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Potentially useful equations Electric Charge and Electric Field : = ! ! ! ! ! ! = ! ! ! = ! ! ! Electric Potential: ! = !" ! ! βˆ† = !" = ! ! = βˆ’ βˆ†! βˆ†! Capacitance: = = ! ! ! = ! ! ! !" !"#$%& = ! ! ! ! Electric Currents: = !! !! = = !" ! = = ! = ! ! ! = ! sin !"# = ! ! ! !"# = ! ! ! Electric Circuits: !" = ! + ! + β‹― ! ! !" = ! ! ! + ! ! ! + β‹― !" = ! + ! + β‹― ! ! !" = ! ! ! + ! ! ! + β‹― = KVL: current into any point = 0 KVL: voltage around any closed loop =0 Magnetic Fields and Forces: F = IlBsinΞΈ F = qvBsinΞΈ B = ! ! ! !!" = ! ! !" ! βˆ₯ Ξ” = ! !"#$ = sin Electromagnetic Induction and Faraday’s Law: ! = cos = βˆ’ !! ! !! = = Asin ! ! ! ! = ! ! ! ! = ! ! ! ! Electromagnetic Waves: ! = ! !! ! !! = ! ! ! ! ! = Light/Geometric Optics: = ! ! = ! ! ! ! ! + ! ! ! = ! ! = ! ! ! ! = βˆ’ ! ! ! ! ! sin ! = ! ! sin ! = ! ! ! ! = ! ! The Wave Nature of Light: Ξ» n = Ξ» n sin = sin = + 1 2 sin = = ! ! ! = Optical Instruments: βˆ’ = ! ! = ! ! = ! ! + 1 = βˆ’ ! ! ! ! β‰… !" ! ! ! ! = !.!!! ! mΞ» = 2dsinΟ† Relativity: Ξ” = Ξ” 0 1βˆ’ 2 2 = Ξ” 0 L = 0 1 βˆ’ 2 2 = 0 = 1 1βˆ’ 2 2 = = 0 1βˆ’ 2 2 = ! = ! ! !! ! ! ! ! ! = ! ! = ! ! ! ! !! ! ! ! ! βˆ’ ! ! = βˆ’ 1 ! ! = + ! ! ! = ! + ( ! ! ) ! Early Quantum Theory: E = nhf E = hf p = ! ! = !! ! = ! ! = ! ! = !! !! ! = βˆ’13.6 ! ! ! ! ! = (5.2910 !!! ) ! Quantum Mechanics: Ξ” ! Ξ” β‰₯ ℏ (Ξ”)(Ξ”) β‰₯ ℏ Nuclear Physics/Radioactivity: X r ∝ ! ! ! ! 1u =1.660566x10 -27 kg =931.5 MeV/c 2 Ξ” = βˆ’Ξ” = ! !!" !! !! = ( !! !! ) ! !!" ! ! = !.!"# ! Nuclear Reactions: a + X β†’ Y + b Q = ! + ! βˆ’ ! βˆ’ ! ! = ! + ! βˆ’ ! βˆ’ ! = 4:10- page 1 of 7 4:10- page 7 of 7 Equation Sheet

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Page 1: Equation Sheet - PhysicsΒ Β· Potentially useful equations Electric Charge and Electric Field !:!=!!!! Electric Potential:!!!! Capacitance:!!=!"!!!!=!" Electric Currents:!=!!!sin!"

Potentially useful equations Electric Charge and Electric Field : 𝐹 = π‘˜ !!!!

!!          πΈ = !

!!    πΈ = π‘˜ !

!!      

Electric Potential:    π‘‰! =!"!!      βˆ†π‘ƒπΈ = π‘žπ‘‰!"    π‘‰ = π‘˜ !

!          πΈ = βˆ’ βˆ†!

βˆ†!

Capacitance:  π‘„ = 𝐢𝑉      πΆ = πΎπœ–!!!    π‘ƒπΈ = !

!𝐢𝑉!   !"!"#$%&

= !!πœ–!𝐸

!

Electric Currents: 𝐼 = !!!!      π‘‰ = 𝐼𝑅    π‘… = !"

!  π‘ƒ = 𝐼𝑉          π‘ƒ = 𝐼!𝑅 = !!

!        πΌ = 𝐼! sin πœ”π‘‘

     πΌ!"# =!!!    π‘‰!"# =

!!!

Electric Circuits: 𝑅!" = 𝑅! + 𝑅! +β‹―    !!!"

= !!!+ !

!!+β‹―    

𝐢!" = 𝐢! + 𝐢! +β‹―    !!!"

= !!!+ !

!!+β‹―    πœ = 𝑅𝐢

KVL: current into any point = 0 KVL: voltage around any closed loop =0 Magnetic Fields and Forces:  F = IlBsinΞΈ    F = qvBsinΞΈ    B = !!!

!!"  π΅ = !!!"

!          

𝐡βˆ₯ Δ𝑙 = πœ‡!𝐼!"#$    πœ = 𝑁𝐼𝐴𝐡 sin πœƒ Electromagnetic Induction and Faraday’s Law: πœ™! = 𝐡𝐴 cos πœƒ        πœ€ = βˆ’π‘ !!!

!!  

 πœ€ = 𝐡𝑙𝑣                      πœ€ = π‘π΅πœ” Asinπœ”π‘‘                 !!!!= !!

!!= !!

!!

Electromagnetic Waves: 𝐼! = πœ–!!!!!!

         π‘ = !!!!!

         π‘ = πœ†π‘“

Light/Geometric Optics:  π‘› = !!        π‘“ = !

!           !

!!+ !

!!= !  

!        π‘š = !!

!!= βˆ’ !!

!!

𝑛! sin πœƒ! = 𝑛!  π‘ π‘–π‘›πœƒ!  sin πœƒ! =!!!!    π‘ƒ = !

!

The Wave Nature of Light:          Ξ»n =Ξ»n      sin πœƒ = π‘š πœ†

𝑑      sin πœƒ = π‘š + 1

2πœ†π‘‘        sin πœƒ = πœ†

𝐷    

𝐼 = 𝐼!π‘π‘œπ‘ !πœƒ    π‘‘π‘Žπ‘›πœƒ! = 𝑛       Optical Instruments: 𝑓 βˆ’ π‘ π‘‘π‘œπ‘ = !

!  π‘€ = !

!𝑀 = !

!+ 1    π‘€ = βˆ’ !!

!!      π‘€ β‰… !"

!!!!        πœƒ = !.!!!

!      

 mΞ» = 2dsinΟ†  

Relativity:  Ξ”𝑑 = Δ𝑑0

1βˆ’π‘£2

𝑐2

= 𝛾Δ𝑑0      L = 𝐿0 1 βˆ’ 𝑣2𝑐2 =

𝐿0

𝛾        π›Ύ =

1

1βˆ’π‘£2

𝑐2

   π‘ = π›Ύπ‘šπ‘œπ‘£ =π‘š0𝑣

1βˆ’π‘£2

𝑐2

 

 π‘š = π›Ύπ‘š! =!!

!!!! !!    πΈ! = π‘š!𝑐!      πΎπΈ =

!!!!

!!!! !!βˆ’π‘š!𝑐! = 𝛾 βˆ’ 1 π‘š!𝑐!      πΈ = 𝐾𝐸 +π‘š!𝑐!      πΈ! = 𝑝𝑐 ! + (π‘š!𝑐!)!

Early Quantum Theory: E = nhf      E = hf      p = !!= !!

!= !

!    πœ† = !

!    πΏ = !!

!!    πΈ! = βˆ’13.6𝑒𝑉 !!

!!

π‘Ÿ! = (5.29π‘₯10!!!π‘š)𝑛!

𝑍

Quantum Mechanics: Δ𝑝! Ξ”π‘₯ β‰₯ ℏ      (Δ𝐸)(Δ𝑑) β‰₯ ℏ Nuclear Physics/Radioactivity:       X        r ∝ 𝐴

!!!

! 1u =1.660566x10-27 kg =931.5 MeV/c2 Δ𝑁 = βˆ’πœ†π‘Ξ”π‘‘    π‘ = 𝑁!𝑒!!"    

!!!!= (!!

!!)!𝑒!!"    π‘‡!

!= !.!"#

!

Nuclear Reactions:  a + X β†’ Y + b      Q = 𝑀! +𝑀! βˆ’π‘€! βˆ’π‘€! 𝑐! = 𝐾𝐸! +𝐾𝐸! βˆ’ 𝐾𝐸! βˆ’ 𝐾𝐸!          π‘Ÿπ‘’π‘š = π‘Ÿπ‘Žπ‘‘  π‘‹  π‘„𝐹

4:10- page 1 of 7

4:10- page 7 of 7

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