Question

(30 points) 1) Prove that: $\vec{r} \times \vec{\nabla} \cdot \vec{T} = \vec{\nabla} \cdot (\vec{r} \times \vec{T})$ Note: remember that $T_{ij} = T_{ji}$ (i.e., the Maxwell's stress tensor is symmetric) (70 points) 2) Prepare notes as if you are going to present a seminar (to graduate students) on why and how Maxwell's Equations and Lorentz force are not fully invariant under a Galilean Transformation. For this purpose, read and summarize the article referenced below (and attached to this HW assignment under MS Teams). \"On the Galilean non-invariance of Classical Electromagnetism\", European J. Phys. 30 (2009) 381-391.

          (30 points)
1) Prove that:
$\vec{r} \times \vec{\nabla} \cdot \vec{T} = \vec{\nabla} \cdot (\vec{r} \times \vec{T})$

Note: remember that $T_{ij} = T_{ji}$ (i.e., the Maxwell's stress tensor is symmetric)

(70 points)
2) Prepare notes as if you are going to present a seminar (to graduate students) on why and how Maxwell's Equations and Lorentz force are not fully invariant under a Galilean Transformation. For this purpose, read and summarize the article referenced below (and attached to this HW assignment under MS Teams). \"On the Galilean non-invariance of Classical Electromagnetism\", European J. Phys. 30 (2009) 381-391.

(30 points)
1) Prove that:
r⃗×∇⃗·T⃗ = ∇⃗· (r⃗×T⃗)

Note: remember that Tij = Tji (i.e., the Maxwell's stress tensor is symmetric)

(70 points)
2) Prepare notes as if you are going to present a seminar (to graduate students) on why and how Maxwell's Equations and Lorentz force are not fully invariant under a Galilean Transformation. For this purpose, read and summarize the article referenced below (and attached to this HW assignment under MS Teams). Ön the Galilean non-invariance of Classical Electromagnetism,̈ European J. Phys. 30 (2009) 381-391.

Added by Jennifer M.

Question

Please give Ace some feedback