Quiz 2 Equation sheet – Sp26 Physics 1251H
𝑒 = 1.602 × 10−19𝐶
𝑄 = 𝐶(∆𝜙)
𝑚𝑒 = 9.109 × 10−31𝑘𝑔
𝐶 = 0𝑑
𝜀 𝐴
𝐶2
𝜀0 = 8.854 × 10−12 𝑁𝑚2
1
𝑈 = 2 𝐶(Δ𝜙)2
1
𝑁𝑚2
= 8.99 × 109 2
4𝜋𝜀0
𝐶
|𝐹⃗12 | = |
1
𝑢𝐸 = 𝜀0 |𝐸⃗⃗|
2
1 𝑞1 𝑞2
|
4𝜋𝜀0 |𝑟⃗12|2
𝐹⃗𝑒 = 𝑞𝐸⃗⃗
𝑁
𝐸⃗⃗ =
1
𝑄𝑖
∑
𝑟̂
|𝑟⃗𝑃𝑖 |2 𝑃𝑖
4𝜋𝜀0
0
∑
𝑎𝑙𝑙 𝑝𝑎𝑖𝑟𝑠 𝑖,𝑗
𝑁
1
𝑄𝑖
𝜙=
∑
|𝑟⃗𝑃𝑖 |
4𝜋𝜀0
𝑖=1
𝜙=
1
𝑑𝑄
∫
4𝜋𝜀0 |𝑟⃗𝑃𝑆 |
𝑟⃗⃗′
Δ𝑉𝑒 = 𝑞Δ𝜙
⃗⃗𝜙
𝐸⃗⃗ = −∇
Δ𝜙 = − ∫ 𝐸⃗⃗ ∙ 𝑑𝑟⃗
Δ𝜙 = −𝐸⃗⃗ ∙ Δ𝑟⃗
𝑛𝑒 2 𝜏
𝐴⃗ = 𝐴𝑛̂ ,
𝑒
= ∫ 𝐽⃗ ∙ 𝑑𝐴⃗
1
1
1
1
𝑒𝑞
1
2
3
𝑄
1
a
𝛥𝜙 = 𝜙𝑎 − 𝜙𝑏 = 𝐶
𝑟̂
| 𝑃𝑁
⃗⃗ =
Outside spherical shell: 𝐸
𝑉𝑒 =
𝜎𝑐 = 𝑚
𝐸⃗⃗
Parallel: 𝑅 = 𝑅 + 𝑅 + 𝑅 + ⋯
⃗⃗ = 𝜎 𝑟̂𝑃𝑁
Infinite sheet: 𝐸
2𝜀
1 𝑞𝑖 𝑞𝑗
4𝜋𝜀0 𝑟𝑖𝑗
𝐽⃗ = 𝜎𝑐 𝐸⃗⃗ ,
𝑚𝑒
Series: 𝑅𝑒𝑞 = 𝑅1 + 𝑅2 + 𝑅3 + ⋯
𝑟⃗⃗ ′
2𝜋𝜀0 |𝑟⃗𝑃𝑁
𝑣⃗𝑑 =
𝛥𝜙 = 𝜙𝑎 − 𝜙𝑏 = 𝑅
1
𝑑𝑄
𝐸⃗⃗ =
∫
𝑟̂
4𝜋𝜀0 |𝑟⃗𝑃𝑆 |2 𝑃𝑆
𝜆
(−𝑒)𝜏
𝐽⃗ = 𝑛𝑞𝑣⃗𝑑 = 𝑛(−𝑒)𝑣⃗𝑑 ,
= 𝐽⃗ ∙ 𝐴⃗ ,
𝑖=1
⃗⃗ =
Infinite line: 𝐸
2
𝑄
4𝜋𝜀0 |𝑟⃗𝑃𝐶
𝑟̂
|2 𝑃𝐶
𝑃 = 𝛥𝜙 = 2 𝑅 =
(𝛥𝜙)2
𝑅
Charging capacitor: (𝑡) = 𝑜 𝑒 −𝑡/𝑅𝐶
𝑄(𝑡) = 𝑄𝑓 (1 − 𝑒 −𝑡/𝑅𝐶 )
Discharging capacitor
𝑄(𝑡) = 𝑄𝑜 𝑒 −𝑡/𝑅𝐶 , (𝑡) = 𝑜 𝑒 −𝑡/𝑅𝐶
Quiz 2 Equation sheet – Sp26 Physics 1251H
𝐴𝑦 𝐵𝑧 − 𝐴𝑧 𝐵𝑦
⃗⃗ = [ 𝐴𝑧 𝐵𝑥 − 𝐴𝑥 𝐵𝑧 ]
𝐴⃗ × 𝐵
𝐴𝑥 𝐵𝑦 − 𝐴𝑦 𝐵𝑥
𝑖̂
= 𝑑𝑒𝑡 |𝐴𝑥
𝐵𝑥
𝑗̂
𝐴𝑦
𝐵𝑦
⃗⃗
𝐹⃗𝑚 = 𝑞 𝑣⃗ × 𝐵
⃗⃗
𝐹⃗𝑚 = 𝐿 ⃗ × 𝐵
⃗⃗||𝑣⃗|
Motional emf: 𝜀 = ∆𝜙 = 𝐿|𝐵
𝑚𝑣
Cyclotron 𝑟 =
𝑞𝐵
Cyclotron 𝑓 =
𝑞𝐵
2𝜋𝑚
𝜇0 = 4𝜋 × 10−7
⃗⃗ =
𝐵
⃗⃗ =
𝐵
𝑇𝑚
𝐴
𝜇0 𝑞
(𝑣⃗ × 𝑟̂𝑃𝑆 )
4𝜋 |𝑟⃗𝑃𝑆 |2
𝜇0
𝑑𝐿
∑
( ⃗ × 𝑟̂𝑃𝑖 )
|𝑟⃗𝑃𝑖 |2
4𝜋
𝑖
⃗⃗ =
𝐵
𝜇0
𝑑𝑙 ′
∫
( ⃗ × 𝑟̂𝑃𝑆 ),
4𝜋 |𝑟⃗𝑃𝑆 |2
𝑟⃗′
𝑟⃗𝑃𝑆 = 𝑟⃗𝑃 − 𝑟⃗𝑆 = 𝑟⃗ − 𝑟⃗ ′
⃗⃗| =
Infinite wire: |𝐵
𝜇0 𝐼
2𝜋𝑟
⃗⃗| =
Center of loop: |𝐵
⃗⃗| =
Solenoid: |𝐵
𝜇0 𝐼
2𝑅
𝜇0 𝐼𝑁
𝐿
𝜇⃗ = 𝐴⃗
⃗⃗
𝜏⃗ = 𝜇⃗ × 𝐵
⃗⃗
𝑉𝑚 = − 𝜇⃗ ∙ 𝐵
𝑘̂
𝐴𝑧 |
𝐵𝑧