Physics Formula Sheet.pdf

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Physics Formula Sheet Chapter 1: Introduction: The Nature of Science and Physics π‘₯=

βˆ’π‘ Β±

βˆšπ‘ 2

𝑅𝑦 = 𝐴𝑦 + 𝐡𝑦 𝑅 = βˆšπ‘…π‘₯2 + 𝑅𝑦2

βˆ’ 4π‘Žπ‘

2π‘Ž π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ πΈπ‘Žπ‘Ÿπ‘‘β„Ž = 6.38 Γ— 106 π‘š π‘€π‘Žπ‘ π‘  π‘œπ‘“ πΈπ‘Žπ‘Ÿπ‘‘β„Ž = 5.98 Γ— 1024 π‘˜π‘” 𝑐 = 3.00 Γ— 108 π‘š/𝑠 π‘π‘š2 𝐺 = 6.673 Γ— 10βˆ’11 π‘˜π‘”2 𝑁𝐴 = 6.02 Γ— 1023 π‘˜ = 1.38 Γ— 10βˆ’23 𝐽/𝐾 𝐽 𝑅 = 8.31 β„π‘šπ‘œπ‘™ β‹… 𝐾 𝜎 = 5.67 Γ— 10βˆ’8 π‘Š/(π‘š2 β‹… 𝐾) π‘˜ = 8.99 Γ— 109 𝑁 β‹… π‘š2 /𝐢 2 π‘žπ‘’ = βˆ’1.60 Γ— 10βˆ’19 𝐢 πœ–0 = 8.85 Γ— 10βˆ’12 𝐢 2 /(𝑁 β‹… π‘š2 ) πœ‡0 = 4Ο€ Γ— 10βˆ’7 𝑇 β‹… π‘š/𝐴 β„Ž = 6.63 Γ— 10βˆ’34 𝐽 β‹… 𝑠 π‘šπ‘’ = 9.11 Γ— 10βˆ’31 π‘˜π‘” π‘šπ‘ = 1.6726 Γ— 10βˆ’27 π‘˜π‘” π‘šπ‘› = 1.6749 Γ— 10βˆ’27 π‘˜π‘” π‘Žπ‘šπ‘’ = 1.6605 Γ— 10βˆ’27 π‘˜π‘” π‘˜π‘” 𝐷𝑒𝑛𝑠𝑖𝑑𝑦 π‘œπ‘“ π‘€π‘Žπ‘‘π‘’π‘Ÿ = 1000 3 π‘š

Chapter 2: Kinematics π›₯π‘₯ = π‘₯𝑓 βˆ’ π‘₯0 π›₯𝑑 = 𝑑𝑓 βˆ’ 𝑑0 π›₯π‘₯ π‘₯𝑓 βˆ’ π‘₯0 𝑣= = π›₯𝑑 𝑑𝑓 βˆ’ 𝑑0 π›₯𝑣 𝑣𝑓 βˆ’ 𝑣0 π‘Ž= = π›₯𝑑 𝑑𝑓 βˆ’ 𝑑0 π‘₯ = π‘₯0 + 𝑣𝑑 𝑣0 + 𝑣 𝑣= 2 𝑣 = 𝑣0 + π‘Žπ‘‘ 1 π‘₯ = π‘₯0 + 𝑣0 𝑑 + π‘Žπ‘‘ 2 2 𝑣 2 = 𝑣02 + 2π‘Ž(π‘₯ βˆ’ π‘₯0 ) π‘š 𝑔 = 9.80 2 𝑠

Chapter 3: Two-Dimensional Kinematics 𝐴π‘₯ = 𝐴 π‘π‘œπ‘  πœƒ 𝐴𝑦 = 𝐴 𝑠𝑖𝑛 πœƒ 𝑅π‘₯ = 𝐴π‘₯ + 𝐡π‘₯

πœƒ = π‘‘π‘Žπ‘›βˆ’1

𝑅𝑦 𝑅π‘₯

2 𝑣0𝑦 2𝑔 2 𝑣0 𝑠𝑖𝑛 2πœƒ0 𝑅= 𝑔 𝑣π‘₯ = 𝑣 π‘π‘œπ‘  πœƒ 𝑣𝑦 = 𝑣 𝑠𝑖𝑛 πœƒ

β„Ž=

𝑣 = βˆšπ‘£π‘₯2 + 𝑣𝑦2 πœƒ = π‘‘π‘Žπ‘›βˆ’1

𝑣𝑦 𝑣π‘₯

Chapter 4: Dynamics: Forces and Newton’s Laws of Motion 𝐹𝑛𝑒𝑑 = π‘šπ‘Ž 𝑀 = π‘šπ‘”

Chapter 5: Further Applications of Newton’s Laws: Friction, Drag, and Elasticity 𝑓𝑠 ≀ πœ‡π‘  𝑁 π‘“π‘˜ = πœ‡π‘˜ 𝑁 1 𝐹𝐷 = πΆπœŒπ΄π‘£ 2 2 𝐹𝑠 = 6πœ‹πœ‚π‘Ÿπ‘£ 𝐹 = π‘˜π›₯π‘₯ 1𝐹 π›₯𝐿 = 𝐿 π‘Œπ΄ 0 𝐹 π‘ π‘‘π‘Ÿπ‘’π‘ π‘  = 𝐴 π›₯𝐿 π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘› = 𝐿0 π‘ π‘‘π‘Ÿπ‘’π‘ π‘  = π‘Œ Γ— π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘› 1𝐹 π›₯π‘₯ = 𝐿 𝑆𝐴 0 1𝐹 π›₯𝑉 = 𝑉 𝐡𝐴 0

Chapter 6: Uniform Circular Motion and Gravitation π›₯𝑠 π‘Ÿ 2πœ‹ π‘Ÿπ‘Žπ‘‘ = 360Β° = 1 π‘Ÿπ‘’π‘£π‘œπ‘™π‘’π‘‘π‘–π‘œπ‘› π›₯πœƒ πœ”= π›₯𝑑 π›₯πœƒ =

𝑣 = π‘Ÿπœ” 𝑣2 π‘ŽπΆ = π‘Ÿ π‘ŽπΆ = π‘Ÿπœ”2 𝐹𝐢 = π‘šπ‘ŽπΆ π‘šπ‘£ 2 𝐹𝐢 = π‘Ÿ 𝑣2 π‘‘π‘Žπ‘› πœƒ = π‘Ÿπ‘” 𝐹𝐢 = π‘šπ‘Ÿπœ”2 π‘šπ‘€ 𝐹=𝐺 2 π‘Ÿ 𝐺𝑀 𝑔= 2 π‘Ÿ 𝑇12 π‘Ÿ13 = 𝑇22 π‘Ÿ23 4πœ‹ 2 3 𝑇2 = π‘Ÿ 𝐺𝑀 π‘Ÿ3 𝐺 = 𝑀 𝑇 2 4πœ‹ 2

Chapter 7: Work, Energy, and Energy Resources π‘Š = 𝑓𝑑 π‘π‘œπ‘  πœƒ 1 𝐾𝐸 = π‘šπ‘£ 2 2 1 1 π‘Šπ‘›π‘’π‘‘ = π‘šπ‘£π‘“2 βˆ’ π‘šπ‘£02 2 2 𝑃𝐸𝑔 = π‘šπ‘”β„Ž 1 𝑃𝐸𝑠 = π‘˜π‘₯ 2 2 𝐾𝐸0 + 𝑃𝐸0 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 𝐾𝐸0 + 𝑃𝐸0 + π‘Šπ‘›π‘ = 𝐾𝐸𝑓 + 𝑃𝐸𝑓 π‘Šπ‘œπ‘’π‘‘ 𝐸𝑓𝑓 = 𝐸𝑖𝑛 π‘Š 𝑃= 𝑑

Chapter 8: Linear Momentum and Collisions 𝑝 = π‘šπ‘£ π›₯𝑝 = 𝐹𝑛𝑒𝑑 π›₯𝑑 𝑝0 = 𝑝𝑓 π‘š1 𝑣01 + π‘š2 𝑣02 = π‘š1 𝑣𝑓1 + π‘š2 𝑣𝑓2

Please Do Not Write on This Sheet Thin rod about axis through center

1 1 2 2 π‘š1 𝑣01 + π‘š2 𝑣02 2 2 1 2 = π‘š1 𝑣𝑓1 2 1 2 + π‘š2 𝑣𝑓2 2 π‘š1 𝑣1 = π‘š1 𝑣1β€² π‘π‘œπ‘  πœƒ1 + π‘š2 𝑣2β€² π‘π‘œπ‘  πœƒ2 0 = π‘š1 𝑣1β€² 𝑠𝑖𝑛 πœƒ1 + π‘š2 𝑣2β€² 𝑠𝑖𝑛 πœƒ2 1 1 1 π‘šπ‘£12 = π‘šπ‘£1β€²2 + π‘šπ‘£2β€²2 2 2 2 + π‘šπ‘£1β€² 𝑣2β€² π‘π‘œπ‘ (πœƒ1 βˆ’ πœƒ2 ) 𝑣𝑒 π›₯π‘š π‘Ž= βˆ’π‘” π‘š π›₯𝑑 𝑣1 π‘š1 + 𝑣2 π‘š2 π‘£π‘π‘š = π‘š1 + π‘š2

Chapter 9: Statics and Torque

π›₯πœƒ π›₯𝑑 𝑣 = π‘Ÿπœ” π›₯πœ” 𝛼= π›₯𝑑 π›₯𝑣 π‘Žπ‘‘ = π›₯𝑑 π‘Žπ‘‘ = π‘Ÿπ›Ό πœƒ = πœ”π‘‘ πœ” = πœ”0 + 𝛼𝑑 1 πœƒ = πœ”0 𝑑 + 𝛼𝑑 2 2 πœ”2 = πœ”02 + 2π›Όπœƒ πœ”0 + πœ” πœ”= 2 𝑛𝑒𝑑 𝜏 = 𝐼𝛼 Hoop about cylinder axis: 𝐼 = 𝑀𝑅2 πœ”=

Hoop about any diameter: 𝐼 = 𝑀 2

𝑀𝑅 2 2

(𝑅12 + 𝑅22 )

Solid cylinder (or disk) about cylinder axis: 𝐼 =

𝑀𝑅 2 2

Solid cylinder (or disk) about central diameter: 𝐼 =

𝑀𝑅 2 4

+

𝑀ℓ2 12

1 = 𝑃2 + πœŒπ‘£22 2 + πœŒπ‘”β„Ž2

12

βŠ₯ to length: 𝐼 = Solid sphere: 𝐼 =

𝑀ℓ2 3 2𝑀𝑅 2 5

Thin spherical shell: 𝐼 =

2𝑀𝑅 2 3

Slab about βŠ₯ axis through center: 𝐼=

𝑀(π‘Ž2 +𝑏 2 ) 12

𝑛𝑒𝑑 π‘Š = (𝑛𝑒𝑑 𝜏)πœƒ 1 πΎπΈπ‘Ÿπ‘œπ‘‘ = πΌπœ”2 2 𝐿 = πΌπœ” π›₯𝐿 𝑛𝑒𝑑 𝜏 = π›₯𝑑

π‘š 𝑉 𝐹 𝑃= 𝐴 π‘ƒπ‘Žπ‘‘π‘š = 1.01 Γ— 105 π‘ƒπ‘Ž 𝑃 = πœŒπ‘”β„Ž 𝑃2 = 𝑃1 + πœŒπ‘”β„Ž 𝐹1 𝐹2 = 𝐴1 𝐴2 𝐹𝐡 = 𝑀𝑓𝑙 πœŒπ‘œπ‘π‘— πΉπ‘Ÿπ‘Žπ‘π‘‘π‘–π‘œπ‘› π‘ π‘’π‘π‘šπ‘’π‘Ÿπ‘”π‘’π‘‘ = πœŒπ‘“π‘™ 𝜌 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 π‘”π‘Ÿπ‘Žπ‘£π‘–π‘‘π‘¦ = πœŒπ‘€ 𝐹 𝛾= 𝐿 4𝛾 𝑃= π‘Ÿ 2𝛾 π‘π‘œπ‘  πœƒ β„Ž= πœŒπ‘”π‘Ÿ 𝜌=

Chapter 10: Rotational Motion and Angular Momentum

1 𝑃1 + πœŒπ‘£12 + πœŒπ‘”β„Ž1 2

Thin rod about axis through one end

Chapter 11: Fluid Statics

𝜏 = π‘ŸπΉ 𝑠𝑖𝑛 πœƒ π‘ŸβŠ₯ = π‘Ÿ 𝑠𝑖𝑛 πœƒ πΉπ‘œ 𝑙𝑖 𝑀𝐴 = = 𝐹𝑖 π‘™π‘œ 𝑙𝑖 𝐹𝑖 = π‘™π‘œ πΉπ‘œ

Ring: 𝐼 =

βŠ₯ to length: 𝐼 =

𝑀ℓ2

Chapter 12: Fluid Dynamics and Its Biological Medical Applications 𝑉 𝑄= 𝑑 𝑄 = 𝐴𝑣 𝐴1 𝑣1 = 𝐴2 𝑣2 𝑛1 𝐴1 𝑣1 = 𝑛2 𝐴2 𝑣2

1 (Δ𝑃 + Ξ” πœŒπ‘£ 2 + Ξ”πœŒπ‘”β„Ž) 𝑄 = π‘π‘œπ‘€π‘’π‘Ÿ 2 𝑣1 = √2π‘”β„Ž 𝐹𝐿 πœ‚= 𝑣𝐴 𝑃2 βˆ’ 𝑃1 𝑄= 𝑅 8πœ‚π‘™ 𝑅= 4 πœ‹π‘Ÿ (𝑃2 βˆ’ 𝑃1 )πœ‹π‘Ÿ 4 𝑄= 8πœ‚π‘™ 2πœŒπ‘£π‘Ÿ 𝑁𝑅 = πœ‚ πœŒπ‘£πΏ 𝑁𝑅′ = πœ‚ π‘₯π‘Ÿπ‘šπ‘  = √2𝐷𝑑

Chapter 13: Temperature, Kinetic Theory, and the Gas Laws 9 𝑇(°𝐢) + 32 5 𝑇(𝐾) = 𝑇(°𝐢) + 273.15 π›₯𝐿 = 𝛼𝐿π›₯𝑇 π›₯𝐴 = 2𝛼𝐴π›₯𝑇 π›₯𝑉 = 𝛽𝑉π›₯𝑇 𝛽 β‰ˆ 3𝛼 𝑃𝑉 = π‘π‘˜π‘‡ π‘˜ = 1.38 Γ— 10βˆ’23 𝐽/𝐾 𝑁𝐴 = 6.02 Γ— 1023 π‘šπ‘œπ‘™ βˆ’1 𝑃𝑉 = 𝑛𝑅𝑇 𝐽 𝑅 = 8.31 π‘šπ‘œπ‘™ β‹… 𝐾 1 2 𝑃𝑉 = π‘π‘šπ‘£ 3 1 3 2 𝐾𝐸 = π‘šπ‘£ = π‘˜π‘‡ 2 2 𝑇(°𝐹) =

π‘£π‘Ÿπ‘šπ‘  = √

3π‘˜π‘‡ π‘š

% π‘Ÿπ‘’π‘™π‘Žπ‘‘π‘–π‘£π‘’ β„Žπ‘’π‘šπ‘–π‘‘π‘–π‘‘π‘¦ π‘£π‘Žπ‘π‘œπ‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 = π‘ π‘Žπ‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘£π‘Žπ‘π‘œπ‘Ÿ π‘‘π‘’π‘›π‘Žπ‘ π‘–π‘‘π‘¦ Γ— 100%

Chapter 14: Heat and Heat Transfer Methods

1.000 π‘˜π‘π‘Žπ‘™ = 4186 𝐽 𝑄 = π‘šπ‘π›₯𝑇 𝑄 = π‘šπΏπ‘“ 𝑄 = π‘šπΏπ‘£ 𝑄 π‘˜π΄(𝑇2 βˆ’ 𝑇1 ) = 𝑑 𝑑 𝑄 = πœŽπ‘’π΄π‘‡ 4 𝑑 𝐽 𝜎 = 5.67 Γ— 10βˆ’8 𝑠 β‹… π‘š2 β‹… 𝐾 4 𝑄𝑛𝑒𝑑 = πœŽπ‘’π΄(𝑇24 βˆ’ 𝑇14 ) 𝑑

Chapter 15: Thermodynamics 3 π‘ˆ = π‘π‘˜π‘‡ 2 π›₯π‘ˆ = 𝑄 βˆ’ π‘Š π‘Š = 𝑃π›₯𝑉 (π‘–π‘ π‘œπ‘π‘Žπ‘Ÿπ‘–π‘ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ ) Ξ”π‘ˆ = 𝑄 βˆ’ 𝑃Δ𝑉 π‘Š = 0 (π‘–π‘ π‘œπ‘β„Žπ‘œπ‘Ÿπ‘–π‘ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ ) Ξ”π‘ˆ = 𝑄 𝑄 = π‘Š (π‘–π‘ π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ ) Ξ”π‘ˆ = 0 𝑄 = 0 (π‘Žπ‘‘π‘–π‘Žπ‘π‘Žπ‘‘π‘–π‘ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ ) Ξ”π‘ˆ = βˆ’π‘Š π‘Š 𝐸𝑓𝑓 = π‘„β„Ž 𝑄𝑐 (π‘π‘¦π‘π‘™π‘–π‘π‘Žπ‘™ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ ) 𝐸𝑓𝑓 = 1 βˆ’ π‘„β„Ž 𝑇𝑐 𝐸𝑓𝑓𝐢 = 1 βˆ’ π‘‡β„Ž π‘„β„Ž πΆπ‘‚π‘ƒβ„Žπ‘ = π‘Š 𝑄𝑐 πΆπ‘‚π‘ƒπ‘Ÿπ‘’π‘“ = πΆπ‘‚π‘ƒβ„Žπ‘ βˆ’ 1 = π‘Š 𝑄𝑐 ⁄𝑑1 𝐸𝐸𝑅 = π‘„β„Ž ⁄𝑑2 𝑄 π›₯𝑆 = 𝑇 π‘„β„Ž 𝑄𝑐 π›₯π‘†π‘‘π‘œπ‘‘ = + =0 π‘‡β„Ž 𝑇𝑐 π‘Šπ‘’π‘›π‘Žπ‘£π‘Žπ‘–π‘™ = π›₯𝑆 β‹… 𝑇0 𝑆 = π‘˜ 𝑙𝑛 π‘Š π‘˜ = 1.38 Γ— 10βˆ’23 𝐽/𝐾

Chapter 16: Oscillatory Motion and Waves 1 𝑓= 𝑇 πœ† 𝑣 = = π‘“πœ† 𝑇 𝐹 = βˆ’π‘˜π‘₯

Please Do Not Write on This Sheet 1 𝑃𝐸𝑒𝑙 = π‘˜π‘₯ 2 2 π‘š 𝑇 = 2πœ‹βˆš π‘˜

𝑃𝐸 π‘ž π›₯𝑃𝐸 = π‘žπ›₯𝑉 π‘Š = π‘žπ‘‰π΄π΅ 𝑉𝐴𝐡 𝐸= 𝑑 π›₯𝑉 𝐸=βˆ’ π›₯𝑠 π‘˜π‘„ 𝑉= π‘Ÿ 𝑄 𝐢= 𝑉 𝐴 𝐢 = πœ–0 𝑑 𝑉=

1 π‘˜ √ 2πœ‹ π‘š

𝑓=

2πœ‹π‘‘ π‘₯(𝑑) = 𝑋 π‘π‘œπ‘  ( ) 𝑇 2πœ‹π‘‘ 𝑣(𝑑) = βˆ’π‘£π‘šπ‘Žπ‘₯ 𝑠𝑖𝑛 ( ) 𝑇 π‘£π‘šπ‘Žπ‘₯ =

2πœ‹π‘‹ π‘˜ = π‘‹βˆš 𝑇 π‘š

π‘Ž(𝑑) = βˆ’

π‘˜π‘‹ 2πœ‹π‘‘ π‘π‘œπ‘  ( ) π‘š 𝑇

π‘£π‘ π‘‘π‘Ÿπ‘–π‘›π‘”

πœ–0 = 8.85 Γ— 10βˆ’12

𝐹 =√ π‘š/𝐿

π‘š 𝑇 𝑣𝑀 = (331 ) √ 𝑠 273 𝐾 𝑃 𝐼= 𝐴 π΄π‘ π‘β„Žπ‘’π‘Ÿπ‘’ = 4πœ‹π‘Ÿ 2 (π›₯𝑝)2 𝐼= 2πœŒπ‘£π‘€

Chapter 17: Physics of Hearing 𝐼 𝛽 = (10 𝑑𝐡) π‘™π‘œπ‘” ( ) 𝐼0 𝑣𝑀 Β± π‘£π‘œ π‘“π‘œ = 𝑓𝑠 ( ) 𝑣𝑀 βˆ“ 𝑣𝑠 𝑓𝐡 = |𝑓1 βˆ’ 𝑓2 | 𝑣𝑀 𝑓𝑛 = 𝑛 ( ) 2𝐿 𝑣𝑀 𝑓𝑛 = 𝑛 ( ) 4𝐿 𝑍 = πœŒπ‘£ (𝑍2 βˆ’ 𝑍1 )2 π‘Ž= (𝑍1 + 𝑍2 )2

Chapter 18: Electric Charge and Electric Field |π‘žπ‘’ | = 1.60 Γ— 10βˆ’19 𝐢 |π‘ž1 π‘ž2 | 𝐹=π‘˜ π‘Ÿ2 𝐸 = 𝐹/π‘ž |𝑄| 𝐸=π‘˜ 2 π‘Ÿ

Chapter 19: Electric Potential and Electric Energy

𝐹 π‘š

𝐴 𝑑 𝑄𝑉 𝐢𝑉 2 𝑄2 = = = 2 2 2𝐢 𝐢 = πœ…πœ–0

πΈπ‘π‘Žπ‘

Chapter 20: Electric Current, Resistance, and Ohm’s Law π›₯𝑄 π›₯𝑑 𝐼 = π‘›π‘žπ΄π‘£π‘‘ 𝑉 = 𝐼𝑅 𝜌𝐿 𝑅= 𝐴 𝜌 = 𝜌0 (1 + 𝛼π›₯𝑇) 𝑅 = 𝑅0 (1 + 𝛼π›₯𝑇) 𝑉2 𝑃 = 𝐼𝑉 = = 𝐼2 𝑅 𝑅 1 π‘ƒπ‘Žπ‘£π‘’ = 𝐼0 𝑉0 2 𝐼0 πΌπ‘Ÿπ‘šπ‘  = √2 𝑉0 π‘‰π‘Ÿπ‘šπ‘  = √2 𝐼=

Chapter 21: Circuits, Bioelectricity, and DC Instruments 𝑅𝑆 = 𝑅1 + 𝑅2 + 𝑅3 + β‹― 1 1 1 1 = + + +β‹― 𝑅𝑃 𝑅1 𝑅2 𝑅3 𝑉 = π‘’π‘šπ‘“ βˆ’ πΌπ‘Ÿ 𝑑

𝑉 = π‘’π‘šπ‘“ (1 βˆ’ 𝑒 βˆ’π‘…πΆ ) 𝜏 = 𝑅𝐢 𝑑

𝑉 = 𝑉0 𝑒 βˆ’π‘ŸπΆ

Chapter 22: Magnetism 𝐹 = π‘žπ‘£π΅ 𝑠𝑖𝑛 πœƒ π‘šπ‘£ π‘Ÿ= π‘žπ΅ πœ– = 𝐡𝑙𝑣 𝐹 = 𝐼𝐿𝐡 𝑠𝑖𝑛 πœƒ 𝜏 = 𝑁𝐼𝐴𝐡 𝑠𝑖𝑛 πœƒ πœ‡0 𝐼 𝐡= 2πœ‹π‘Ÿ πœ‡0 𝐼 𝐡= 2𝑅 𝐡 = πœ‡0 𝑛𝐼 𝐹 πœ‡0 𝐼1 𝐼2 = 𝑙 2πœ‹π‘Ÿ

Chapter 23: Electromagnetic Induction, AC Circuits, and Electrical Technologies 𝛷 = 𝐡𝐴 π‘π‘œπ‘  πœƒ π›₯𝛷 π‘’π‘šπ‘“ = βˆ’π‘ π›₯𝑑 π‘’π‘šπ‘“ = 𝑣𝐡𝐿 π‘’π‘šπ‘“ = π‘π΄π΅πœ” 𝑠𝑖𝑛 πœ”π‘‘ 𝑉𝑆 𝑁𝑆 𝐼𝑃 = = 𝑉𝑃 𝑁𝑃 𝐼𝑆 π›₯𝐼2 π‘’π‘šπ‘“1 = βˆ’π‘€ π›₯𝑑 π›₯𝐼 π‘’π‘šπ‘“ = βˆ’πΏ π›₯𝑑 π›₯𝛷 𝐿=𝑁 π›₯𝐼 ΞΌ0 𝑁 2 𝐴 𝐿= β„“ 1 2 𝐸𝑖𝑛𝑑 = 𝐿𝐼 2 𝐼 = 𝐼0 (1 βˆ’ 𝜏=

𝑑 𝑒 βˆ’πœ )

𝐿 𝑅

Please Do Not Write on This Sheet 𝑅 π‘π‘œπ‘  πœ™ = 𝑍 π‘ƒπ‘Žπ‘£π‘’ = πΌπ‘Ÿπ‘šπ‘  π‘‰π‘Ÿπ‘šπ‘  π‘π‘œπ‘  πœ™

Chapter 24: Electromagnetic Waves 𝑐=

1 βˆšπœ‡ 0 πœ–0

𝐸 =𝑐 𝐡 𝑐 = π‘“πœ† π‘πœ–0 𝐸02 πΌπ‘Žπ‘£π‘’ = 2 𝑐𝐡02 πΌπ‘Žπ‘£π‘’ = 2πœ‡0 𝐸0 𝐡0 πΌπ‘Žπ‘π‘’ = 2πœ‡0

Chapter 25: Geometric Optics πœƒπ‘– = πœƒπ‘Ÿ 𝑐 𝑛= 𝑣 𝑛1 𝑠𝑖𝑛 πœƒ1 = 𝑛2 𝑠𝑖𝑛 πœƒ2 𝑛2 πœƒπ‘ = π‘ π‘–π‘›βˆ’1 𝑛1 1 𝑃= 𝑓 1 1 1 = + 𝑓 π‘‘π‘œ 𝑑𝑖 β„Žπ‘– 𝑑𝑖 π‘š= =βˆ’ β„Žπ‘œ π‘‘π‘œ 𝑅 𝑓= 2

𝑑

Chapter 28: Special Relativity π›₯𝑑 =

𝛾=

Chapter 27: Wave Optics πœ†π‘› =

πœ† 𝑛

sin πœƒ = π‘š

πœ† 𝑑

2

√1 βˆ’ 𝑣2 𝑐 1 2

√1 βˆ’ 𝑣2 𝑐

𝑣2 𝑐2 𝑣𝐿𝑇 + 𝑣𝑇𝐺 𝑣𝐿𝐺 = 𝑣 𝑣 1 + 𝐿𝑇 2 𝑇𝐺 𝑐 𝑒 1+ 𝑐 πœ†π‘œπ‘π‘  = πœ†π‘  √ 𝑒 1βˆ’ 𝑐 𝑒 𝑐 𝑒 1+ 𝑐 π‘šπ‘£

π‘“π‘œπ‘π‘  = 𝑓𝑠 √ 𝑝=

1 1 + π‘‘π‘œ 𝑑𝑖 π‘š = π‘šπ‘œ π‘šπ‘’ 𝑁𝐴 = 𝑛 𝑠𝑖𝑛 𝛼 𝑓 1 𝑓/# = β‰ˆ 𝐷 2𝑁𝐴 𝑑𝑖 = π‘“π‘œ π‘“π‘œ 𝑀= 𝑓𝑒

π›₯𝑑0

𝐿 = 𝐿0 √1 βˆ’

Chapter 26: Vision and Optical Instruments 𝑃=

𝐼 = 𝐼0 𝑒 βˆ’πœ 𝑉 𝐼= 𝑋𝐿 𝑋𝐿 = 2πœ‹π‘“πΏ 𝑉 𝐼= 𝑋𝐢 1 𝑋𝐢 = 2πœ‹π‘“πΆ 𝑉0 π‘‰π‘Ÿπ‘šπ‘  𝐼0 = π‘œπ‘Ÿ πΌπ‘Ÿπ‘šπ‘  = 𝑍 𝑍 𝑍 = βˆšπ‘…2 + (𝑋𝐿 βˆ’ 𝑋𝐢 )2 1 𝑓0 = 2πœ‹βˆšπΏπΆ

1 πœ† 𝑠𝑖𝑛 πœƒ = (π‘š + ) 2 𝑑 πœ† 𝑠𝑖𝑛 πœƒ = π‘š π‘Š πœ† πœƒ = 1.22 𝐷 πœ†π‘› 2𝑑 = 2 2𝑑 = πœ†π‘› I = Β½ I0 𝐼 = 𝐼0 π‘π‘œπ‘  2 πœƒ 𝑛2 π‘‘π‘Žπ‘› πœƒπ‘ = 𝑛1

𝐸=

1βˆ’

2

√1 βˆ’ 𝑣2 𝑐 2 π‘šπ‘

2

√1 βˆ’ 𝑣2 𝑐 𝐸0 = π‘šπ‘ 2 π‘šπ‘ 2 πΎπΈπ‘Ÿπ‘’π‘™ = βˆ’ π‘šπ‘ 2 2 √1 βˆ’ 𝑣2 𝑐 2 2 𝐸 = (𝑝𝑐) + (π‘šπ‘ 2 )2

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