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PHY122 - Possibly Useful Equations & Laws ∆𝑥 𝑣 = ∆𝑡 𝑣𝑖 + 𝑣𝑓 𝑣 = 2 ∆𝑣 𝑎 = ∆𝑡 1 ∆𝑥 = 𝑣𝑖 𝑡 + 𝑎𝑡 2 2

𝑣𝑓2 = 𝑣𝑖2 + 2𝑎∆𝑥 𝑣𝑖2 sin 2𝜃 𝑅= 𝑔

Σ𝑭 = 𝑭𝑛𝑒𝑡 = 𝑚𝒂 𝑓𝑘 = 𝜇𝑘 𝑁 𝑓𝑠 ≤ 𝜇𝑠 𝑁

𝐺𝑃𝐸 = 𝑚𝑔ℎ 1

𝐸𝑃𝐸 = 𝑘𝑥 2 2 𝐹𝑒 =

𝑘𝑞1 𝑞2

= 𝑞𝐸

𝑅2 (point charge)

𝑘=

1 4𝜋𝜖0

𝑘𝑞 𝑅2 (point charge) 2𝑘𝜆 𝑄 (𝜆 = ) 𝐸= 𝐿 𝑅 (uniform line of charge) 𝑄 𝐸= 𝜖 𝐴 0 (two parallel plates) 𝑞 𝑉 = 𝑘Σi 𝑅𝑖

𝐸=

𝑖

(point charges) 𝑘𝑞1 𝑞2

𝑈=

𝑅 (point charges)

𝜖0 A 𝑑

𝐶=

(two parallel plates)

1 𝑈 = 𝑄𝑉 2 1 𝑈 = 𝐶𝑉 2 2

𝐼𝑟𝑚𝑠 = 𝑉𝑟𝑚𝑠 = 𝑉2

𝑃 = 𝐼𝑉 = 𝐼 2 𝑅 =

𝑅

𝐹𝐵 = 𝑞𝑣𝐵 sin 𝜃 𝐹𝐵 = 𝐵𝐼𝐿 sin 𝜃 𝐵𝑤𝑖𝑟𝑒 =

𝐵𝑠𝑜𝑙 = 𝐵𝑐𝑜𝑖𝑙 =

𝜇0 𝐼 2𝜋𝑅

𝜇0 𝑁𝐼 𝐿

𝜇0 𝐼 2𝑅

𝑓𝑠𝑚𝑎𝑥 = 𝜇𝑠 𝑁

𝑊 = 𝑞∆𝑉

𝜙𝑚𝑎𝑔 = 𝐵𝐴𝑐𝑜𝑠𝜃

𝐺𝑚1 𝑚2 𝑅2

𝑉 = 𝐸𝑑

𝜀 = 𝐵𝐿𝑣

𝐹𝑔 =

𝐹𝑔 = 𝑤 = 𝑚𝑔 𝑚𝑣 2 Σ𝐹𝑛𝑒𝑡 = 𝐹𝑐 = 𝑅 𝑣2 𝑎𝑐 = 𝑅 2𝜋𝑅 𝑣 = 𝑇

𝑄 = 𝐶𝑉 𝑅= 𝐼=

𝜌𝐿 𝐴

∆𝑞 ∆𝑡

𝑉 = 𝐼𝑅

𝜀 = |−

Δ𝜙𝑚𝑎𝑔 | Δ𝑡

𝜏 = 𝑅𝐶

−𝑡

𝑄 = 𝐶𝑉0 (1 − 𝑒 𝑅𝐶) −𝑡

𝑉 = 𝑉0 (1 − 𝑒 𝑅𝐶 ) 𝑉0 −𝑡 (𝑒𝑅𝐶 ) 𝑅

𝑊 = 𝐹∆𝑥 cos 𝜃 = ∆𝐾𝐸

𝑅𝑠 = ∑ 𝑅𝑖

𝑊 𝑃= = 𝐹𝑣 ∆𝑡

𝐼=

1 1 = ∑ 𝑅𝑃 𝑅𝑖

𝑉 = 𝑉0 (𝑒 𝑅𝐶 )

𝐸𝑛𝑒𝑟𝑔𝑦 = 𝑃∆𝑡 𝐾𝐸 =

1 𝑚𝑣 2 2

𝑖

𝑖

−𝑡

1 1 = ∑ 𝐶𝑠 𝐶𝑖

𝑄 = 𝐶𝑉0 (𝑒 𝑅𝐶 )

𝐶𝑝 = ∑ 𝐶𝑝

𝜔 = 2𝜋𝑓

𝑖

𝑖

𝑓=

−𝑡

1 𝑇 𝐼𝑚𝑎𝑥

√2

𝑉𝑚𝑎𝑥

√2

𝑉 = 𝑉0 (cos 𝜔𝑡) 𝑃𝑟𝑚𝑠 = 𝐼𝑟𝑚𝑠 𝑉𝑟𝑚𝑠 2 𝑃𝑟𝑚𝑠 = 𝐼𝑟𝑚𝑠 𝑅 =

𝑉𝑃

𝑉𝑆

=

𝑁𝑃

𝑁𝑆

,

𝑋𝐶 =

𝐼𝑆 𝐼𝑃

2

𝑉𝑟𝑚𝑠

=

1 𝜔𝐶

𝑅

𝑁𝑃

𝑁𝑆

Δ𝐼

𝜀𝐿 = 𝐿

Δ𝑡

𝑋𝐿 = 𝐿𝜔 1 𝑓𝑟𝑒𝑠 = 2𝜋√𝐿𝐶

𝑍 = √𝑅 2 + (𝑋𝐿 − 𝑋𝐶 )2 𝑣 = 𝑓𝜆 󰇍 𝑥𝑩 󰇍󰇍 = 𝑺󰇍󰇍 𝑬 𝜃𝑖 = 𝜃𝑅 𝑛=

𝑐

𝑣

𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 𝑛1 𝜆1 = 𝑛2 𝜆2 sin 𝜃𝑐 =

𝑛𝑙𝑜𝑤

𝑛ℎ𝑖𝑔ℎ...