Electrostatics and Magnetostatics

Electric field  :

• Let \((\Pi)\) be a symmetric plane for the charge distribution.

  If \(M'=sym(M)_{/\Pi}\) : \(\vec E (M')=sym(\vec E(M))_{/\Pi}\)

• Let \((\Pi)\) be an anti-symmetric plane for the charge distribution.

  If \(M'=sym(M)_{/\Pi}\) : \(\vec E (M')=-sym(\vec E(M))_{/\Pi}\)

• Let \( (\Pi)\) be a symmetric plane for the charge distribution passing through point M, where we want to determine the electric field. Then :

  \(\vec E(M) \in (\Pi)\)

• Let \( (\Pi)\) be an anti - symmetric plane for the charge distribution passing through point M, where we want to determine the electric field. Then :

  \(\vec E(M) \bot (\Pi)\)

Magnetic field :

• Let \((\Pi)\) be a symmetric plane for the current distribution.

  If \(M'=sym(M)_{/\Pi}\) : \(\vec B (M')=-sym(\vec B(M))_{/\Pi}\)

• Let \((\Pi)\) be an anti-symmetric plane for the current distribution.

  If \(M'=sym(M)_{/\Pi}\) : \(\vec B (M')=sym(\vec B(M))_{/\Pi}\)

• Let \( (\Pi)\) be a symmetric plane for the current distribution passing through point M, where we want to determine the magnetic field. Then :

  \(\vec B(M) \bot (\Pi)\)

• Let \( (\Pi)\) be an anti - symmetric plane for the current distribution passing through point M, where we want to determine the magnetic field. Then :

  \(\vec B(M) \in (\Pi)\)