chiing toi neu len nhu'ng chii y can thiet ve kien thiJc va ki nang giai bai tap. Do la nhu'ng lufu y quan trpng giiip dinh hu'dng va tranh nhu'ng sai sot khi giai cac bai tap cua chuyen de. C-Cac bai tap cua chuyen de: He tho'ng bai tap d day kha da dang du'dc s^p xep ttf de den kho, tCf ddn gian den phiJc tap va di/dc giai kha chi tiet nen rat phii hdp vdi nhieu do'i tU'dng ban doc. Trong qua trinh bien soan chiing toi tham khao rat nhieu nguon tai lieu trong va ngoai niTdc, dac biet la cdc bo sach G/a/ loan Vat U do thay Biii Quang Han lam chu bien - Nha xuat ban Giao due 1998, bo sach Bai tap va Un gidi Vat li do OS. Yung Kuo Lim lam chu bien - Nha xuat ban Giao due Viet Nam 2010, bo sach Ca sd Vat li do David Halliday lam chu bien - Nha xuat ban Giao due 2002... de lam phong phU them phan kien thiJc cung nhiTphan Idi giai cac bai tap trong bo sich. Vdi SLf gop siJc cua cac thay c6 giao da va dang cong tac tai cdc tnTdng chuyen, cac thay c6 giao da tijfng tham gia boi difdng hoc sinh gioi Vat l i cua cac tinh thanh trong ca ni/dc, hi vong bo sach se la tai lieu tham khao thie't thifc, bo ich cho nhieu doi tifdng ban doc yeu thich bo mon Vat l i . Mac dil da dau tiT bien soan kha kl ludng nhiftig nhu'ng han che, sai sdt la dieu khong the tranh khoi. Rat mong nhan difdc sif dong gop, chia se cua cac thay c6 giao va cac em hoc sinh tren ca nifdc; Moi y kien dong gop xin gufi ve dia chi [email protected] hoac khang [email protected]. Xin tran trong gidi thi^u bo sach den quy thay c6 giao va cic em hoc sinh! Chu bi6n ThS. Nguyin Phii Dong thvrnhat mdn TfNH N» LlTC TlJfdNG TAC TINH DIEN Chuxendil: A-TOMTAxKliNTHtrC •^^mt^.^ag^ I . Dien tich - S\i tifdng tac giffa cac di^n tich 1. Di^n tich: Cd hai loai dien tich: dien tich du'dng va dien tich am. Cac dien tich cung loai thi day nhau, cac dien tich khac loai thi hut nhau. 2. Djnh luat Culong: LiTc ti/dng tac giufa hai dien tich diem diJng yen ti le thuan vdi tich dp Idn ciia hai dien tich va ti le nghjch vdi khoang each giiJa Chung. + k lq£2| e' r^ xjflq •'• e la h^ng so' dien moi ciia moi triTdng ( 8 = 1 : chan khong hoac khong khi). + r la khoang each giffa hai dien tich qi, q2. / " ^ j Chii y : Dinh luat Culong du'dc ap dung cho: - hai dien tich diem. ^f'^ ^ \ ^ - hai qua cau tich dien phan bo deu. 11. Djnh luat bao toan di^n tich " ^1 i< t '•'''^^O Trong mot he CO lap ve dien, tdng cac dien tich dtfdc bao toan: q, + q2 + ... = const j „ ^t^, ^^,(^-,3 B. NHONG C H O t KHI GIAI B A I T A F - Khi dp dung djnh luat Culong ve siT tU'dng tac giffa cdc dien tich dffng yen can chu y: + dieu kien ap dung: hai dien tich diem hoac hai qua cau tich dien phan bo deu. + cac hien tU'dng thiTc te" thffdng gap: • cho hai qua cau nho dan dien nhiT nhau da nhiem dien tiep xiic nhau hoac no'i vdi nhau bKng doan day dan roi tdch rdi ra thi tdng dien tfch se chia deu cho hai qua cau: q'l = q'2 = • ' ' khi cham tay vao mot qua cau nho dan dien da tich dien thi qua cau se mat dien tich va trd thanh trung hoa. 3 Bdi diiOng hgc sinh gi6i Vat ly 11, t$p 1 - Nguyin Phu D6ng - Cty TNHH MTV DVVHUhang Vi?t Khi mot dien tich diem q chju tac dung ctia nhieu life tac dung Fp F j , ... do c. C A C B A I T A P vi; Lye T U O N G T A C TITOI D I E N 1. Tl/CfNG T A C G I 0 A CAC D I E N T I C H D I E M DlfNG YfeN cac dien tich diem qi, q2, ... gay ra thi hcJp life tac dung len q la: 1.1. Hai dien tich diem bang nhau dat trong chan khong, each nhau doan R = 4cm. Li/c day tTnh dien giffa chiing 1^ F = 10'^N. -f De xac djnh do Idn cua hdp luTc F ta c6 the diTa vao: ** a) Tim do Idn moi dien tich. + djnh l i ham cosin: F^ - Fj^ + F2 + 2FjF2Cosa (a la goc hdp bdi Fj va ). b) Tim khoang each R, giffa chiing de liTc day tTnh dien la F, = 2,5. lO^^N. Bai giai • F, va F2 cung chieu thi: F = F, + F2 (a = 0, cosa = 1). • F, va F2 ngiTdc chieu thi: F = IF, - F2I (a = n, cosa = -1). ^ a) Do Idn mSi dien tich _ Vi: + Hai dien tich day nhau nen q, va q2 cung dau. + Hai dien tich bang nhau nen: qi = q2. • F, va F2 vuong goc thi: F= ,JF^ + F^ • Fj va F2 cung do Idn (Fi = F2) thi: F = 2Fi cos y . (a = 90°, cosa = 0). - Theo dinh luat Cu-16ng: -5 F =k = RJ^ R^ + phiTdng phap hinh chieu: F = ^jF[+F^ (F, = Fu + F2x + - Fy = F,y + F2y + F2 + R' -f Cac life tac dung len dien tich q thi/dng gap la: 8 Vdi khoang each R: F = k - ' ^ R^ (1) - Vdi khoang each R,: F' = k - 3 - (2) + liTc cSng day T. R: ne'u q, va q2 trai dau; \\ic day ne'u q, • va q2 Cling dau). , 1,3.10"'C ^2 - + trong life: P = mg (luon hu'dng xuong). .SiSl. Q^^Q 1,3.10 ' C b) Khoang each R, giffa chung de life day tTnh dien la F, = 2,5.10"^'N ...) ... = 6 + life tTnh dien: F = =4.10-1 j i ^ 9.10^ Vay: Do Idn cua moi dien tich la Khi mot dien tich q du'ng yen thi help luTc tac dung len q se bang 0: F = F, + .. . '1 - 10r5 Suy ra: R, = R. — = 4. = 8cm. y 2,5.10"^ , Vay: De life day tTnh dien giffa hai dien tich la F, = 2,5.10 ''N thi khoang ; u + lircdanh6icual6xo:F = k . A / = k ( / - / o ) . •I fi each giffa chiing la R| = 8cm. FM 1.2. Hat bui trong khong khi d each nhau mot doan R = 3cm, moi hat mang dien tichq =-9,6.lO-'^C. _ H : a) Tinh life tTnh dien giffa hai hat. 'iff'' b) Tinh so electron dirtrong moi hat bui, biet dien tich moi electron la e = 1,6.10-"C. *" y-• Bai giai a) Lffc tTnh dien giffa hai hat Vuong goc Ciang do Idn Ta cd: F = k = k^=9.10'. R' R^ - ^ . r. , 1'\ ,-13x2 (-9,6.10-'-') = 9,216.10'^C ' (3.10-^)2 Vay: Life tTnh dien giffa hai hat la F = 9,216.10-'^C A\ 4 Cty TIMHH MTV UWH khang V i ^ B6i diiBng hpc sinh gi6i Vjt ly 11, t?p 1 - IMguygn Phu B6ng Bai giai b) So electron diT trong moi hat bui -9,6.10" Ta c6: ne = — e = ^,, , a) Dp Idn life hU'dng tarn dat len electron Vi life hU'dng tam trong chuyen dong tron cua electron quanh hat nhan chinh = 6.10'. -19 1,6.10 Smi la life tTnh dien nen: v'c,fy ::r"!,;..I Vay: So' electron d\X trong moi hat bui la ne = 6.10^ ^-19 1.3. Moi proton c6 khoi liTdng m = l,67.10""kg, dien tich q = 1,6.10""C. Hoi life FM =k ^1^2 (-1,6.10~'^).1,6.10 = 9.10". = 9,2.10-* N R^ day Culong giiya hai proton Idn hdn li/c hap dan giffa chiing bao nhieu Ian? (5.10"")2 Vay: Do Idn life hU'dng tam dat len electron la: Fh, = 9,2.10"* N. Bai giai *"- ^ b) Van toe va tan so chuyen dong cua electron - L\ic day Cu-16ng giffa hai proton la: F = k = kTa c6: Fh, = - Lire hap dan giifa hai proton la: F ' = G m,m2 = Gm R^ R^ - F' G m Suy ra: — = —. F k Vay: 1,67.10 Vay: 1,6.10 9.10^ ' ' Life day Cu-16ng giffa hai proton Idn hdn life hap dan giCfa chung « 0,71.10"/s. Van to'c va tan so' chuyen dong cija electron la Fh, « 2,25.lO' m/s va nhau bang life F = 1,8N. Dien tich to'ng cong cua hai vat la Q = 3.10"^C. Tinh dien tich moi vat. Life tmh dien giiJa hai vat la: F = k 11^2 R^ /. - 2 Life hap dan giifa hai vat la: F' = G R^ FR2 ^1^2 -G m R^ =1,6.10-'^ kinhR = 5.10""m. a) Tinh do Idn life hifdng tarn dat len electron. b) Tinh van toe va tan so'chuyen dong cua electron. Coi electron va hat nhan trong nguyen tur hidro tUdng tac theo djnh luat tTnh dien. (1) 9.10'^ •;t, .1 - VT hai dien tich day nhau nen qi va q2 cung dau va ciing du'dng (suy ra tif de bai). Do do: 1,86.10-kg. 1.5. Electron quay quanh hat nhan nguyen tuT hidro theo quy dao tron vdi ban = 2.10-10 Matkhac: 6,67.10"" 1,86.10"^ kg. 1,8.1^ - qiq2 = Vay: De life tTnh dien b^ng life hap dan thi khoi lifdng cua moi vat phai la m= ^1^2 R^ D e F = F'thi: .J^ Theo dinh luat Cu-16ng, taed: F = k = kR^ mjmj m = -.1 :v ^ ' Bai giai Bai giai k ^ = G i ^ R^ R^ , M , 2,25.10'm/s 2.3,14.5.10'" de life tlnh dien bang life hap dan. - « 1.6. Hai vat nho mang dien tich dat trong khong khi each nhau doan R = Im, day 1.4. Hai vat nho giong nhau, moi vat thifa mot electron. Tim kho'l lu'dng m6i vat - 9,1.10 -31 n « 0,71.10"/s. 1,35.10^'' Ian. - 1-11 9,2.10"'.5.10" i m 2,25.10^ 27tR = 1,35.10,36 -19 ,2 va n = -27 6,67.10 mv R , , ^1+^2 - Q = 3.10"^ ,-10 2.10 q , + q 2 = 3.10-' - - (2) d') ^ (2') /, - > Giai he (1') va (2') ta difdc: r " ® ^ ^ k r - - ^ ' q, = 2.10' C va q2 = l O ' C hoac q, = 10"' C va q2 = 2.10-' C. Vay: Dien tich moi vat la: q, = 2.10-' C va q2 = l O ' C hoac q, = 10 C v^ q2 = 2.10 •' ' C. 1.7. Hai qua cau kim loai nho nhu nhau mang cac dien tich qi, q2 dat trong khong khi each nhau R = 2cm, day nhau bang life F = 2,7.10^N. Cho hai qua cau Cty TNHH MTV DWHJ qiq2 = 12.10'^ _ Lire tdc dung len qs: F3 = Fjj + F23 q;q2 .F3 R^ => F' = k (q,+q2)= R^ -4 ±2RJ|^ = ±2.2.10"' 3,6.10 V 9.10^ 2. H ; G TONG HglP TAG DyNG LEN MOT D l t N TIGH 1.8. Ba dien tich diem q, = -10"'C, q2 = 5.10"'C, = 4.10"'C Ian lu-dt dat tai A, B, C trong khong khi, AB = Scm, AC = 4cm, BC = 1cm. Tinh life tac dung len moi dien tich. , , , Bai giai Ta c6: AB = 5cm, AC = 4cm, BC = 1cm => AB = AC + CB C nkm trong doan AB. c B e- Life tac dung len qi: =>F, =k 1211 AB' +k F, = 4 , 0 5 . 1 0 " ' N •" "" q3 q2 Fj = F 2 j + F 3 1 =^ Fi = F21 + F31 (F^^pPsi I3I1 AC^ 5.10"V-10"'') = 9.10'.( ( 5 . 1 0 " ' ) ' (10"')2 '^""g'^hilu) 4.10-'.(-10"^) ( 4 . 1 0 -2x2 "') => F3 = F13 + F23 = k I l l s + k ^ ' ' ' ' = 9.10'.( AC^ (-10"^).4.10" (4.10 ' ) ' (F,3;F23 + cung chieu) 5.10 ^4.10" (10"')' 1.9. Ba dien tich diem q, = 4.10"^C, q2 = -4.10"^C, q3 = 5.10"*C dat trong khong khi tai ba dinh ABC cua mot tarn giac deu, canh a = 2cm. Xac dinh vectd life tac dung len q3. , ; „,,:•< is^jj. , . Bai giai =^(q,+q2)= ±8.10-^ (2) -v-9 - Giai he (1) va (2) ta di^dc: q, = 6.10"' C va qz = 2.10 ' C; q, = -6.10"' C va q2 = -2.10"' C hoac q, = 2.10"' C va qz = 6.10"' C; q, = -2.10"' C va qz = -6.10"' C. Vay: Dien tich cua cac qua cau khi chU'a tiep xiic nhau la: qi = 6.10"'C va q2 = 2.10"'C; q, = -6.10"'C va qs = -2.10"'C hoac q, = 2.10"'C va q2 = 6.10"'C; qi=-2.10"'Cvaq2 = -6.10"'C. qi 4.10"^5.10- .F3 = 2 0 , 2 5 . 1 0 " ' N q ; = q ^ = ^ ^1+^2 qiq2 1 3 ^ 2 = 9.10'. ( - 1 0 " ' ) . 5 . 1 0 " (5.10-^)' AB= BC^ .F2= 16,2.1 0 " ' N - Khi cho hai qua cau tiep xiic nhau roi tach ra xa nhau thi: F' = k vai: =k (Fj2;F32 ngiTdcchieu) F12-F32 ) Ta c6: Vi ll F3 = ^^3 + =12 F23, .F,3 vdi F,3 = ; F23 a" =k a = F23Va a = (F,3,F23) 13'*23 = 120° 4.10"'.5.10 = 45.10-^N (2.10"')' Vay: Vectd life tdc dung len q3 c6: + diem dat: tai C. + phi/dng: song song vdi AB. + chieu: tiTAdenB. + doldtn:F3 = 45.10"^N. _i i 1.10. Ba dien tich diem qi = qj = q3 = q = 1,6.10""C dat trong chan khong tai ba dinh tarn giac deu canh a = 16cm. Xac djnh lire tac dung len dien tich q3. Bai giai Taco: F3 = F,, + F23, vdi =>F3 = F,3 = F23 = 9.10' I1I3 Fi3 =k F23 = k I2I3 a a B6i duBng hoc sinh gi6i V$t 1^ 11, tjp 1 - NguySn PhO Dflng . F,3 = F23 C t y T N H H MTV DVVti |-,lunu UiAt va a = (F,3,F23) = 60° => F 3 = 2F,3Cos-^ = 2 k \0 ^ F 3 = 2.9.10-/''^-'^7f.^ = 15,6.10-N (i6.io"2)2 2 I r 64.10"^(-10"'') = 9.10". = 36.10^N F23 = k (4.10"')^ >/F^TF^ = V(27.10-^)^+(36.10"^)^ =45.10'^N h2% Vay: Vectd liTc tac dung len q^ cd: + diem dat: tai C. + phiTdng: CO (O la trung diem AB). _ 13 _ AC ) (tan OCB = F23 BC + chieu: tiT C den O. + do Idn: F3 = 45.10"'N. \: - Fio = k——; vdi F20 = F30 ( V I qi Vay: Vectcf liTc tac dung len q3 c6: + diem dat: tai C. + phu'dng; vuong gdc vdi AB. + chieu: ra xa AB. + do l d n : F 3 = 15,6.10-^'N. 1.11. Ba dien tich diem qj = 27.10'^C, qj = 64.10"^C, q3 = -10"'C dat trong khong khi tai ba dinh tam giac ABC vuong goc tai C. Cho AC = 30cm, BC = 40cm. Xac dinh vectd liTc tac dung len q3. Bai giai Taco: ^ = + , vdi: a = 27.10"".(-10"'') (F,3,F23) = 90° 111.! F„ = k = 9.10^ = 27.10^N (3.10"')^ AC^ =>F3= vdi q i % 1.12. Tai ba dinh tam giac deu canh a = 6cm trong khong khi cd dat ba dien tich q, = 6.10'"C, q2 = q3 = - 8.10"'C. Xac dinh liTc tac dung len qo = 8.10~'C tai tam tam giac. Bai giai , T a c d : ^ = F , , + E , o - f 4 = F,o+F23, 1,! ^ => F23 = 2F20COS va F23 = 9.10 F,o =k =>F,o = 9.10". F20 -k = q3); b 12% ;F3o =k = |h = =^ va a = {F^^'^o) = J20° - = 2k ^ 2 % .cos60° = '2F0 6.10^8.10"^ e.io-^Vi = 3,6.10^N 92 „.:d3f:! f|.:>f& 'O'ff! f'V iMs sill • Ann =^ Fo = 3,6.10^ + 4,8.10"^ = 8,4.10"'N Vay: Vectd life tac dung len qo cd: , + diem dat: tai O. + phiTdng: vuong gdc vdi BC. \ + chieu: tij" A den BC. + doldn:Fo = 8,4.10-^N. " ^ 1.13. Hai dien tich q, = 4.10'^C, q2 = -12,5.10"*C dat tai A, B trong khong khi, AB = 4cm. Xac dinh lire tac dung len qj = 2.10"'C dat tai C vdi CA 1 AB va F ' CA = 3cm. Bai giai Tacd: F 3 = F , 3 + F 2 3 = ^ F3 = J F ,X' + F,^y ; Ox n^m ngang, Oy thdng diJng. Fn =k 11% = 9.10'^ 4.10^210"^ ,-2x2 (3.10-^) .!)':' AC = 8.10^N 5 B B6i clL0ng hpc sinh gi6i Vjt ly 11, tgp 1 - Nguygn Phd Dfing F23 =k 1213 Cty TNHH MTV DWH Khang Vi?t Vay: LiTc tac dung len m 6 i dien tich c6: (-12,5.10"^).210"^ = 9.10^ = 9.10-^N (5.10-2)2 BC^ Fx = F , 3 ( x , + F23(x, = 0 + F 2 3 . C O S B = F 2 3 . ^ = 9.10^. ^ = 7,2.10-^N BC • + chieu: ttr tarn luc giac ra. + do Idn: F = k- + phU'cfng: hdp vdi A C mot goc P: cosP = dung len m o i dien tich. - j (8.10^'*)^ +(7,65.10"*)" tich tai D tren hinh ve. „2 -(9.10~^)2 T a c o : F = F , + F 2 + F 3 = F , + F 2 3 , v d i : F, = F2 = F 3 = k ^ . « 0,34 => p « 70° 2 2.8.10"^7,65.10~^ dp l d n : F 3 = 7,65.1 O ^ N . ^'-^ ' ' C - vty,, V''"' 1.14. C6 6 dien tich q b^ng nhau dat trong khong k h i tai 6 dinh luc giac deu canh a. T i m lire tac dung len m o i dien tich. D o tinh doi xiJng nen ta chi can khao sat mot dien tich ba't k i , ch^ng han dien R '23 \r „ AD^+HD^-AH^ cosp = • 2.AD.HD a2 + Ta c6: F = F, + F3 + F4 + F5 + F,, v d i : ,2 120° aV3 1V3 2 V 2a. 2 , =>F,3 = F, = F3 = kf =>F^ = F 3 = k 4 = k - ^ = k - 3 i (c = 2a) D 2^ 2 + _ w5 2 r t. 2V B a a J 4a2 Q2 2 F4 = Ffi = k \ k - 3 - ; b ' = ( 2 a ) ' - a ' = 3 a ^ p = 60° b^ 3a2 F 4 6 = 2F4Cos30° = 2k 3a2 F =F , . F 3 . F . =k 12 = ^ / i k ^ n^m tren diTdng cao H D . tich tai B tren hinh ve. (2a)2 r V i F2 = F 3 ; B D C = 60° =^ F 2 3 = 2F2Cos30° = 2 k ^ . — 2 2 va F^ = F^ + F23 + 2 F 1 F 2 3 C O S P , v d i : »| B a i giai c^ B a i giai Do tinh doi xu'ng nen ta chi can khao sat mot dien tich ba't k i , ch^ng han dien 2F13F3 F, = F 3 = k 5 - ; a = 12 ^ ' d i e m dat: tai C. tSm luc giac. (15 + 4 ^ 3 ) q2 c6: + + phU'cfng: AvtUng thang noi dien tich 1.15. Bon dien tich q giong nhau dat d 4 dinh tu" dien deu canh a. T i m life tac = > F 3 = V(7,2.10~'*)2+(2,6.10-^)2 = 7,65.10-^•N => cosP = d i e m dat: tai cac dien tich. + 5 AC Fy = F,3(y, + F23(y, = F , 3 - F23.sinB = F , 3 - F 2 3 . ^ = 8.10"^ - 9.10^. - = 2,6.10^N BC Vay: Vectd life tac dung len + 2 4.k4.k^ 4a2'"3a2 V a y : Life tdc dung len m o i dien tich c6: + d i e m dat: tai cac dien tich. (3) .k4/'^"^^ '" a^ ' 12 ' '•u > + phiTcfng: hdp v d i mat tur dien mot g6c a: cosa ^ — 2 F E23 — ^3 13 Cty TNHH MTV DVVH Khang ViSt B6i du8ng hpc sinh gi6i V?t ly 11, tjp 1 - Nguygn Phu B6ng f cosa = I 2> 2 2 2 > ( — - J a' ( TiTdng tir doi v d i cac d i e n tich q2, qs va q4. 2\- I Vay: D o Idn liTc tac dung len m o i dien tich la F « 0,45.10"'N. 2V2 ^ J a = 160°30' 2V^k^.Vik%+ do \dn:F= Do'i v d i q,: Fi - F^, + V6k^. + F^j + F,,, + F2,i + Vy, + V^., v d i : F2, = F 4 , = F r i = k \ ; F 3 , = k (aVi)' 1.16. ffinh lap phiTdng A B C D , A ' B ' C ' D ' canh a = 6.10"'°m dat trong chan khong, Xac djnh life tac dung len m o i dien tich, ne'u: k a) Co 2 dien tich q , = q2 = 1,6.10-"C tai A, C; 2 dien tich qa = q4 = - 1 , 6 . 1 0 - " C t a i B ' va D ' . b) Co 4 d i e n tich q = 1,6.10""C va 4 dien tich - q dat xen ke nhau d 8 dinh cua hinh lap phiTdng. F21(x) - + F3, + F^,, Do'ivdiqi: F, = F31(z) vdi: F21 = F31 = F41 2a^ F 2 , = k \ ; F 2 , ( y ) = 0;F2,(z) = 0 4 •\2'_. = 0 F41(x) „2 : 0; F4i(y) = F41 = k \ ; F 4 i ( z ) = 0 2i = k (aV2)^ •= k- 2a^ Fri(x) = 0; Fn(y) = 0; Fn(z) = F n - k - F21(x) = F21(y) = - F 2 l C 0 S 4 5 ° = -k- F^r.(x) j-Uxl = —.F2.„z) = -F2-,cos45° = - k - ^ ^ . — =-—• '2a2'2 2 4 F2.,(y) = 9 k \ a^ „2 F3UX, = F 3 , ( . , = F3,cos45° = F4i(y) = F4i(z, = F4iCos45° = - = > F i x = F2i(x) + F3i(x) = — k 4 F ,ly v -= r2l(y) F2HV, + + F4UV) r4i(y), = - 2a2 2 2a2 2 ^ +• a^ — 4 a. 2 2 k 4 = Fruy) = Fruz) = F r . c o s A ' A C = k • 4-l(x) = ' 0; F4-i(y) = F4'i(z) = - F 4 ' , c o s 4 5 ° = => F u = F2l(x) + F3i(x) + F4i(x) + Fn(x) a- ^ a2 F3'i(x) ^k^' k ^ 4~2k ^ 4 + — ^ K — 4 = k if r 3 | ( 2 ) + ^41(2) = /I ;v' 72 q^ 2a^ 14 (aV2)' = -k2a2' 2 a) Ta c6: riz - • = k- F j K x ) = F31(y) = - F 3 l C O S 4 5 ° B a i giai - = k3a^ 1 Fri = F 3 i = F 4 i = • q'4 ^2 = q2 = I 3 " I 4 0 Taco: ^ a^ '23^ ' 2 a^ a' 4 + F2-i(x) + FS-KX) + F4-l(x) 4 4 a^ 9 a^ = 0 a- 4 '"-2 .9.10\ 2 -k 9 • =0 2 + Sa^'aVi 9 a^ /iSIO&snU:- => F,y = F21(y) + F31(y) + F4|(y) + Fi'Ky) + F2-l(y) + Fs'Ky) + F4'l(y) 2 '— « 0,45.10"'N (6.10-'0)2 1 B6i duSng hpc sinh gioi Vat ly 11, tgp 1 - IMguygn Phu D6ng TCr do: + C nam tren du'dng thang A B , ngoai doan A B , ve phia A . F l z = F2I(z) + F3i(z) + F4i(z) + Fri(z) + F2-l(z) + FS-KZ) + F4-i(z) ' > * M + BC = 3AC = 3 ( B C - Vay: Phai dat " a - a 2 9 a- b) Dau va dp Idn cua q3 de qi, q2 cung can bang C - De qi va q2 cung can bang thi: AB^ a- ^.12 = 4cm. A B F|2 + F32 AC ^2 3' va F12 = F32. -7 1,8.10 AB = 0,45.10"'C _ V i q , < 0 ; q 2 > 0 ^ q 3 > 0 : qj = 0,45.10"'C. F,=v^.t(,-:^.:^)k4]=(V^-Vi:?4)ki a F21 = F 3 , =0 1i'l2 , 1312 , ^3^1 =k va k = k AB' AC^ BC' 13 = I 2 9 A C = 4 H ^2^1 2 | . 8 = 12cm va -Q- a- . 9 BC = | A B = tai C , vdi A C = 4cm; B C = 12cm thi q3 se nam can bang, F2, + F31 = 0 va 2 AB) ,^ , Vay: De q, va qa cung can bang thi qj = +0,45.lO'^C. 1.18. Tai ba dinh tarn giac deu, ngu'di ta dat 3 dien tich giong nhau qi = q2 = q3 = F, = ( ^ / 3 - ^ / ^ 5 + l ) • 9 . 1 0 ^ ^ i ^ ^ : l ^ « 0,54.10-^N 3 (6.10-'°)2 - TiTdng tiT cho cac dien tich khac. • q = 6.10~^C. Phai dat dien tich thuf tUqo d dau, la bao nhieu de he can bang? " ' i.' Bai giai > - VSy: Do Idn cua life dien tac dung len moi dien tich la F « 0,54.1 O - ' N . •fW •-'"n 3. SlJ C A N B A N G C U A D I E N T I C H • , - . ,1,/. ,|i ^''^ Cac lire dien tac dung vao qo: FJQ , FJQ va FJQ . De qo can b^ng thi: • F,Q + F2Q + FJQ = 0 Vi qi = q2 = q3 = q = 6. lO^C => qo n^m d tarn tarn giac ABC. 1.17. Hai dien tich q, = -2.10"^C, q2 = 1,8.10"^C dat trong khong khi tai A va B, - AB = / = 8cm. Mot dien tich qa dat tai C. Hoi: V i tinh doi xiJng cua he nen de he can bang ta a) C ct dau de q3 n^m can bhng? Ichi can xet them dieu kien can bang cua mot b) Da'u va do Idn cua qs de qi, q2 cung can bang. Itrong ba dien tich kia, chang han q3. De q3 can * * Ib^ng thi: Fo3 + Fj3 + F23 = 6 B^igiai a) V i tri cua C de qs nhm can b^ng r ^ F o 3 = F'3 = 2F,3Cos30° = 2k - Cac life dien tac dung len qs: F j j . F j j . ' - De q3 nkm can bing thi: F^J + F23 = 0 => F j j = - F j j => F j j . F j j cung phu'dng, 3k I0 ^2 A 18 9 t- = V3k 1113 B jVi I1I3I 73 (Fo3 2 = k = Vik 3 q,, q2, q3 > •Il = 0 nen I1I3 (F,3 = F 2 3 = k Ills ) I0I3 a BC^ AC^ [BCJ I0I3 a' ngifdc chieu va c&ng do Idn: Fo = F23 <=> k fAcV ^ 3 2 3 .6.10-''= 3,46.10-^C 3 qo < 0. I Vay: De he can bang tW ph; j.io-'c. 17 .16 Bfii dugng hpc sinh gi6i V^t ly 11, t^p 1 - NguySn PhCi B6ng 1.19. d moi dinh hinh vuong canh a c6 dat dien tich Q = lO'^C. Xac dinh dau, dp Idn dien tich q dat d tarn hinh vuong de ca he dien tich can bang? Bai giai - Vi dien tich d cac dinh hinh vuong nh\S nhau nen dien tich q dat d tarn hinh vuong luon can bhng. - Vi he CO tinh doi xufng nen chi can xet dieu kien can b^ng cua mot trong cac dien tich con lai, chdng han dien tich dat d D. - De dien tich dat d D nam can bang thi: Fj4 + F24+F34+Fq= 6 =:>F'4 + F24 = Fq ( F , 4 + F 3 4 - F 4 ) CtyTNHH MW'DWHJm = (lV2)^g.tan45° 2l2g.tan45° -T\2 - De Q ct D n^m can bhng thi q < 0 q = -—(2yf2 + \). 4 Vay: De ca he can bang thi q = - ^ ( 2 ^ / 2 +1). 1.20. Hai qua cau kirn loai nho giong nhau moi qua c6 dien tich q khoi li/cfng m = lOg, treo hd'i hai day ciing chieu dai / = 30cm vao ciing mot diem. GiiJ qua cau I co djnh theo phifdng th^ng diirng, day treo qua cau II se lech goc a = 60" so vdi phiTdng thang diifng. Cho g = lOm/sl Tim q. Bai giai - Cac life tac dung len qua cau II: trpng life P , lUccSngday f va li/cdien F . H - Qua cau II nhm can bhng nen: P + f + F = 6. - Tarn giac liTc "gach gach" 1^ tarn gidc deu n6n: F = P. P IR, •. . . . • 9.10 .(4.10'0 m= 2.(2.10')^10.1 = l,8.10-\g=l,8g. Vay: Kho'i lu'dng cua moi qua cau la m = l,8g. b) Dien tich truyen them cho mot qua cau - Khi truyen cho mot qua cau dien tich q' thi goc giffa hai qua cau giam nen q' < 0. Vi hai qua cau van day nhau nen (q + q') > 0. - Dien tich cua qua cau di/Pc truyen them dien tich la (q + q'). q.(q + q') = mg.tan30° (r' = 1} - ri^dngtiTcaua, t a c 6 : F ' = P t a n a ' o k mg.tan30°.l^ q + q' kq 1,8.10"^10.^.(2.10"')^ 9.10^.4.10 -7 = 1,15.10-'C ' 19 B6i du8ng hoc sinh gioi Vat ly 1 1 , t j p 1 - Nguygn Phu D6ng Cty TNHH M T V DVVHj^h.nj Viet V i q > 0 ; q ' , ? =T Goi q, m la dien tich ban dau va khoi liTcJng cua moi qua cau. - (2]sin-1)2 Trirdc khi cham tay vao mot qua cau, dieu kien can bang cua mot qua cau cho: 2 2 tana = - « — P 21 a ~— a^mg Trong dien moi E: (F = k ^ ; P = mg) a => a + Cac lire tac dung vao mot qua cau: trong lire P, li/c cSng day 3 ^ 2kq^l F2 va lire day Ac-si-met F^ . (1) mg 21 + Dieu kien can bang cua mot qua cau cho: a. F2 = (P-FA)tan- Khi cham tay vao mot qua cau, qua cau do se ma't he't dien tich, life dien giiJa hai qua cau khong con nffa, hai qua cau se cham vao nhau va dien tich lai du'cfc phan bo deu cho hai qua cau (q' = ~ ) ' hai qua cau lai day nhau va = (D,-D2)Vg.tan cau lijc nay ta suy ra: - 2kq^ 3 — • . -1 q sin a, tan—*- 2 «2 2 a, 2«1 n _ D,-D, • D, tan ' sm ^ Ot, 2 -J-tan-i sm^-^tan-^ "4 •w 3,15cm => a = ^ TiJ(l) va (2)suyra: (2) mg (2) a •2 \2 e(2/sin--?) khoang each giiJa chiing la a', lu'dng tiT, tCf dieu kien can bang ciia mot qua a , lire dien Vay: Gia tri cua £ theo D,, D2, a,, a2 la 8 = > i i "I .'Mi( moi long cd khoi lUdng rieng D2, gdc giila 2 day treo la a2 < a i . _ Vay: Gia tri cua D, de a, = aj la D, = a) Tinh e cua dien moi theo Di, D2, a i , a2. b) Dinh D, de aj = a,. , ' ' Bai giai i>? , ^ "f , 20 Trong khong khi: 1-24. Hai dien tich q, = 2.10'^C va q2 = -8.10"'C dat tai A va B trong khong khi, A B = 8cm. Mot dien tich qa dat d C. Hoi: ^) C 6 dau de q., can bang? Khi qj can bang, qj phai cd dau nhu" the nao de can a) Tinh e cua dien moi theo Di, D2, tti, a2 - ^^2 E ^ ' • bang nay la can bang ben? khong ben? Cty TNHH MTV DWH ku,^ ^|^, B6i dU3ng hoc sinh gi6i V$t ly 11, t$p 1 - Nguygn Phu D6n9 b) Oa'u va do Idn cua qj de he can bang? K h i he can hKng, tW can bang cua he va k B a i giai ^AC^^ a) V i t r i cua C de q3 n ^ m can bang va dang can bang - <" V i tri cua C • + Cac \\ic d i e n tac dung l e n qf. F j j . F j , . + D e q3 nam can bang thi: F , , + AB^ AC^ AB^ I ben hay khong ben? q3 = • , + ! ' ' _ = 0 => F,3 = -F23 => Fi3,F23 cung phiTdng, q2 BC^ (-8.10"'') vAB, • t = 8.10X 7 V i qi > 0; q2 < 0 => q3 < 0: qj = - 8 . 1 0 ' C . I Dang can bling cua he: K h i q3 < 0, can bang cua q3, q,, q2 deu la can b^ng ben nen can bang cua he la can bang ben. V a y : D e qi va q2 cQng can bang thi q^ = -8.10'^C va can bhng cua he la can ngiTdc chieu va cung dp Idn: F o = F23 o k C ^2 ^BcJ 8 4 bang ben. BC' AC^ F' Chung day nhau, each nhau doan a = 3 V3 cm. T i m q ? Cho g = 1 Om/sl B a i giai C nam tren du-dng thang A B , ngoai doan A B , ve phia A . - Dang can bang: + K h i ba qua cau each nhau mot doan a => he can bang. V i he do'i xi?ng nen chi • can xet mot qua cau, chang han qua cau tai C. B C = 2 A C = 2(BC - A B ) => BC = 2 A B = 2.8 = 16cm va A C = - .16 = 8cm. - - , chieu dai / = 5cm vao cung mot diem O. K h i tich cho moi qua cau dien tich q, Tur do: • , 1.25. Co 3 qua cau cung khoi lu^dng m = lOg treo b^ng 3 sdi day manh cCing B A , V d i qua cau tai C: + Cac lire tac dung len qua cau: cac lire dien F,3,F23; trong lire P3 va liTc N e u q j < 0: K h i difa q j lech cang day T 3 . k h o i vj tri can bang thi hdp lire (F,3+F23) se hirdng du^a + Qua cau can bang nen: F j j + F23 + P3 + 73 = 6 => F3 + P3 + CO xu 2/7 trd ve vj tri =>F'3 = P3tana, vdiP3 = mg;F'3 = 2F,3Cos30° = can bang cu nen day la can bang ben. + Vik- N e u q3 > 0: K h i diTa q3 lech = mg.tana k h o i vj t r i can b^ng thi hdp lire ( F j 3 + F 2 3 ) se - CO xu Tarn giac OGC cho: tan a = (1) GC GO hu^dng diTa q^ ra xa vj tri v d i : G C = ^ C K = i ^ . ^ ; . 3 3 2 3 can bang cu nen day la can bhng khong ben. V a y : Phai dat q3 tai C, v d i A C = 8cm; BC = 16cm thi q3 se nam can bang va ==>tana= , ^ (2) can bang do la can bang ben hay khong ben tuy thuoc vao da'u cua q3. b) Da'u va do \dn cua q3 de q i , q2 cung can bang, dang can bhng cua he - Da'u va do Idn cua q3 de he can bang + D e q , va q2 cung can bang thi: F21 + F 3 , = 0 va F,2 +F32 - 0 va F,2 = F32. => F21 = F3, - T i y ( l ) va ( 2 ) s u y r a : y f s k - ^ = mga' = 0 2 2k3-.— =Vsk^ ,2 2 B6i duSng hoc sinh gi6i Vgt ly 11, tjp 1 - IMguygn Phu D6ng mga = a L6 xo CO chieu dai / ( 2 L >l> lo) nhuThinh ve. Xac dinh gia trj cua q? 0,01.10.373.10"^ = 3 ^ 3 .10^1 3.9.10% B a i giai na, vrs-it'nu'-i' ; V i he C O tinh doi xifng nen ta ehi can xet mot qua cau, chang han qua cau (5.10-^)^-^^:'?">! ben phai (hinh ve): Cac liTc tac dung l e n qua cau: trong life P ; life dien F ; liTc dan hoi F , ; life .10'^ = 1,14.10^C V a y : D i e n tich cua m o i qua cau la q = ± 1,14.10"^C. quan tinh F^ ; liTc cang day T . • fjiiVi-.'sri'fiCr 1,26. M o t vong day ban kinh R = 5cm tich dien Q phan bo deu tren vong, vong dat trong mat phang thang diJng. Qua cau nho m = I g tich dien q = Q diTdc treo bKng mot day manh each dien vao diem cao nha't cua vong day. K h i can bang, qua cau nam tren true cua vong day. Chieu dai cua day treo qua cau la _ Qua cau nam can bang nen: P + F + Fj + F + T = 0 _ Tir(l)suyra: F - F, = (P + F;,)tana i giai - Cac lire tac dung len qua cau: trong liTc P ; life dien F ; liTc cang day T . - Qua cau nam can bang nen: P + F + T = 0 . - Tarn giac lU'c "gach gach" cho: F = P '•^isl ,. . - i ^ ^ . g ^2 3 :^ k ^ l = ^mg. , , vdi: F = I d F (tong cac liTc dien . ' UJ 3mgl + 2k'(l-lo) kq I' V a y : D i e n tich cua m o i qua cau la ZdQ.cosa= kQ' mg —-^.cosa = tana kQ^ mg mgl sma R Q V 10--\l0.7,2.10"^ = 9.10-^C. •)OQ:ilmmT 9.10'^.5.10"^ V a y : D i e n tich cua vong day la Q = ± 9. IO"*C. 3mgl + 2k'(l-lo) THirC I. Di^ntrirt/ng =7,2.10-1, " kR A. T O MT A TKIEN =1 DIEN TRi/dNG Chmendil: (sina = y ) (2) +k'(/-/o) tana cua cac phan tuf nho cua vong day tac dung len q) P = mg; F = ZdF.eosa = W i. k ^ - k ' ( / - / o ) = (mg + m | ) . 1^ / = 7,2cm, tinh Q. Bai (1) ' 1. Di^n triftfng: D i e n triTdng sinh ra bdi dien tich Q la viing khong gian ton tai xung quanh dien tich Q va tac dung liTc dien l e n dien tich khdc dat trong no. M 1.27. Hai qua cau nho cung khoi \\idng m, du'dc tich dien giong nhau q. Chiing 2. CiftJfng dp dipn trvliing: CiTdng dp dien du'dc no'i vdi nhau bang mot 16 xo nhe each dien, chieu tn/5ng do dien tich diem Q gay ra tai diem Q>0 dai tif nhien cua lo xo la /o, dp ciJng k ' . M o t sdi chi, M each Q mot doan r eo: 0-—^ E Q<0 each dien, manh, nhe khong dan, c6 chieu dai 2 L , moi + D i e m dat: T a i M . dau day ehi dUdc gan vdi mot qua cau. Cho diem giffa + Phu-Png: Dirdng thang noi Q va M . O cua sdi day chi chuyen dong thang duTng hu'dng len + Chieu: HiTdng ra xa Q neu Q > 0; hiTdng ve Q neu Q < 0. vcti gia toe a , c6 dp Idn bang ^ (g gia toe rPi tif do). + Do Idn: E = - . e r (k = 9 . 1 0 ' ^ ( ^ ^ ) ; e: h^ng so dien m o i ) . M Bfii dUSng hpc sinh gidi Vat ly 11. tjp 1 - Nguygn Phu Dong Cty TNHH MTV DVVH Khang Vi^t 3 . MO'i quan h$ giffa ctfcfng do di§n trUcfng Itfc d i ^ n trtfcfng: K h i dat dien + Neu(Ej,E2)=a tich thur q trong dien trong dien truf&ng E thi q se chju tac dung ciia life " i - - ... dien trUtJng F , v d i : " j ' i-- Tri/cJng hdp dien tich nam can bang trong dien triTdng thi tit d i e u k i e n can • u + C h i e u : q > 0 : F , E cung chieu; q < 0: F , E ngiTOcchieu. + Do Idn: F = IqlE. : 4. N g u y e n l i c h o n g cha't d i $ n t r t f t f n g : N e u trong * bingvllirc: - ta CO the diTa vao phifdng phap "tam giac life", phiTdng phap hinh chieu nhiT da E, M F = F,+F2+... = 6 diing cf chuyen de 1 de xac dinh cac dai lu'dng can tim theo cac dai lu'dng da cho. khong gian c6 nhieu dien tich d i e m Q i , Q2, ... thi Do'i vdi nhffng vat c6 kich thffdc (c6 hinh dang dac biet), de tinh cffdng dp dien trUdng tdng h d p do cac dien tich nay gay ra dien trffdng do vat do gay ra ta c6 the dung mot trong hai each sau: tai d i e m M each Q i , Q2, ... Ian lUdt la r i , Vj, ... la: + E = E,+E2+... 1. D i ^ n thong: Dien thong (thong liTdng Cac/i 7: Phi^cJng phap vi phan: • E dien • TCf tinh doi xilng cua vat ta xac dinh dffdc hufdng va dp Idn cua E . N = ES.cosa ( a la goc hdp bdi vectd E va phap tuyen n cua dien tich S ) + 2. D j n h If O s t r o g r a d s k i - Gauss; D i e n thong qua mat k i n c6 gia trj Cdch 2: Phu'dng phap dung dinh l i 0 - G : • bang tong dai so' cac dien tich c6 mat ben trong mat do chia cho SQ : , ; - vf^'-"".: Chia vat thanh nhieu vat raft nho, moi vat nho do dffdc coi nhiT mot dien do nhieu vat ra't nho (dien tich diem) gay ra: E = l A E j tru'dng) qua dien tich S la dai lu'dng xac dinh b d i : N = — E q ; = 47iklq; • Tinh dien thong: N = ES.cosa ( a la goc hdp bdi hiTdng cua E va hffdng phap tuyen n ciia S). • ^' Dung djnh l i 0 - G : N = — S q ; = 47tklq; ^0 ^0 B. NHtJNQ CHU Y KHI GlAl BAI TAP C. C A C BAI T A P V £ DIEN - 1. Can phan biet giffa yeu cau " t i n h " va "xac d i n h " cffdng dp dien trffdng: tinh K h i bieu dien vectd cffdng dp dien trffdng do mot dien tich d i e m gay ra can chu y den dau cua dien tich: Q > 0 ( E hudng xa Q ) , Q < 0 ( E hiTdng ve Q ) . + N e u E j , E 2 ngi/dc chieu thi E = IE, - E2I. + N e u E p § 2 vuong goc thi E = ^E^+E^ . T A C DVNG L E N D I E N T I C H D I E M la mat dp dien mat (S: dien tich mat cau) each be mat qua cau doan 5cm. B a i giai dp dien trffdng E , , E 2 t h i ta dung nguyen l i chong cha't dien trffdng de xac N e u E p E 2 Cling chieu thi E = Ej + E 2 . TRUCJNG Cho a = 8,84.10''' C / m l Hay tinh dp Idn cua ciTdng dp dien triTdng tai diem Trffdng hdp c6 nhieu dien tich d i e m Q i , Q 2 , . . . gay ra tai d i e m M cac ciTdng + ' s ra vdi r la khoang e a c h tCr tam qua cau den d i e m ta xet. trffdng tong hdp tai M can chii y cac trUdng hdp dac biet sau: * DO D I E N TRl/OfNG DO D I ^ N T I C H D I E M G A Y R A . LlJC T a dat a = dung de tinh cffdng dp dien trffdng do mot qua cau tich dien phan bo deu gay dinh cirdng dp dien triTdng tong hdp tai M . D e tinh dp Idn ciTdng dp dien TRUdNQ 2.1. Q u a cau bang k i m loai, ban kinh R = 5cm dffdc tich dien diTdng q, phan bo deu. Cong thUiC tinh cffdng dp dien triTdng do dien tich d i e m gay ra cung di/dc - CUOING DIEN (tinh do Idn), xac dinh (ca d i e m dat, phffdng, chieu va dp Idn). - ^ ' tich d i e m . rJy->'y^r 'ii','' • ••' • • Cffdng dp dien trffdng do vat gay ra la tong hdp cua cffdng dp dien triTdng 11. D i n h h' O s t r o g r a d s k i - Gauss '{ va E, = E 2 thi E = 2 E , . c o s | . Chpn mat Gauss la mat cau S' dong tam vdi qua cau, ban kinh r = 10cm. ~ D i e n thong qua m a t s ' l a : N = ES'.cos a = E S ' = E . 4 7 I T ^ ~ Theo dinh l i 0 - G ta cd: N = 4 r t k l q i = 47tkoS = 47ika.47tR^ = 167r^R^ka. =>E.47cr2 = 1 6 7 r ^ R 2 k o = > E = 4 7 i k ( - ) ^ a =>E = 4.3,14.9.10^(—)^8,85.10-^ = 2 , 5 . l O W / m . 10 27 • B6i duBng hpc sinh gi6i Vjt ly 11, tjp 1 - Nguy§n Phu D6ng Vay: Dp Idn cua cUdng dp dien trUdng tai diem each be mat qua ciu doan 5cmla E = 2,6.1 OW/m. 2.2. Proton dirpcdat vao dien tru'dngdeuE= 1,7.1 OV/m. a) H, trung diem AB. M each A 1cm, each B 3em. c) N hdp vdi A, B thanh tarn giac deu. ,• i'' Bai giiii a) Tinh gia toe cua proton, biet mp = 1,7.10 " k g . ^ Vectd cirdng dp dien triTdng tai trung diem 11 cua AB b) Tinh van toe proton sau khi di dU'pe doan du'dng 20cm (van toe dau bang khong). Ta c6: E^=E^+E^ Bai giai . ' ' Vi Ej eung chieu vdi Ej nen EH = E I + E2. a) Gia toe cua proton: Bo qua trpng li/c tac dung vao proton, gia toe cua proton la: F a= — 'm . . A H = B H - — = - = - = lcm =10-^m vdi E, = k — i - ; E 2 = k 2 2 2 BH' AH^ ^-19 ^ = mp 1,6.10" m/s' 1,7.10'^' . I' ,9 4.10 . E H = 9.10^ Vay: Gia toe eiia proton trong dien tru'dng la a = 1,6.10''* m/s^. b) Van toe proton sau khi di dU'pe doan du'dng 20cm Taco: v 2 - V ( ^ = 2 a s =^ v = ^ v ^ + 2as = +2.1,6.10''*.0,2 =8.10^m/s ^ ! V i electron mang dien tich am nen life dien tru'dng F tac dung len electron se ngu'de chieu vdi chieu dien tru'dng E nghla la ngu'dc chieu vdi chieu , chuyen dpng cua electron nen electron se chuyen dpng cham dan deu, cung chieu vdi chieu du'dng sdc dien tru'dng vdi gia toe: 2a - 0 - ( 4 10^)^ ' f— = 0,05m = 5cm 2.(-I,6.10'^) Taco: E^=E^+E^ - V i A M = AB + B M = > M nam tren diTdng thang AB, ngoai doan AB, ve phia A. - V i E , ngi/dc chieu vdi E2 nen EM = | E I - E J -10 4.10 = 36.10' V/m. = 9.10^. vdi E, = kAM^ (10-')' ,-10 E2= k BM' .= 9.10'. = > E M = 36.10^-4.10-^ + phufdng: diTdng thang AB. 28 , , = 4.10'V/m. E, EM M E^ A + chieu: hiTdng ra xa A (eung chieu vdi E , do E i > E2). + dp Idn: EM = 32.10'V/m. c) Vectd eirdng dp dien trUdng tai diem N Taed: E N = E , + E 2 AB = a = 2em. Xac dinh vectd eiTdng dp dien tru'dng E tai: , Vay: Vectd cu'dng dp d i e n triTdng tai M c6: (a' = -a = l,6.10'Ws^) va chuyen dpng nhanh dan deu theo chieu ngiTdc lai 2.4. Cho hai dien tich q, = 4.10'°C, qz = ^ . l O ' ^ C dat d A, B trong khong khi, 01} = 32.10' V/m d i e m dat: tai M . D I E N TRUOfNG ,-2x2 rV (3.10"^) + 2. S\J CHONG C H A T D I E N TRl/OlNG - D I E N T I C H C A N BANG TRONG B b) Vectd cu'dng dp dien triTdng tai diem M Sau khi diTng lai, dU'di tac dung cua liTc dien tru'dng, electron se thu gia toe a' (ngu'de chieu vdi dien tru'dng). EH + dp Idn: E H = 72.10'V/m. „ , £ . : £ ^ . < - ' . ' ^ - ' ° - " ) ; ' " ' > . - 1 . 6 . 1 0 " nvs' m m 9,1.10"^' = E2 + chieu: ttj" A den B (eung chieu vdi E, va E^). deu CLing chieu du'dng siJe. Mo ta chuyen dpng ciia eleetron sau do. Bai giai H ^ + phu'dng: du'dng thang AB. trU'cJng deu, cUdng dp dien tru'dng E = 910 V/m, V Q eilng chieu diTdng siJc dien tru'dng. Tinh gia toe va quang du'dng electron chuyen dpng cham dan ©- - + diem dat: tai H. 2.3. Electron dang chuyen dpng vdi van toe VQ = 4.10^m/s thi di vao mot dien v^-v^ E, Vay: Vectd cu'dng dp dien triTdng tai H eo: Vay: Van toe proton sau khi di dU'pe doan du'dng 20cm la v = 8.10'' m/s. va quang du'dng: s = = 72.10' V/m i\o~^f (10-^)^ V 'oi M - ' ' 1 s«:^>5,n,} n e Bfii duBng hoc sinh gidi Vat ly 11, t j p 1 - Nguygn Phu D6ng Cty TNHH MTV DVVH KhangVigt ; N A = N B = a; a = 120° = > E N = E l = E2 = k Vi E N = 9.10'. 4.10 -10 (2.10-2)2 = 9.10'V/m + d i e m dat: tai M . + phiTdng: dirdng thang A B . + chieu: hu'dng ra xa A. + d p l d n : E M = 40.10'V/m. K ^2 M Vectd eirdng dp dien tru'dng tai d i e m N V a y : Vectcf ciTdng dp dien trirdng tai N c6: d i e m dat: tai N. Tacd: + phi/Png: dirdng thang A B . V i qi| = |q2|;NA = N B = a ; a = 60° + chieu: tiT A den B. + dp Idn: E N = 9 . 1 0 ' V / m . A E N = 2Eieos30° = 2 k ^ a R 2.5. Cho hai dien tich qi = q2 = 4 . 1 0 " ' ° C dat d A, B trong khong k h i , A B = a = 2cm. Xac dinh vectP ciTdng dp dien triTdng E t a i : ,E„ = 2.9.I0'. , a) H , trung d i e m A B . -'° -2x2 (2.10"')' cos30° 73 « N 15,6.10^ V/m 2 Vay: Vectd cu'dng dp dien tru'dng tai N eo: b) M each A 1cm, each B 3cm. + d i e m dat: tai N. c) N hpp vdti A, B thanh tam giac deu. Bai giai a) VectP cu'dng dp dien triTdng tai trung diem H cua A B = > E H = 9.10^4-'° phu'dng: vuong goe vdi A B . + chieu: hu'dng ra xa A B . B A 15,6.10^ V/m. 2.6. Hai dien tich qi = S.IO'^C, qj = -S.IO^^C dat tai A, B trong khong k h i , A B = nen E H = |E, ^2 El = k;E2= AH^ -10 + + dp Idn: E N * +E2 V i E , ngirpe chieu v d i vdi A EN=E,+E2 + Ta c6: Ej^ = E j B A kBH' -9A0'. -E^ ; AH = BH = 4.10-'° TT (10-')' 4cra. T i m vectd cu'dng dp dien tru'dng tai C tren trung triTc A B , each A B 2em, AB a 2 2 2 2 ^ =0 suy ra life tac dung len q = 2 . 1 0 ' C dat d C. Bai giai - Vectd cu'dng dp dien trUdng tai diem C Ta c6: E^, = E , A H E, +E2 B V a y : VeetP cu'dng dp dien tru'dng tai H c6 dp Idn bang 0. Vi 12 ; C A = C B = V C H ' + A H ' ; c o s -2 = cosA = A H b) V e c t d eirdng dp dien tru'dng tai diem M Tacd: Ej^=E,+E2 Ec = 2 E , c o s - - V i A M = A B + B M = > M nlm - V i Ej Cling chieu vdi E2 nen E M = E I + E2. E l = kAM E2= = 9.10^.^-^0 (10-')' = 36.10'V/m. ^2 k.= 9 . 1 0 ^ . ^ : 1 ° — = 4 . 1 0 ^ V/m. BM' (3.10-')' = > E M = 36.10^ + 4 . 1 0 ' = 40.10^ V/m V a y : V e c t d ciTdng dp dien triTdng tai M eo: 30 2.10,-2 = 9>^.10^(V/m) [(2.10-')' + ( 2 . 1 0 - ' ) ' ] • 7 ( 2 . 1 0 - ' ) ' + ( 2 . 1 0 - ' ) ' ^-10 vdi A H ' ( C H ' + A H ' ) ' V C H ' + A H ' 8.10- Ec = 2.9.10^ VCH' + AH =2k 2 tren diTdng thang A B , ngoai doan A B , ve phia A. A H V a y : V e c t d cu'dng dp dien triTdng tai C c6: 1+ d i e m dat: tai C. i+ phi/dng: song song vdi A B . chieu: tijf A den B. It dp Idn: E c = 9^2.10^ (V/m). 31 BoiduSng hoc sinh gioi Vat ly 11, tap 1 - Mguyen Phi'i Dong - Cty TNHH MTV DVVH Khang Vigt D o Idn life tac dung len q dat tai C: Fc = Ec = 2 . 1 0 ' ' . 9^.\0^ » k_ii_ 25,4.10"'N. d i e m dat: tai C. E 3 = + phU'dng: song song vdi A B . ' + chieu: cting chieu vdi E,;. (do q > 0). + do Idn: Fc « 25,4. l O ^ N . ' Xac dinh vectd E tai M tren trung triTc A B , each A B = 4cm. A H = 10 *C; cosa = TT~-~ MA 9.10'* (32.10"^)^ 1024 10^_9T0^ 36 \ 1024 = 246 V/m. Vay: D o Idn cu^dng do dien tru'dng tai H la E H = 246 V/m. tai tarn O hinh vuong trong tru'dng hdp bo'n dien tich Ian liTdt cd dau sau: =5cm. a) + + + +. b) + - + - . c)+--+. B a i giai 3 5 V/m. 2.9. Cho bo'n dien tich cdng do Idn q dat tai bon dinh hinh vuong canh a. T i m E B a i giai • 4^+3' 576 / V/m. 10,-9 = 9.10". 2 9.10' 2.7. Hai dien tich q, = -IQ-'^C, q2 = lO^C dat tai A , B trong khong k h i , A B = 6cm. Vi ^3 CH' =>EH = Ta c6: M A = M B = V A H ' + H M k- 36 (18.10"^)^ BH' Vay: Life tac dung len dien tich q dat tai C c6: + 1^ 10-^ =9.10^ " e n Ei = E2 = k - MA^ .4. aV2 V i q i = q2 = q3 = q4 = q ; r, = r j = r j = r4 = - y - nen E i = E2 = E 3 = E 4 . 10"^ 3 = > E M = 2 E , c o s a = 2.9.10^(5.10"^)^ 5 a) Trufdng hdp dau cua cac dien tich Ian lu'dt la + + + +: E o = E i + E 2 + E 3 + E 4 = E,3+E24 ^ E o = 0 = 0,432.10^ V/m. ';J ' Vay: Tru'dng hdp dau cua cac dien tich Ian li/dt la + + + + t h i Eo = 0. Vay: Cifdng do dien tri/dng tai d i e m M c6: b) Tru'dng hdp dau cua cac dien tich Ian liTdt la + - + - : + d i e m dat: tai M . + phi/dng: song song vdi A B . + chieu: ttr B den A . + do Idn: E M = 0,432.10'V/m. EQ :\ = Ej + E2 + E 3 + E^ = E,3 + E24 => Eo = 0 Vay: Tru'dng hdp dau cua cdc dien tich Ian lu'dt la + - + - thi Eo = 0. ' ®^ 2.8. T a i 3 dinh tarn giac A B C vuong tai A canh a = 50cm, b = 40cm, c = 30cm. Ta dat cac dien tich q, = q2 = qj = 10"'C. Xac dinh E tai H , H la chan difdng cao ke tiT A . c) Trufdng hdp dau cua cac dien tich Ian liTdt la + - - +: E o = E , + E 2 + E 3 + E 4 = E,3+E24 • Eo = 2E,3Cos45° = 2.2Eicos45° = 4 k : ' •' • B a i giai ' i-u u u b ^ 40^ = 32cm. Ta co: C H = b.cosC = b. — = — = a a 50 B H = a - H C = 5 0 - 3 2 = 18cm. a72' ^ A H = VHB.HC = - V32.I8 = 24cm. ^3 A ® — E j ~i~ E2'^ • V i E, I E 2 3 = > E H = Vdi: E,= +E^3 = 9 . 1 0 ' . _ i ^ (24.10"^)^ 32 :9B D o Idn cua ct/dng do dien tru'dng tai H : Ej ~i~ ^2 - Vay: Tru'dng hdp dau cua cac dien tich Ian liTdt la + - - + thi Eo = 4V2 — . ' F ^^Ef+(E2-E3)2 = ^ V / m . 576 Trirdng hdp a D C Trirdng hdp b D Trirdng hdp c C 33 Cty TNHH MTV DWH Khang Vi$t B6i duSng hgc sinh gi6i V$t ly 11. tjp 1 - IMguy§n Phu D6nq 2.10. Tai ba dinii A, B, C ciia hinh vuong ABCD canh a dat 3 di^n tich q giong Ta c6: E,^ = E, + nhau (q > 0 ) . Tinh E tai: ' a) Tarn O hinh vuong. , , E, = b)DinhD. E 2 = k- . V i q, = qj = q ; A q _ = k M =B M ; cosa = cosA = a^+h^ A M ' Va^ + h^ Bai giai ^EM a) CiTcfng do dien tru'dng tai tarn O: - VI q, = q2 = q3 = q; r, = = rj = nen Ej = nen = 2E|COsa = 2 k kqa = 2- E2 = E3. vay: CiTcJng do dien triTdng E M tai M tren trung triTc cua A B c6: • - Eo = E , + E 2 + E 3 = E , 3 + E 2 + d i l m dat: tai M . V i E, \h E 3 ngiTdc chieu nen £ , 3 = 6 nen Eo = Ej. => E n = k + phiWng: song song vdi AB. 'i an.i 'nis! + chieu: tir A d e n B. _ 21cq q ^n&'i/if ;,3 .ev • , ^ ^ , + d61dn:EM= 2 (a2+h2)2 Vay: CiTcJng dp dien triTdng tai tam O la Eo = b) Gid tri cua h de E M dat ciTc dai 2kq a b) CifcJng do dien triTcJng tai dinh D V i f i = r3 = a; r2 = aV2 nen Ei = E 3 = k — ; E 2 = A EM ciTc dai khi h = 0 va EM(max) = Vay: De k EM ^ a B ciTc dai thi h = 0 va EM(,„ax) = . 2a2 - •J suy ra (a^+h^)2 Ta c6: Ep = Ej + Ej + E3 = Ej3 + E2 - kqa TirEM= 2 2kq : q ^ a , 'Mi ';.r'I.: c) 2.12. Tai ba dinh ABC cua tu" dien deu SABC canh a trong chan khong c6 ba dien tich diem q giong nhau (q < 0). Tinh do Idn cu'dng do dien tri/cJng tai dinh Mat khac, vi E, va E 3 vuong goc nhau nen: S cua tu" dien. Xac dinh hiTdng cua cu'dng do dien tru'dng nay. •f 3 - E,3 = E.V^ = V i E , 3 va E2 k4^ CLing chieu nen: Bai giai ED = E | 3 + E2 2a^ Ta c6: E^ = Ej + E j + E3 = E, + E23. ! 1 , kq , - VI q, = q2 = q3 = q < 0; r i = rz = - V I a = ( E j . E j ) = 60° nen t ulri;:;, B . ( v > ' r3 = a nen El = E2 = E3 = k ^ . 2'n2 Vay: CircJng do dien trirdng tai dinh D la E D = ( \ / 2 + - ) ^ . 2.11. Hai dien tich qi = q > 0 va q2 = - q dat tai A , B trong khong khi. Cho A B = 2a. a) Xac dinh ciTdng do dien tru'dng E M tai M tren trung triTc cua A B , cdch A B E23 = 2E2Cos30° = 2 k W. : / l = Vik 4 a^ 2- '' E23 n\m tren duTdng cao SH cua tam giac SBC. doan h. b) Xac djnh h de E M dat ciTc dai. Tinh gid tri ciTc dai nay. Bai giai a) CiTcJng do dien trUdng E M tai M tren trung trifc cua A B Suy ra: E^ = E^ + E23 + 2EjE23Cosp, v<3i cosp = , - ; SH^+SA^-AH^ 2SA.SH 35 Bi5i du3ng hpc sinh gi6i Vat ly 11, tjp 1 - Nguyin Phu Bfing 2 Cty TNHH MTV DVVH Khang Vi§t va EBD- = 2EBCOsa2 = 2. 2 cosP = 2a. V I E ^ c '^""S 2 ^/I + 2. k4 V 8^3 k q 9 kq 3 = EAC + EBD' 1673 k q 9 a^ Vay: Do Idn ciTdng do dien triTdng tai tarn O iiinh lap phiTdng la j . ,; ^ y I6V3 k|q| va E 5 hiTdng ve tarn tam giac ABC. .Es= A / 6 - Vi ^B'D' 8V3 k q > Eo — 9 N2 = 6 4 kq 3 a2 a y 2.14. Cho hai dien tich diem qi va q2 dat d A, B trong khong khi, AB = 100cm. Vay: VecW ciTdng do dien triTdng tai dinh S cua tu" dien c6: Tim diem C tai do ciTdng do dien triTdng tdng hdp bang khong vdi: a) qi = 36.10-^C; q2 = 4.10-^C. + dpldn:Es= Bai giai a) Khiq, = 36.10-'^C;q2 = 4.10-''C + hirdng: tiT S den O (ban doc tiT chUng minh!). 2.13. Hinh lap phiTdng A B C D A ' B ' C ' D ' canh a trong chan khong. Hai dien ticii Qi = q2 = q > 0 dat d A, C; hai dien tich qj = q4 = - q dat 6 B ' , D ' . Tinh do Idn Ta c6: E^ = Ej + E j . De E^ = 0 => E, = - § 2 , siiy ra: + C nam trong doan AB (vi q,, q2 ciing dau). curdng do dien triTdng tai tam O hinh lap phiTdng. + E| = E2 <=> k Bai giai Ta c6: EQ = E^ + Ec + E 3 , + E^. = E^^ + ^g.^, = 7a2+(aV2)2 BC = aVs i = > A O = C O = B'0 V ^2 =3 vaAC + BC=:AB = 100cm = D'0= — 2 = —^-^ BC 36.10 -6 -6 4.10 AC A C = A ' C = VAA'^+A'C^ ^2 =k AC^ s AC = 75cm va BC = 25cm — 2 Vay: Khi q, = 36.10-'C; q2 = 4.10^^C, de E^ = 0 thi AC = 75cm va BC = 25cm. b) Khi q, = -36.10'C; qj = 4. lO'^C AO = CO ndn EA = Ec = CC'_ a _73 = k rr\2 .71 3 a2 36 V y 4 kq 7^ 3 a2 3 BC 873 k q =k k AC" B ^2 ^2 1 4.10 -6 = 3 —> e- BC 36.10 -6 AC 2 = > EAC = 2 E A C 0 s a i = 2. + E, = E, o 4 kq f ,i . + C nam ngoai doan AB, ve phia B (vi q,, q2 trai dau; q, > q 2 ) • CA'"a73" 3 EB- = ED- , , Taco: E ( , = E | + E 2 . D e E^-^O => E, = - E 2 , suy ra: = B'0 = D'0; costti = cosa2 = B (3) 1 fllH I 'i v a A C - B C = AB = lOOcm (4) => AC = 150cm va BC = 50cm V§y; Khiq,=-36.10-^C;q2 = 4.10-'^C, de' £ ^ - 0 thi AC = 150cm va BC = 50cm. 37 Cty TNHH MTV D W H Khann Vi$t B6i du3ng hqc sinh gidi vat ly 11, t?p 1 - NguySn Phu D6n9 B a i giai 2.15. Cho hai dien tich q,, q2 dat tai A va B, A B = 2cm. B i e t q, + q2 = 7.10^^C va Cdc lyc tdc dung len hon b i : d i e m C each qi 6cm, each qa 8cm c6 ciTdng do dien triTcJng E = 0. T i m qi, q2:f. ;.; B a i giai , + Trong li/c P = mg (hi/dng xuo'ng). .* Ta c6: + A B + BC = A C => C nam ngoai doan A B nen qi va q2 trai dau. = Ej + + Li/c dien tru-dng: F = qE (hiTdng xuong neu q > 0; hiTdng len neu q < 0). = 0 => E, = E2 <=> Ic BC^ 8^ H6nbinimcanbang(lc(lijrng)khi: AC^ BC' E = mg-DVg 36 ~ 9 16 q2 = - - q , B E Viq<0 va q, + q2 = 7.1 O^^C =^ q, =-9.10"^C va q2 = 16.1 Q-^C. V a y : Gia trj cac dien tich q,, q2 la q, = -9.10^^C va 4,1.10' Hai qud cau nho A va B mang nhiJng dien tich Ian lUdt N B a i giai - a" 2 = V2k => k dai bang nhau. Hai d i e m treo day M v^ N cdch nhau 2cm; de du'a cde day treo trd ve vj tri thang dufng ngu'di ta phai * dung mot dien tru'dng deu c6 hufdng n i o va do Idn bao B nhieu? B a i giai a' - De E D = 0 thi phai dat tai B dien tich q ' sao cho E2 = E ^ . ' => k BD' 2.10^'C va 2 . 1 0 ' C diTdc treo d dau hai sdi day t d each dien khi can bang, vj t r i cac day treo c6 dang nhi/ hinh ve. H o i gay ra tai D la: E j j = Ej + E 3 . V i q, = q3 = q; A D = C D = a nen E.j = 2EiCOs45°. S ^ Vay: D i e n tich cua bi de no can bhng Id lufng trong dau la q = -2.10"'C. = 16.10"*C. dat d B dien tich bao nhieu de curing do dien tru'dng d D bkng khong? q • ^ nen q = - 2 . 1 0 ' C . 2.16 Cho hinh vuong A B C D , tai A va C dat cac dien tich q, = qj = q. H o i phai = ^ E n = 2k ' , ^ m g - D ^ g = 9.10"^ 10-800.10'*'. 10 ^ 2 10'^C (1) Cu'dng do dien tru'dng do qi, P+ F^+F =0 O F + F = 6 V I P > FA nen P ' = P - FA => F phai hu'dng len => q < 0 va F = P - FA. 64^_I6 AC^ - 1 + Lire day A c - s i - m e t F ^ - - D V g (hiTdng len) + B C > AC Vi , can phai tac dung liTc dien tru'dng ngUdc E„ ^ = V2k De diTa cac day treo trd ve vj tri thang dilng chieu vdi liTc tmh dien va ciing do Idn vdi lire tinh dien: F ' = F . = V2k =>q'=-2^q. V a y : Phai dat d B dien tich q ' = , ,5; „2 - E,3 . -l4lq V d i qua cau A : Gid s i q > 0 de cu'dng do dien triTcJng 3 D bang khong. 2.17. M o t hon bi nho bang kirn loai dU'cIc dat trong dau. Bi c6 the tich V = 10mm\ khoi lU'cfng m = 9.10"'kg. Dau c6 khoi liTcfng rieng D = 800kg/m\t ca difdc dat E = kAB' iJi;bl!!i .,0, 2.10-^ = > E = k= 4,5.10" V/m. = k• = 9.10^. AB' MN' (2.10"^)^ VI q, < 0 nen E ngiTdc chieu v d i F nghla la cilng chieu v d i F (hirdng tuf ^ a i sang phai). V d i qua cdu B: TiTdng tir. ^ \ trong mot dien tru'dng deu, E hudng thang duTng tif tren xuong, E = 4,1.10^V/ni- ^%r. De dira cac day treo trd ve vi tri th^ng diJng can phai dung mot dien trirdng deu c6 hiTdng tCr trai sang phai va cd do Idn E = 4,5.10" V/m. T i m dien tich cua bi de no can bang Id lijfng trong dau. Cho g = lOm/s^. 39 Cty TNHH MTV DWH Khang Vi$t Bfli duang hoc sinh gi6i Vjtt 1^ 11, tjp 1 - Nguygn Phu B6ng Cl/dNG D O D I E N TRl/OfNG D O V ^ T MANG D I E N CO KICK THl/OfC TAORA 2.19. Mot ban phang rat Idn dat thang dilng, tich dien deu vdi mat dp dien mat a, a) Xac djnh E do mat phang gay ra tai diem each mat phang doan h. Neu dac diem cua dien truTdng nay. ^ b) Mot qua cau nho kho'i lUdng m dien tich q cung dau vdi mat phang, diTcfc treo vao mot diem co djnh gan mat phang bang day nhe khong dan, chieu dai /. Coi q khong anh hu'dng den sif phan bo' dien tich tren mat phang va khi can , bang day treo nghieng goc a vdi phu'dng thang di^ng. Tinh q. Bai giai a) Cu'dng do dien tru'dng do ban phang gay ra * Chon mat Gauss la hinh tru c6 dudng sinh vuong g6c vdti day, hai day hinh tron CO dien tich S va each deu ban phang doan h. - Dien thong qua mat Gauss: N = Nj + N2. + Phan dien thong qua mat ben: N| = ZEiAScosai = 0 (vl cosai = 0). + Phan dien thong qua hai day: N2 = SEiAScosa2 = 2ES. => N = 2ES 3. -I, Theo djnh li Ostrogradski - Gaus: N = 2ES = — laAS = ^0 a.2S + < E= 28„ Vay: Cu'dng do dien tru'dng do mat phang gay ra tai diem each mat ph^ng doan h: + la dien triTctng deu, c6 hu'dng vuong goc • + J • E + khong phu thuoc vao khoang each ttr diem ta xet den ban ph^ng. b) Tinh dien tich q - Cac life tac dung len q: trong life P, liTc dien tru'dng F, liTc cang day f . 2mgeo ^'i^^ -1 = E2 <— + + - Vdi hai mat phang: E = Ej+E2 + Ben trong hai mat phang: E, va E2 cung chieu nen E = E, + E , = 2- g _ g ; g., 2e 0 ~ e"0 + Ben ngoai hai mat phang: E, va E, ngUdc chieu nen a = 0. 2e. b) Tru'dng hdp hai mat phang hdp vdi nhau goc a Vi El = E2 nen: + Ben trong hai mat phang: „-„.a - CT . a a . a E = 2Eism — = 2 . sm — = — .sm — . . a a a 2 28o 2 So 2 .cos— = — cos—. 2 So 2 + Ben ngoai hai mat phang: E = 2E1COS— = 2 — E = E, - E, = • mg 2mgSQ.tana Vay: Dp Idn cua dien tich q la 2 20. Tinh ciTdng dp dien tru'dng gay bdi 2 mat phang rpng v6 han: a) Dat song song, mat dp dien mat a > 0 va -a. b) Hdp vdi nhau goc a va c6 ciing mat dp dien matCT> 0. Bai giai ' Si'H'a) Tri^ng hdp hai mat phang dat song song • Vdi mot mat phang: Chpn mat Gauss la hinh tru c6 dtfdng sinh vuong goc vdi ddy, hai day hinh tron c6 dien tich S va each deu ban phang doan h. + Dien thong qua mat Gauss: N = ZEiAScosa2 < ,• + = 2EiS. + Theo dinh li Ostrogradski - Gaus: + N=-Iqi h => 2E,S = — l a A S = — CT.2S 28, h vdi vdi ban phang, c6 do Idn E = - Tam giac liTc cho: tana = — = 2mg£o.tana Vdi q > 0 41