Tiêu đề 2. P2C2.-Static-Electricity For FRB_2024_With Solve_Ridoy 15.04.25.pdf ✅

w ̄’i Zwor  Final Revision Batch 1 wØZxq Aa ̈vq w ̄’i Zwor Electrostatics Topicwise CQ Trend Analysis UwcK 2016 2017 2018 2019 2022 2022 2023 2024 †gvU Kzj¤^ m~Î I †ÿÎ Ñ Ñ Ñ Ñ 1 Ñ 3 Ñ 4 we›`y Pv‡R©i Zwor ej 1 3 Ñ 1 1 Ñ Ñ Ñ 6 Zwor †ÿÎ cÖvej ̈ 3 3 1 2 3 6 4 2 24 Zwor wefe 2 2 1 4 4 7 8 4 32 avi‡Ki aviYv, aviKZ¡, †kÖwY I mgvšÍivj ms‡hvM, Zzj ̈ aviKZ¡, kw3 I e ̈envi 3 3 Ñ 3 7 5 9 5 35 * we.`a.: 2020 mv‡j GBPGmwm cixÿv AbywôZ nqwb, 2021 mv‡j kU© wm‡jev‡m Aa ̈vqwU AšÍfz©3 wQjbv| weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ GKwU mgvšÍvij cvZ avi‡Ki cvZ؇qi ga ̈eZx© `~iZ¡ 4 cm Ges GwU evqy Øviv c~Y©| aviKwU‡Z 9.6 c PvR© cÖ`vb Kivq cvZØq‡i g‡a ̈ 200 N/C Zwor cÖe‡j ̈i m„wó nq| cieZx©‡Z aviKwUi cvZ؇qi ga ̈eZx© ̄’v‡b K = 1.5 gv‡bi civ‣e`y ̈wZK gva ̈g Øviv c~Y© Kiv n‡jv| [e. †ev. 24] (K) GbUawc Kx? (L) iæ×Zvcxq cÖmvi‡Y wm‡÷g kxZj nq e ̈vL ̈v Ki| (M) cÖ_g †ÿ‡Î aviKwUi aviKZ¡ wbY©q Ki| mgvavb: Avgiv Rvwb, Zwor wefe, V = Ed  V = 200  0.04  V = 8 V aviKZ¡, C = Q V  C = 9.6 C 8V  C = 1.21 F myZivs, cÖ_g †ÿ‡Î aviKwUi aviKZ¡ 1.2 F (Ans.) (N) wØZxq †ÿ‡Î avKwUi mwÂZ kw3i cwieZ©b MvwYwZKfv‡e we‡kølY Ki| mgvavb: ÔMÕ n‡Z cvB, cÖ_g †ÿ‡Î, avi‡Ki aviKZ¡, C1 = 1.2 F avi‡Ki wefe, V1 = 8V  avi‡K mwÂZ kw3, U1 = 1 2 C1V 2 1 = 1 2  1.2  10–6  8 2 = 3.84  10–5 J wØZxq †ÿ‡Î, avi‡Ki aviKZ¡, C2 = KC1  C2 = 1.5  1.2 F  C2 = 1.8 F awi, Dfq †ÿ‡Î eZ©bxi wefe GKB _vK‡e,  V2 = V1 = 8V avi‡K mwÂZ kw3, U2 = 1 2 C2V 2 2 = 1 2  1.8  10–6  8 2 = 5.76  10–5 J  kw3i cwieZ©b = U2 – U1 = 5.76  10–5 – 3.84  10–5 = 1.92  10–5 J myZivs, wØZxq †ÿ‡Î aviKwUi mwÂZ kw3 1.92  10–5 J e„w× cv‡e| (Ans.) 1| wP‡Î evqy gva ̈‡g eM©‡ÿ‡Îi A, B I C we›`y‡Z h_vμ‡g q1 = 2  10–9 C, q2 = 3  10–9 C I q3 = – 4  10–9 C PvR© Av‡Q| eM©‡ÿ‡Îi| cÖwZwU evûi •`N ̈© 1m. [P. †ev. 24] 1m A B 1m D 1m 1m C +C +1C p q1 = 2  10–9C q3 = 4  10–9C (K) aviK Kx? (L) Pv‡R©i ZjgvwÎK NbZ¡ Zwor cÖve‡j ̈i0 ̧YÑ e ̈vL ̈v Ki| (M) eM©‡ÿ‡Îi †K›`a P †Z Zwor cÖvej ̈ wbY©q Ki| mgvavb: A B D C P E1 E3 E2 Enet 90 q2 = 3nC q3 = – 4nC q1 = 2nC wP‡Î, AP = BP = CP = 2 2 = 1 2 m
2  HSC Physics 2nd Paper Chapter-2 P we›`y‡Z 2 nC Pv‡R©i Rb ̈ Zwor cÖvej ̈, E1 = K  q1 AP2  E1 = 9  109  2  10–9     1 2 2 = 36 NC–1 (AC eivei) P we›`y‡Z – 4 nC Pv‡R©i Rb ̈ Zwor cÖvej ̈, E3 = K  q3 CP2 E3 = 9  109  4  10–9     1 2 2 = 72 NC–1 (PC eivei)  AC eivei wbU Zwor cÖvej ̈, E4 = E1 + E3 = 108 NC–1 (AC eivei) P we›`y‡Z 3 nC Pv‡R©i Rb ̈ Zwor cÖvej ̈, E2 = K  q2 BP2 E3 = 9  109  3  10–9     1 2 2 = 54 NC–1 (BD eivei)  E2 I E4 Gi jwä, Enet = E 2 2 + E 2 4 + 2E2E4 cos (90) = 542 + 1082 = 54 5 NC–1 Avevi, tan = E2 sin90 E4 + E2 cos90 = 54 108   = 26.56 (E4 Gi mv‡_) E2 E4  Enet myZivs, eM©‡ÿ‡Îi †K›`a P †Z Zwor cÖvej ̈ 54 5 NC–1 hv PC Gi mv‡_ 26.56 †KvY Drcbœ K‡i| (Ans.) (N) †h †Kv‡bv PvR©‡K D we›`y n‡Z P we›`y‡Z Avb‡Z KvR m¤úvw`Z n‡e wKÑbvÑMvwYwZKfv‡e we‡kølY Ki| mgvavb: P we›`y‡Z †gvU Zwor wefe, VP = 1 40     q1 AP + q2 BP + q3 CP = 1 40        2  10–9 1 2 + 3  10–9 1 2 + – 4  10–9 1 2  VP = 12.728 V Avevi, D we›`y‡Z †gvU Zwor wefe, VD = 1 40     q1 AD + q2 BD + q3 CD = 9  109      2  10–9 1 + 3  10–9 2 + – 4  10–9 1 = 1.091 V  q Avavb‡K D we›`y n‡Z P we›`y‡Z Avb‡Z K...ZKvR, W = q V = q (VP – VD) = q (12.728 – 1.091) = 11.637q J  †h‡Kv‡bv PvR©‡K D we›`y n‡Z P we›`y‡Z Avb‡Z KvR m¤úvw`Z n‡e| (Ans.) 2| [Kz. †ev. 24] B A + 1.5  10–3 C C – 2.5  10–3 D C 1.5 m 1.5 m 2 m 2 m Dc‡ii wPÎvbyhvqx evqy gva ̈‡g Aew ̄’Z ABCD AvqZ‡ÿ‡Îi A I C we›`y‡Z h_vμ‡g + 1.5  10–3 C Ges – 2.5  10–3 C PvR© ̄’vcb Kiv n‡jv| [є0 = 8.854  10–12C –2N –1m –2 ] (K)we›`y PvR© Kv‡K e‡j? (L) †Kv‡bv gva ̈‡gi civ‣e`y ̈wZK aaæeK 2.5 ej‡Z Kx eyS? e ̈vL ̈v Ki| (M) B we›`y‡Z Zwor cÖvej ̈ wbY©q Ki| mgvavb: q1 = 1.5  10–3C A D q2 = – 2.5  10–3C C B E1  E2 Enet 2m 1.5m 1.5m 2m A we›`yi q1 Pv‡R©i Rb ̈ B we›`y‡Z Zwor cÖvej ̈, E1 = 1 40 q1 r 2 1 = 9  109  1.5  10–3 (2) 2 = 3.375  106 NC–1 (AB eivei) C we›`yi q2 Pv‡R©i Rb ̈ B we›`y‡Z Zwor cÖvej ̈, E2 = 1 40 q2 r 2 2 = 9  109  2.5  10–3 (1.5) 2 = 1  107 NC–1 (BC eivei)  E = E 2 1 + E 2 2 + 2 E1E2cos90 = (3.375  106 ) 2 + (1  107 ) 2  B we›`y‡Z Zwor cÖvej ̈ 1.06  107 NC–1 (Ans.) (N) hw` B I D we›`y‡K GKwU avZe Zvi Øviv hy3 Kiv nq Z‡e abvZ¥K Avavb †Kvb w`K n‡Z cÖevwnZ n‡e? MvwYwZK we‡køl‡Yi gva ̈‡g gZvgZ `vI| mgvavb: A I C we›`yi PvR©Ø‡qi Rb ̈ B we›`y‡Z Zwor wefe, VB = VA + VC = 1 40  qA rAB + 1 40  qC rBC = 9  109     1.5  10–3 2 + – 2.5  10–3 1.5 = – 8.25  106 V Abyiƒcfv‡e, A I C we›`yi PvR©Ø‡qi Rb ̈ D we›`y‡Z Zwor wefe, VD = VA + VC = 1 40  qA rAD + 1 40  qC rCD = 9  109     1.5  10–3 1.5 + – 2.5  10–3 2 = – 2.25  106 V A_©vr, VD > VB abvZ¥K Avavb D”P wefe †_‡K wb¤œ wef‡ei w`‡K PjvPj K‡i| AZGe, B I D we›`y‡Z avZe Zvi Øviv mshy3 Ki‡j abvZ¥K Avavb D †_‡K B Gi w`‡K cÖevwnZ n‡e| (Ans.)
w ̄’i Zwor  Final Revision Batch 3 3| 2cm 150 V wPÎ Abyhvqx MwVZ avi‡K mwÂZ kw3 cvIqv †Mj 9.96  10–9 J| aviKZ¡ e„w×i †K.kj ̄^iƒc 2 mm cyiæ‡Z¡i Ges 4 civ‣e`y ̈wZK aaæeKm¤úbœ GKwU e ̄‘ cvZ؇qi gv‡S ̄’vcb Kiv n‡jv| [Xv. †ev. 24] (K) MvDwmqvb Zj Kx? (L) ÒPvwR©Z †Mvj‡Ki †K‡›`a cÖvej ̈ k~b ̈ÓÑ e ̈vL ̈v Ki| (M) avi‡Ki cv‡Zi †ÿÎdj wbY©q K‡iv| mgvavb: Avgiv Rvwb, avi‡Ki mwÂZ kw3, U = 1 2 CV2  U = 1 2  0KA d  V 2  A = 2dU 0KV2  A = 2  0.02  9.96  10–9 8.854  10–12  1  1502  A = 2  10–3 m 2 myZivs, avi‡Ki cv‡Zi †ÿÎdj 2  10–3 m 2 | (Ans.) (N) aviKZ¡ e„w×i †K.kj mwVK n‡qwQj wKbv? MvwYwZK we‡køl‡Yi gva ̈‡g gZvgZ `vI| mgvavb: ÔMÕ n‡Z cvB, avi‡Ki cv‡Zi †ÿÎdj, A = 2  10–3 m 2  cÖ_g †ÿ‡Î avi‡Ki aviKZ¡, C1 = 0kA d  C1 = 8.854  10–12  1  2  10–3 0.02 C1 = 8.854  10–13 F wØZxq †ÿ‡Î, Avgiv Rvwb, †Kv‡bv avi‡Ki cvZ؇qi ga ̈eZx© `~iZ¡ d Ges cv‡Zi †ÿÎdj A n‡j, hw` cvZ؇qi gv‡S t cyiæZ¡ I K civ‣e`y ̈wZK aaæeK wewkó gva ̈g cÖ‡ek Kiv‡bv nq Z‡e aviKZ¡, C2 = 0kA d – t    1 –  1 ke = 8.854  10–12  2  10–3 0.02 – 0.002 + 0.002 4  C2 = 9.57  10–13 F  C2 > C1 myZivs, aviKZ¡ e„w×i †K.kj mwVK n‡qwQj| (Ans.) 4| P(1 kg) Q(1.5  10–9 C) 90 2 2 m 2 2 m R(1.5  10–9 C) wP‡Î PQR GKwU mg‡KvYx mgwØevû wÎfzR| wPÎvbymv‡i P we›`y‡Z ̄’vwcZ e ̄‘wU fvimvg ̈fv‡e Sz‡j _vK‡e wKbv Zv cixÿv Kiv nw”Qj| [Xv. †ev. 24] (K) mv›U Kx? (L) Kvk©‡di cÖ_g m~Î Pv‡R©i msiÿY bxwZ †g‡b P‡jÑ e ̈vL ̈v K‡iv| (M) DÏxc‡Ki P we›`y‡Z wef‡ei gvb KZ? mgvavb: P we›`y‡Z Q I R we›`y‡Z Aew ̄’Z Pv‡R©i `iæb VP = V1 + V2 Zwor wefe, VP = 1 40      q1 r1 + q2 r2 = 9  109     1.5  10–9 2 2 + 1.5  10–9 2 2 = 9.546 V myZivs, P we›`y‡Z wef‡ei gvb 9.546 V (Ans.) (N) DÏxc‡Ki P we›`y‡Z ̄’vwcZ e ̄‘wU‡K k~‡b ̈ Szwj‡q ivLv hv‡e wKbv? MvwYwZKfv‡e hvPvB Ki| mgvavb: Q q1 = 1.5 nC R q2 = 1.5 nC P F2 F1 1 kg r = 2 2 m r = 2 2 m Fnet W = mg awi, P we›`y‡Z ̄’vwcZ e ̄‘wUi PvR© q  Q we›`y‡Z Aew ̄’Z PvR© KZ...©K P we›`y‡Z cÖhy3 ej, F1 = 1 40  qq1 r 2 = 9  109  1.5  10–9 q (2 2) 2 = 1.6875q N R we›`y‡Z Aew ̄’Z Pv‡R©i Rb ̈ P we›`y‡Z ej, F2 = 1 40  qq1 r 2 = 9  109  1.5  10–9 q (2 2) 2 = 1.6875 q N F1 I F2 e‡ji ga ̈eZx© †KvY 90  Fnet = F 2 1 + F 2 2 = 2 F1  Fnet = 2  1.6875 q N P we›`y‡Z ̄’vwcZ e ̄‘wU‡K k~‡b ̈ Szwj‡q ivL‡Z, Fnet = mg  2  1.6875 q = 1  9.8  q = 4.106 C myZivs, P we›`y‡Z ̄’vwcZ e ̄‘wU‡K k~‡b ̈ Szwj‡q ivL‡Z 4.106 C Avavb cÖ`vb Ki‡Z n‡e| (Ans.)
4  HSC Physics 2nd Paper Chapter-2 5| wPÎwU jÿ ̈ Ki: [w`. †ev. 24] A B 0.4 m C –2c 0.4 m +6c [C we›`y‡Z 2 kg f‡ii GKwU e ̄‘ Ges 0.2C PvR© ̄’vcb Kiv nj|] (K) Kvj `xN©vqb Kx? (L) †ZRw ̄¿qZv ̄^Ztd‚Z© wbDK¬xq NUbvÑ e ̈vL ̈v Ki| (M) C we›`y‡Z (PvR© ̄’vc‡bi c~‡e©) Zwor wefe wbY©q Ki| mgvavb: wP‡Î, AC = AB2 + BC2  AC = 0.42 + 0.42 = 0.565 m  C we›`y‡Z Zwor wefe, VC = 1 40     qA AC + qB BC = 9  109     6  10–6 0.565 + – 2  10–6 0.4 = 50575.22 V myZivs C we›`y‡Z PvR© ̄’vc‡bi c~‡e© Zwor wefe 50575.22 V| (Ans.) (N) 'C' we›`y‡Z PvwR©Z e ̄‘wU w ̄’i _vK‡e wK bvÑ MvwYwZKfv‡e we‡køY Ki| mgvavb:    mg 0.2 C –2 C B + 6 C A 0.4m 0.4m C F2  F1 wPÎ n‡Z, F1 = 9  109  2  10–6  0.2 0.42 = 22500 N (CB eivei)  CB eivei wbU ej, F3 = F1 – mg  F3 = 22500 – 2  9.8 = 22480.4 N Avevi, F3  90 F F2  6 C PvR© Øviv cÖhy3 ej, F2 = 9  109  6  10–6  0.2 0.5652 = 33831.937 N  F2 I F3 Gi ga ̈eZx© jwä ej, F= F 2 2 + F 2 3 + 2F2 .F3 cos  = (33831.937) 2 + (22480.6) 2 + 2 33831.937 22480.6 cos135 = 23966.220 N GLv‡b, tan = BC AB = 0.4 0.4   = 45 Avevi,  = 90+ 45 = 135 tan = F2 sin135 F3 + F2cos 135  tan = 33831.936 sin 135 22480.6 + 33831.937  cos 135   = – 86.55 A_© ̈vr A I B Pv‡R©i `iæY, C we›`y‡Z e ̄‘wUi Dci GKwU jwä ej wμqv K‡i| hvi d‡j e ̄‘wU w ̄’i _vK‡e bv| (Ans.) 6| cixÿvMv‡i †`Lv hvq, GKwU mgvšÍivj cvZ avi‡Ki cÖ‡Z ̈KwU cv‡Zi †ÿÎdj 1.55 m2 | cvZ؇qi ga ̈eZ©x `~iZ¡ 2 cm Ges Zv evZvm Øviv c~Y© Av‡Q| cvZ؇qi wefe cv_©K ̈ 50 V| cvZ؇qi g‡a ̈ WvBB‡jKwUaK aaæeKwewkó c`v_© Øviv c~Y© Ki‡j mwÂZ kw3i cwieZ©b nq| G‡ÿ‡Î 0 = 8.854  10–12C 2N –1m –2 | [h. †ev. 24] (K) Zwo”PvjK ej Kv‡K e‡j? (L) mvwK©‡U mv›U e ̈envi Kiv nq †Kb? e ̈vL ̈v Ki| (M) DÏxcK Abymv‡i aviKwUi aviKZ¡ wbY©q K‡iv| mgvavb: Avgiv Rvwb, aviKwUi aviKZ¡, C = 0kA d  C = 8.854  10–12  1  1.55 0.02  C = 6.86  10–10 F (Ans.) (N) aviKwU WvBB‡jKwUaK c`v_© Øviv c~Y© Ki‡j mwÂZ kw3i †h cwieZ©b nq Zv MvwYwZKfv‡e we‡kølY Ki| mgvavb: ÕMÕ n‡Z cvB, evqyc~Y© Ae ̄’vq avi‡Ki aviKZ¡, C1 = 6.86  10–10 F  mwÂZ kw3, U1 = 1 2 C1V 2  U1 = 1 2  6.86  10–10  502  U1 = 8.575  10–7 J WvBB‡jKwUaK c`v_© Øviv c~Y© Kivi ci, avi‡Ki aviKZ¡, C2 = KC1 = 2.5  6.86  10–10 = 17.15  10–10 F  mwÂZ kw3, U2 = 1 2 C2V 2  U2 = 1 2  17.15  10–10  502  U2 = 2.143  10–6 J  mwÂZ kw3 e„w× cv‡e, U = U2 – U1 = 2.143  10–6 – 8.575  10–7 = 1.2855  10–6 J myZivs, aviKwU WvBB‡jKwUaK c`v_© Øviv c~Y© Ki‡j mwÂZ kw3 1.2855  10–6 J e„w× cv‡e| (Ans.)