Vector algebra for physics | Study notes Physics

U5UB”0Kb=BK c

PVK +BGV π V/G V/GV αKB’ /V K/K π GVBεK B K w πGK Bα K/B’l

U5UB”=B BVb”WU b1Y =K BVb”bBU”=K=BK c

HBK BK G/ π παBKB’ B/G’K K’KG Bα G’K p  o K yl

–’KG BK KεB/K’ GVBεKαw  BK //K’ GVBεKα Bα K BK GVBεK ’Kl

PVKK BK VKK K π BK BGGα/ε  GαG// Bα K///l

/y QαG pGVBεK GB/K BK +/’K K’KGyl

//y x’B pGVBεK GB/K BK /+/’K K’KGyl

///y ]K/GαG pGVBεK GB/K BK +/’K K’KG o V’Kyl

U5UB”=B BVb”WUK c

x / VK +B/G K π BK αK  V/GV K’KG/G Bα BεK/G KππKG pK’KGBεK/G KππKGy

αGK Bα B BKl

:KKα B   [l

x / B GB’B B/ l

]lxl / v Q’+ pQyl

Qlεll / v –’KGB/G /  ]B Q’+

,QSM,gdE ]B Q’+l

3/εVK /  1BBα Bα 9K /  1KR’/l

α/K/ v j”P…l

PVKK BK  K π GVBεK v k//K GVBεK py Bα FKεB/K pK’KGyl

QVBεK π K’KG Bα  S  S ,l(  ,gd,E Ql

HB π K’KG S El,  ,gdM, Rεl

HB π  S ,l(  ,gd.& Rεl

HB π  / εKBK VK B π K’KG Bα Bε/αK π GVBεK π K’KG Bα  /

BKlsB π  Bα K / BKl

-”0-U”=UK 0’ BVb”WUc

9/RK GVBεK KK’ KBGV VK Bα ’/RK GVBεK BBG KBGV VKl

b  v PB’ GVBεK π B +α / VK B’εK+B/G  π B’’ GVBεK GB/ //αK /l

B   v QVBεK GB K/VK +K GKBKα  +K αKKα / B /’BKα Kw /

GB ’ BπK π K +α  BVK +αl x KB K GVBεK π B +α  K / B’B

GBw VKK / /’’ BπK π K +α  BVKl

Electrostatic

Electric charges and its characteristics

Electric charge

Properties of charge

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U5UB7”0K7b7=BK c

x PVK +UBQGV Rπ SV\V/GV ZV/GV αKB’V Z/WV SURSKUW/KV Rπ GVBUεK BW UKVW w πRUGK BQα SRWKQW/B’l

U5UB7”=B BVb”WU b1Y =7K BVb”bB7U”=K7=BK c

x HBWWKU BUK GRQV/VW Rπ πXQαBPKQWB’ SBUW/G’KV K’KGWURQV BQα QXG’KRQV p SURWRQ o QKXWURQ yl x –’KGWURQV BUK QKεBW/YK’\ GVBUεKαw SURWRQV BUK SRV/W/YK’\ GVBUεKα BQα QKXWURQV BUK GVBUεK ’KVVl x PVKUK BUK WVUKK W\SKV Rπ PBWWKU BGGRUα/Qε WR GRQαXGW/Y/W\ BQα UKV/VW/Y/W\l /y QRQαXGWRU pGVBUεK GBUU/KUV BUK PR+/’K K’KGWURQVyl //y xQVX’BWRU pGVBUεK GBUU/KUV BUK /PPR+/’K K’KGWURQVyl ///y ]KP/GRQαXGWRU pGVBUεK GBUU/KUV BUK PR+/’K K’KGWURQV o VR’KVyl

U5UB7”=B BVb”WUK c

x xW /V WVK +BV/G SURSKUW\ Rπ PBWWKU αXK WR ZV/GV K’KGWU/G BQα PBεQKW/G KππKGWV pK’KGWURPBεQKW/G KππKGWVy SURαXGKV BURXQα B PBWWKUl :KQRWKα BV ³T´ RU ³[´l xW /V B VGB’BU TXBQW/W\ l ]lxl XQ/W v QRX’RP+ pQyl QlεlVl XQ/W v –’KGWURVWBW/G XQ/W ± ]WBW QRX’RP+ ,Q S M [ ,gdE^ ]WBW QRX’RP+l 3/εVKVW XQ/W ± 1BUBα BQα 9RZKVW XQ/W ± 1UKQR’/Ql α/PKQV/RQ v j”P…l

x PVKUK BUK WZR W\SKV Rπ GVBUεKV v kRV/W/YK GVBUεK pSURWRQy BQα FKεBW/YK pK’KGWURQyl QVBUεK Rπ K’KGWURQ BQα SURWRQ S T S ,l( [ ,g d,E^ Ql HBVV Rπ K’KGWURQ S El, [ ,g dM,^ Rεl HBVV Rπ SURWRQ S ,l( [ ,g d.&^ Rεl HBVV Rπ SURWRQ /V εUKBWKU WVKQ PBVV Rπ K’KGWURQ BQα PBεQ/WXαK Rπ GVBUεK Rπ K’KGWURQ BQα SURWRQ /V VBPKlsPBVV Rπ SURWRQ BQα QKXWURQ /V VBPKl

-”0-U”7=UK 0’ BVb”WUc

x 9/RK GVBUεKV UKSK’ KBGV RWVKU BQα XQ’/RK GVBUεKV BWWUBGW KBGV RWVKUl x bGGLWLYH QDWXUH v PRWB’ GVBUεK Rπ B +Rα\ /V WVK B’εK+UB/G VXP Rπ B’’ GVBUεKV GRQWB/Q /QV/αK /Wl

x BRQVHUYDWLRQ RI FKDUJH v QVBUεK GBQ QK/WVKU +K GUKBWKα QRU +K αKVWUR\Kα /Q BQ /VR’BWKα V\VWKPw /W GBQ RQ’\ WUBQVπKU πURP RQK +Rα\ WR BQRWVKU +Rα\l xW PKBQV QKW GVBUεK Rπ B +Rα\ RU V\VWKP /V B’ZB\V GRQVWBQWw VRZKYKU /W Z/’’ WUBQVπKU πURP RQK +Rα\ WR BQRWVKUl

x 2XDQWL]DWLRQ RI FKDUJH v PVK GVBUεK Rπ BQ R+4KGW /V WVK /QWKεUB’ PX’W/S’K Rπ ,l( [ ,g d,E^ pK’KGWURQ/G GVBUεKyl xW PKBQV K’KGWURQV GBQ +K WUBQVπKU /Q /QWKεKUl HBWVKPBW/GB’’\ T S QKw ZVKUK Q S ,w.wM« Q S QR Rπ πUKK K’KGWURQ WUBQVπKUUKαl K S ,l( [ ,gd,E [XBQW/]BW/RQ Rπ GVBUεK /V /εQRUKα RQ B ’BUεK VGB’K +KGBXVK WVK K’KPKQWBU\ GVBUεK /V K[WUKPK’
VPB’’ BQα YKU\ ’BUεK QXP+KU Rπ K’KGWURQV BUK /QYR’YKα BQα αXK WR /W GVBUεK ’RRRV ’/RK GRQW/QXRXVl x BKDUJH LV LQYDULDQW v NQ’/RK PBVVw WVK K’KGWU/G GVBUεK RQ BQ R+4KGW /V QRW BππKGWKα +\ WVK PRW/RQ Rπ GVBUεKl

xU7V0Y 0’ BVb”W=1W c

x ” +Rα\ GBQ +K GVBUεK +\ WUBQVπKUU/Qε WVK K’KGWURQVl x 1HXWUDO ERG\ c 6VKQ B +Rα\ GRQWB/QV VBPK QXP+KU Rπ K’KGWURQV BQα SURWRQV WVKQ /W /V VB/α WR +K QKXWUB’l

x 6VKQ B +Rα\ εB/QV K’KGWURQ /W Z/’’ +KGRPK QKεBW/YK’\ GVBUεKαl x 6VKQ B +Rα\ ’RVKV K’KGWURQ /W Z/’’ +KGRPK SRV/W/YK’\ GVBUεKαl

x HBVV Rπ QKεBW/YK’\ GVBUεKα +Rα\ /V B’ZB\V εUKBWKU WVKQ SRV/W/YK’\ GVBUεKα +Rα\ +KGBXVK QKεBW/YK’
GVBUεKα +Rα\ VBV PRUK GRQVW/WXKQW SBUW/G’KV WVKQ SRV/W/YK +Rα\l

BVb”W=1W y< ’”=B7=01 c

x 6VKQ WZR +Rα/KV BUK UX++Kα Z/WV KBGV RWVKU K’KGWURQV εKW WUBQVπKU πURP RQK +Rα\ WR BQRWVKUl x %Rα\ ZV/GV K’KGWURQV BUK ’RRVK’\ SBGRKα WUBQVπKU WVK K’KGWURQV BQα εKW SRV/W/YK’\ GVBUεKαl i 6VKQ K+RQ/WK URα /V UX++Kα Z/WV πXU –+RQ/WK URα S dYK 1XU S iYK i 6VKQ ε’BVV URα /V UX++Kα Z/WV V/’R =’BVV URα S iYK ]/’R S dYK

1 S - ^ ͳ^ ʹ ʹ^

w ZVKUK ³-´ /V RQRZQ BV K’KGWURVWBW/G GRQVWBQWl

1 S ͳ Ͷʌİ (^) Ͳ

(^) ͳ (^) ʹ ʹ

x |B’XK Rπ ͳ

Ͷʌİ (^) Ͳ

S E [ ,gE^ FP.^ t Q.

W”b-VKc

-U”x=77=9=7< c

x PVK SURSKUW/KV Rπ B PKα/XP ZV/GV RSSRVKV WVK πRUGK +KWZKKQ GVBUεKV V GB’’Kα SKUP/WW/Y/W\l x NQ/W v Q.^ t FP. x :/PKQV/RQ S jH d,^9 dMPu” .…

x |B’XK Rπ ઽ ૙ Q sdsu [ vtFve

x PVKUK BUK WVUKK W\SKV Rπ SKUP/WW/Y/W
x kKUP/WW/Y/W\ Rπ πUKK VSBGK x kKUP/WW/Y/W\ Rπ PKα/XP

”U5b7=9U -U”x=77=9=7< c

x PVK UBW/R Rπ SKUP/WW/Y/W\ Rπ PKα/XP WR WVK SKUP/WW/Y/W\ Rπ πUKK VSBGK /V GB’’Kα UK’BW/YK SKUP/WW/Y/W\l x xW /V BQ XQ/W ’KVV BV ZK’’ BV α/PKQV/RQ’KVV TXBQW/W\l

Vector algebra for physics, Study notes of Physics

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U5UB7”0K7b7=BK c

U5UB7”=B BVb”WU b1Y =7K BVb”bB7U”=K7=BK c

U5UB7”=B BVb”WUK c

-”0-U”7=UK 0’ BVb”WUc

xU7V0Y 0’ BVb”W=1W c

BVb”W=1W y< ’”=B7=01 c

w ZVKUK ³-´ /V RQRZQ BV K’KGWURVWBW/G GRQVWBQWl

x |B’XK Rπ ͳ

S E [ ,gE^ FP.^ t Q.

W”b-VKc

-U”x=77=9=7< c

x |B’XK Rπ ઽ ૙ Q sdsu [ vtFve

”U5b7=9U -U”x=77=9=7< c

x AKSUKVKQW BV ³ ઽ ܚ ´ RU ³. ´

x ઽ ܚ Q

U’’UB7 0’ xUY=8x c

x 6VKQ PKα/XP /V /QWURαXGKα +KWZKKQ WZR GVBUεKV πRUGK /Q PKα/XP /V UKαXGKα +\ ³-´

W/PKVl

x 1 PKα S 1 B/U t - w /lK πRUGK /Q B/U /V B’ZB\V εUKBWKU WVKQ πRUGK /Q PKα/XPl

B0850xy¶K 5b: =1 9UB70” ’0”x c