Physics II Formulas Sheet - PHY201 Exam Prep

Physics II, PHY201 Formulas sheet 𝑚𝑒 = 9.11 10−31 𝑘𝑔 𝑘 = 9 109 Midterm/Final Exams 𝑒 = 1.6 10−19 𝐶 𝑁.𝑚2 𝑚𝑝 = 1.67 10−27 𝑘𝑔 𝐶2 𝑚 𝑜 = 8.85 10−12 𝑁𝑚2 𝐶2 𝑁𝐴 = 6.02 1023 𝑚𝑜𝑙 −1 𝑜 = 4  10−7 𝑔 = 9.81 2 𝑠 𝑇.𝑚 1 𝑒𝑉 = 1.6 10−19 𝐽 𝐴 4 𝐶𝑖𝑟𝑐𝑙𝑒: 𝑐 = 2𝑟, 𝐴 = 𝑟 2 𝑆𝑝ℎ𝑒𝑟𝑒: 𝐴 = 4𝑟 2 , 𝑉 = 𝜋𝑟 3 3 𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟: 𝐴𝑙𝑎𝑡𝑒𝑟𝑎𝑙 = 2𝑟ℎ , 𝑉 = 𝑟 2 ℎ 𝑣2 𝑜 sin (2𝜃𝑜 ) 𝑅𝑎𝑛𝑔𝑒 = 𝑊𝑛𝑒𝑡 = Δ𝐾 𝐸𝑤𝑖𝑟𝑒 = 𝑞 𝑞 𝐸=𝑘 2 𝑟 𝜆 2𝜋𝜀 0 𝑅 𝑉 = 𝑘∫ 𝑟 𝐸𝑥 = − 𝐶= 𝑞 𝑉 𝐶𝑒𝑞 = 𝐶1 + 𝐶2 + 𝐶3 𝑚𝑣 2 𝑑𝑞 𝑟 𝜕𝑉 𝜕𝑥 𝐶= 𝐾𝜀𝑜 𝐴 𝑑 𝑟 𝑑𝑞 𝐸 = ∫𝑘 2 𝑟 𝐸𝑟𝑖𝑛𝑔 = 𝑘 ( 2 𝑄𝑥 3 𝑥 +𝑎2 ) ⁄2 𝑞𝑒𝑛𝑐 𝜀𝑜 𝐾 = 𝑚𝑣 2 2 Δ𝑈 = 𝑞Δ𝑉 𝐹⃗ = 𝑞𝐸⃗⃗ 𝐸𝑑𝑖𝑠𝑐 = 𝜎 2𝜀 0 [1 − 𝑥 √𝑥2 +𝑅 2 Φ = 𝐸𝐴𝑐𝑜𝑠𝜃 𝑏 ∆𝑉 = − ∫𝑎 𝐸⃗⃗ ⋅ 𝑑𝑟⃗ 𝜕𝑉 𝜕𝑦 𝑞1 𝑞2 𝑈=𝑘 𝑟 1 Δ𝐾 = − Δ𝑈 𝐾𝑖 + 𝑈𝑖 = 𝐾𝑓 + 𝑈𝑓 ⃗⃗⃗ = Φ𝑛𝑒𝑡 = ∮ ⃗⃗⃗ 𝑬 ∙ 𝑑𝑨 𝑉=𝑘 2 𝑊 = − Δ𝑈 𝑟 2𝜀 0 1 ∆𝑥 = 𝑣𝑜 𝑡 + 𝑎𝑡2 𝐹𝑐 = 𝑞 𝑞 𝜎 2𝑔 𝑓𝑟 = 𝜇𝑁 𝐹 = 𝑘 12 2 𝐸𝑝𝑙𝑎𝑛𝑒 = 𝑔 𝑣 2 − 𝑣𝑜2 = 2𝑎∆𝑥 𝑣 = 𝑣𝑜 + 𝑎𝑡 𝐹𝑛𝑒𝑡 = 𝑚𝑎 𝑣2 sin2 𝜃0 𝐻𝑚𝑎𝑥 = 𝑜 Δ𝑉 = −𝐸𝑑 ∆𝑉 = 𝜕𝑉 𝜕𝑧 𝐸𝑦 = − 𝐸𝑧 = − 𝐶 = 𝐾𝐶𝑜 (𝐾 = 1 for vacuum, air) 𝑞2 1 2 1 𝑈= = 𝐶𝑉 = 𝑞𝑉 2𝐶 2 2 1 1 1 1 𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = + + 𝐶𝑒𝑞 𝐶1 𝐶2 𝐶3 𝑆𝑒𝑟𝑖𝑒𝑠 ∆𝑈 𝑞𝑜 ] 𝐼= 𝑞 𝑡 𝐼 𝐴 𝑅=𝜌 𝜌 = 𝜌𝑜 [1 + 𝛼 (𝑇 − 𝑇𝑜 )] 𝐽 = 𝑛𝑞𝑣𝑑 𝐼= 𝑉 𝑅= 𝑑𝑞 𝑑𝑡 𝐽= 𝑉 = 𝐼𝑅 𝐼 𝑙 𝐴 1 𝜌 𝐸 = 𝜌. 𝐽 𝑛= 𝑁𝑣 𝑁𝐴 𝜌𝐷 𝑀 𝑉2 𝑃 = 𝐼2 𝑅 𝑃= 1 1 1 1 = + + 𝑅𝑡 𝑅1 𝑅2 𝑅3 𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑃 = 𝐼𝑉 𝑅𝑡 = 𝑅1 + 𝑅2 + 𝑅3 𝑆𝑒𝑟𝑖𝑒𝑠 𝜎= 𝑅 Charging 𝑡 𝑄(𝑡) = 𝑄𝑚𝑎𝑥 (1 − 𝑒 −𝑅𝐶 ) 𝐼𝑅 = 𝐼𝑚𝑎𝑥 𝑒 𝑡 − 𝑅𝐶 𝐼𝑚𝑎𝑥 = 𝑡 𝑉𝑐 = 𝑉𝑏 (1 − 𝑒 −𝑅𝐶 ) 𝑄𝑚𝑎𝑥 = 𝐶𝑉𝑏 𝑉𝑏 𝑈 = 𝑈𝑚𝑎𝑥 (1 − 𝑒 𝑅 𝑡 − 𝑅𝐶 2 ) 𝜏 = 𝑅𝐶 Discharging 𝑡 𝑡 𝑄(𝑡) = 𝑄𝑜 𝑒−𝑅𝐶 𝑉𝑐 = 𝑉𝑜 𝑒 −𝑅𝐶 𝑡 𝐼 = 𝐼𝑜 𝑒− 𝑅𝐶 ⃗⃗⃗ 𝑭𝑩 = 𝑞𝒗 ⃗⃗ × ⃗⃗⃗ 𝑩 𝐼𝑜 = 𝜔= ⃗⃗⃗ = 𝜇𝑜 𝐼𝑑𝒍⃗×𝒓̂ 𝑑𝑩 2 4𝜋 𝐵= 𝜇𝑜 𝐼 2𝜋𝑟 𝑟 𝑉𝑜 𝑄𝑜 = 𝑅 𝑅𝐶 𝑣 𝑟 𝑟= 𝑇= 1 𝑓 𝑩 ∙ 𝑑𝒍⃗ = 𝜇 𝑜 𝐼𝑒𝑛𝑐𝑙 ∮ ⃗⃗⃗ (long wire) 2𝑡 𝑚𝑣 sin 𝜃 𝑞𝐵 𝑣= 𝑄0 𝐶 𝑈 = 𝑈𝑜 𝑒−𝑅𝐶 ⃗⃗⃗ 𝑭𝑩 = 𝐼𝒍⃗ × ⃗⃗⃗ 𝑩 |𝐹𝐵 | = 𝑞𝑣𝐵 sin 𝜃 ⃗⃗⃗𝑩 = 𝐼𝑑𝒍⃗ × ⃗⃗⃗ 𝑑𝑭 𝑩 𝑉0 = |𝐹𝐵 | = 𝐼𝐿𝐵 sin 𝜃 𝑝 = 𝑣𝑇 cos 𝜃 2𝜋𝑟 𝑇 𝑇= 2𝜋𝑚 𝑞𝐵 𝜇 𝐼 𝐼 |𝐹𝐵 | = 𝑜 1 2 𝑙 (pair of wires) 2𝜋𝑑 𝜇 𝑁𝐼 𝐵𝑠 = 𝜇𝑜 𝑛𝐼 = 0 𝑙 ⃗⃗⃗ ⃗⃗⃗ + 𝒗 𝑭 = 𝑞 (𝑬 ⃗⃗ × ⃗⃗⃗ 𝑩) (solenoid) 𝑛= 𝑁 𝑙

Physics II Formulas Sheet - PHY201 Exam Prep

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