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Chapter 10: Q13P (page 517)

鈭�B鈭�t=-鈭�脳E

Short Answer

Expert verified

鈭�B鈭�t,鈭�脳Eare both axial vectors.

Step by step solution

01

Given information.

Physics definitions are given.

02

Definition of one of Maxwell’s equations.

Define one of Maxwell鈥檚 equations.

鈭�B鈭�t=-鈭�脳E

03

Write about the nature of various vectors.

It is proved that B is an axial vector and E is a polar vector.

This implies that 鈭�B鈭�t,鈭�脳E are both axial vectors.

This is based on one of Maxwell鈥檚 relations.

鈭�B鈭�t=-鈭�脳E

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Most popular questions from this chapter

Verify for a few representative cases that (5.6)gives the same results as a Laplace development. First note that if伪,尾,纬=1,2,3 , then (5.6)is just(5.5) . Then try letting伪,尾,纬= an even permutation of 1,2,3, and then try an odd permutation, to see that the signs work out correctly. Finally try a case when 蔚伪尾纬=0(that is when two of the indices are equal) to see that the right hand side of(5.6) is zero because you are evaluating a determinant which has two identical rows.

XijAk=Bijk.

Parabolic cylinder.

Show that the transformation equation for a 2nd-rank Cartesian tensor is equivalent to a similarity transformation. Warning hint: Note that the matrix C in Chapter 3 , Section 11 , is the inverse of the matrix A we are using in Chapter 10 (comparer'=Arandr=Cr'). Thus a similarity transformation of the matrix T with tensor componentsTij isT'=ATA-1. Also, see 鈥淭ensors and Matrices鈥� in Section 3 and remember that A is orthogonal.

Show that 未ij系klmis an isotropic tensor of rank 5. Hint: Combine equations (5.4) and (5.7).
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