by fisher garry » Sat Dec 28, 2019 6:13 pm
This is taken from a physics book but since it is mathematical I thought I could ask here. In the text they use kronecker delta notation. However I am not sure about the notation.In (8.18) what does the subscript j mean in [tex](\textbf{a}\cdot \overleftrightarrow{\textbf{T}})_j=\displaystyle\sum_{i=x,y,z}a_i T_{ij}[/tex]
Could someone perhaps write out that first equation in (8.18) as well?
And in
[tex](\nabla\cdot \overleftrightarrow{\textbf{T}})_j=\epsilon_0[(\nabla\cdot\textbf{E})E_j+(\textbf{E}\cdot\nabla)E_j -\frac{1}{2}\nabla _j E^2+\frac{1}{\mu_0}[(\nabla\cdot\textbf{B})B_j+(\textbf{B}\cdot\nabla)B_j -\frac{1}{2}\nabla _j B^2][/tex]
Can someone derive this by uing (8.18). I am a bit lost
[url=https://ibb.co/vmJ5qZ7][img]https://i.ibb.co/ctN53DG/griffiths-chapter-8.png[/img][/url]
This is taken from a physics book but since it is mathematical I thought I could ask here. In the text they use kronecker delta notation. However I am not sure about the notation.In (8.18) what does the subscript j mean in [tex](\textbf{a}\cdot \overleftrightarrow{\textbf{T}})_j=\displaystyle\sum_{i=x,y,z}a_i T_{ij}[/tex]
Could someone perhaps write out that first equation in (8.18) as well?
And in
[tex](\nabla\cdot \overleftrightarrow{\textbf{T}})_j=\epsilon_0[(\nabla\cdot\textbf{E})E_j+(\textbf{E}\cdot\nabla)E_j -\frac{1}{2}\nabla _j E^2+\frac{1}{\mu_0}[(\nabla\cdot\textbf{B})B_j+(\textbf{B}\cdot\nabla)B_j -\frac{1}{2}\nabla _j B^2][/tex]
Can someone derive this by uing (8.18). I am a bit lost