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Potentially useful equations Electric Charge and Electric Field : 𝐹 = 𝑘 !!!!
!! 𝐸 = !
!! 𝐸 = 𝑘 !
!!
Electric Potential: 𝑉! =!"!! ∆𝑃𝐸 = 𝑞𝑉!" 𝑉 = 𝑘 !
! 𝐸 = − ∆!
∆!
Capacitance: 𝑄 = 𝐶𝑉 𝐶 = 𝐾𝜖!!! 𝑃𝐸 = !
!𝐶𝑉! !"!"#$%&
= !!𝜖!𝐸
!
Electric Currents: 𝐼 = !!!! 𝑉 = 𝐼𝑅 𝑅 = !"
! 𝑃 = 𝐼𝑉 𝑃 = 𝐼!𝑅 = !!
! 𝐼 = 𝐼! sin 𝜔𝑡
𝐼!"# =!!! 𝑉!"# =
!!!
Electric Circuits: 𝑅!" = 𝑅! + 𝑅! +⋯ !!!"
= !!!+ !
!!+⋯
𝐶!" = 𝐶! + 𝐶! +⋯ !!!"
= !!!+ !
!!+⋯ 𝜏 = 𝑅𝐶
KVL: current into any point = 0 KVL: voltage around any closed loop =0 Magnetic Fields and Forces: F = IlBsinθ F = qvBsinθ B = !!!
!!" 𝐵 = !!!"
!
𝐵∥ Δ𝑙 = 𝜇!𝐼!"#$ 𝜏 = 𝑁𝐼𝐴𝐵 sin 𝜃 Electromagnetic Induction and Faraday’s Law: 𝜙! = 𝐵𝐴 cos 𝜃 𝜀 = −𝑁 !!!
!!
𝜀 = 𝐵𝑙𝑣 𝜀 = 𝑁𝐵𝜔 Asin𝜔𝑡 !!!!= !!
!!= !!
!!
Electromagnetic Waves: 𝐼! = 𝜖!!!!!!
𝑐 = !!!!!
𝑐 = 𝜆𝑓
Light/Geometric Optics: 𝑛 = !! 𝑓 = !
! !
!!+ !
!!= !
! 𝑚 = !!
!!= − !!
!!
𝑛! sin 𝜃! = 𝑛! 𝑠𝑖𝑛𝜃! sin 𝜃! =!!!! 𝑃 = !
!
The Wave Nature of Light: λn =λn sin 𝜃 = 𝑚 𝜆
𝑑 sin 𝜃 = 𝑚 + 1
2𝜆𝑑 sin 𝜃 = 𝜆
𝐷
𝐼 = 𝐼!𝑐𝑜𝑠!𝜃 𝑡𝑎𝑛𝜃! = 𝑛 Optical Instruments: 𝑓 − 𝑠𝑡𝑜𝑝 = !
! 𝑀 = !
!𝑀 = !
!+ 1 𝑀 = − !!
!! 𝑀 ≅ !"
!!!! 𝜃 = !.!!!
!
mλ = 2dsinφ
Relativity: Δ𝑡 = Δ𝑡0
1−𝑣2
𝑐2
= 𝛾Δ𝑡0 L = 𝐿0 1 − 𝑣2𝑐2 =
𝐿0
𝛾 𝛾 =
1
1−𝑣2
𝑐2
𝑝 = 𝛾𝑚𝑜𝑣 =𝑚0𝑣
1−𝑣2
𝑐2
𝑚 = 𝛾𝑚! =!!
!!!! !! 𝐸! = 𝑚!𝑐! 𝐾𝐸 =
!!!!
!!!! !!−𝑚!𝑐! = 𝛾 − 1 𝑚!𝑐! 𝐸 = 𝐾𝐸 +𝑚!𝑐! 𝐸! = 𝑝𝑐 ! + (𝑚!𝑐!)!
Early Quantum Theory: E = nhf E = hf p = !!= !!
!= !
! 𝜆 = !
! 𝐿 = !!
!! 𝐸! = −13.6𝑒𝑉 !!
!!
𝑟! = (5.29𝑥10!!!𝑚)𝑛!
𝑍
Quantum Mechanics: Δ𝑝! Δ𝑥 ≥ ℏ (Δ𝐸)(Δ𝑡) ≥ ℏ Nuclear Physics/Radioactivity: X r ∝ 𝐴
!!!
! 1u =1.660566x10-27 kg =931.5 MeV/c2 Δ𝑁 = −𝜆𝑁Δ𝑡 𝑁 = 𝑁!𝑒!!"
!!!!= (!!
!!)!𝑒!!" 𝑇!
!= !.!"#
!
Nuclear Reactions: a + X → Y + b Q = 𝑀! +𝑀! −𝑀! −𝑀! 𝑐! = 𝐾𝐸! +𝐾𝐸! − 𝐾𝐸! − 𝐾𝐸! 𝑟𝑒𝑚 = 𝑟𝑎𝑑 𝑋 𝑄𝐹
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