Qiita Teams that are logged in
You are not logged in to any team

Log in to Qiita Team
Community
OrganizationAdvent CalendarQiitadon (β)
Service
Qiita JobsQiita ZineQiita Blog
1
Help us understand the problem. What is going on with this article?
@campbel2525

電磁気まとめ

More than 1 year has passed since last update.

シリーズ

物理・数学・プログラムのページについて

ローレンツゲージにおけるマクスウェルの方程式

証明はここ

    \boldsymbol{A} = \left(\frac{\phi}{c}, A_x, A_y, A_z \right)        \tag{電磁ポテンシャル}
    \boldsymbol{i} = \left(\rho c, i_x, i_y, i_z \right)        \tag{4元電流密度}
    \Box \boldsymbol{A} = - \mu_0 \boldsymbol{i}        \tag{ローレンツゲージにおけるマクスウェルの方程式}
    \mathbf{div} \boldsymbol{A} + \frac{1}{c^2} \frac{∂ \phi}{∂t} = 0       \tag{ローレンツ条件}

相対論的なマクスウェルの方程式

証明はここ

    \boldsymbol{A} = \left(\frac{\phi}{c}, A_x, A_y, A_z \right)        \tag{電磁ポテンシャル}
    \boldsymbol{i} = \left(\rho c, i_x, i_y, i_z \right)        \tag{4元電流密度}
    \Box A^\mu - ∂^\mu \left(∂_\nu A^\nu \right)
    = - \mu_0 i^\nu        \tag{相対論的なマクスウェルの方程式}
    ∂_\nu i^\nu = 0        \tag{相対論的な電荷の保存則}
    ∂_\nu A^\nu = 0        \tag{相対論的なローレンツ条件}

ゲージ変換

    \boldsymbol{A}^{’} = \boldsymbol{A} + \mathbf{grad} \chi
    \phi^{’} = \phi - \frac{∂ \chi}{∂t}

電磁気でよく使用するベクトル公式

    \mathbf{rot} (\mathbf{rot} \boldsymbol{X}) = \mathbf{grad} (\mathbf{div} \boldsymbol{X}) - \triangle \boldsymbol{X}
    \mathbf{rot} \cdot\mathbf{grad} \phi = \boldsymbol{0}
        \mathbf{div} \cdot\mathbf{rot} \boldsymbol{X} = 0
1
Help us understand the problem. What is going on with this article?
Why not register and get more from Qiita?
  1. We will deliver articles that match you
    By following users and tags, you can catch up information on technical fields that you are interested in as a whole
  2. you can read useful information later efficiently
    By "stocking" the articles you like, you can search right away
campbel2525
myblog: https://campbel.love/ facebook: https://www.facebook.com/campbel2525/ twitter: https://mobile.twitter.com/campbel2525/ instagram: https://www.instagram.com/campbel2525/

Comments

No comments
Sign up for free and join this conversation.
Sign Up
If you already have a Qiita account Login
1
Help us understand the problem. What is going on with this article?