Eletromagnetismo_EE Formulário 2019/2020
DF-UM (TLA) 1/2
Constantes: 𝜺𝟎= 𝟖, 𝟖𝟓×𝟏𝟎−𝟏𝟐 𝑭/𝒎 ; 𝝁𝟎=𝟒𝝅×𝟏𝟎−𝟕 𝑻. 𝒎/𝑨 ; 𝒆 = 𝟏,𝟔 ×𝟏𝟎−𝟏𝟗 𝑪
𝒎𝒆−= 𝟗, 𝟏𝟏×𝟏𝟎−𝟑𝟏 𝒌𝒈 ; 𝒎𝒑+= 𝟏, 𝟔𝟕×𝟏𝟎−𝟐𝟕 𝒌𝒈 ; 𝟏 𝒆𝑽 = 𝟏, 𝟔× 𝟏𝟎−𝟏𝟗 𝑱
𝐹
= 1
4𝜋𝜀0 |𝑞1||𝑞2|
𝑟2𝑟 𝐹
= 𝑞𝑜 𝐸
𝑑𝐸
= 1
4𝜋𝜀0 𝑑𝑞𝑐𝑟𝑖𝑎𝑑
𝑟2 𝑟
𝐸
=∫𝑑𝐸
𝑡𝑜𝑑𝑎 𝑞 𝑐𝑟𝑖𝑎𝑑
𝑝 = 𝑞𝑑 𝑢
−+ ; |𝐸
| = 1
2𝜋𝜀0 𝑝
𝑧3 (𝑧 ≫ 𝑑)
∮ 𝐸
∙𝑑𝐴
∀sup𝑓𝑒𝑐ℎ𝑎𝑑𝑎 =𝑞𝑐𝑟𝑖𝑎𝑑 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟
𝜀0
𝑊 = ∫𝐹
∙𝑑𝑠
𝑓
𝑖= −∆𝑈 ; 𝑊
𝑞𝑜=∫𝐸
∙𝑑𝑠
𝑓
𝑖= −∆𝑈
𝑞𝑜= −∆𝑉 ; 𝑈 = 𝑞𝑜 𝑉
𝐸
= −𝑔𝑟𝑎𝑑 𝑉 ; 𝐸
= − (𝜕𝑉
𝜕𝑥 𝑖 + 𝜕𝑉
𝜕𝑦 𝑗 + 𝜕𝑉
𝜕𝑧 𝑘
)
𝑉 = 1
4𝜋𝜀0 𝑞
𝑟 /// |∆𝑉|=𝐸𝑑
𝐶 = |𝑄|
∆𝑉 ; 𝜀 = 𝜅𝜀0 ; 𝑈 = 𝑞2
2𝐶 =1
2𝐶𝑉2 /// 𝐶 = 𝜀0𝐴
𝑑 |𝐸
|= 𝜎
𝜀0
𝐶𝑒𝑞 =∑𝐶𝑗
𝑛
𝑗=1 1
𝐶𝑒𝑞 =∑1
𝐶𝑗
𝑛
𝑗=1
∆𝑉 = ℰ(1 −𝑒−𝑡 𝜏
⁄) ; 𝑄 = 𝐶ℰ(1 −𝑒−𝑡 𝜏
⁄) ; 𝐼 = 𝑑𝑞
𝑑𝑡 = (ℰ
𝑅)𝑒−𝑡 𝜏
⁄ ; 𝑄′ = 𝑄0(𝑒−𝑡 𝜏
⁄) ; 𝜏 = 𝑅𝐶
I = dq
dt ; 𝑃 = 𝐼𝑉 ; ℰ = 𝑑𝑊
𝑑𝑞
𝑅 = 𝑉
𝐼 /// 𝑅 = 𝜌𝐿
𝐴 ; 𝜌− 𝜌0= 𝜌0𝛼(𝑇− 𝑇0)
𝑅𝑒𝑞 =∑𝑅𝑗
𝑛
𝑗=1 ; 1
𝑅𝑒𝑞 =∑1
𝑅𝑗
𝑛
𝑗=1
