(a) Express the spherical unit vectors f, 0, $ in terms of the Cartesian unit vectors Î, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas, giving ✰, ŷ, 2 in terms of f, ô, § (and 0, 4). Calculate af/00 and Əf/3, and express them in terms of spherical unit vectors. (b) Express the cylindrical unit vectors ŝ, $, 2 in terms of the Cartesian unit vec- tors Â, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse formulas, giving Â, ŷ, 2 in terms of ŝ, §, 2 (and ø). Show that dî/0¢ = §.
(a) Express the spherical unit vectors f, 0, $ in terms of the Cartesian unit vectors Î, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas, giving ✰, ŷ, 2 in terms of f, ô, § (and 0, 4). Calculate af/00 and Əf/3, and express them in terms of spherical unit vectors. (b) Express the cylindrical unit vectors ŝ, $, 2 in terms of the Cartesian unit vec- tors Â, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse formulas, giving Â, ŷ, 2 in terms of ŝ, §, 2 (and ø). Show that dî/0¢ = §.
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![(a) Express the spherical unit vectors ê, ê, in terms of the Cartesian unit vectors
✰, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas,
giving ✰, ŷ, 2 in terms of f, 0, $ (and 0, $). Calculate af/00 and af/ap, and
express them in terms of spherical unit vectors.
(b) Express the cylindrical unit vectors ŝ, , 2 in terms of the Cartesian unit vec-
tors î, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse
formulas, giving x, ŷ, 2 in terms of ŝ, $, 2 (and ). Show that af/0 = $.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29c74d06-0f3b-4eb2-9c9d-dbbc1918002c%2F598889dc-80df-4d85-93f0-23d4018a9565%2Fr2nwstw_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Express the spherical unit vectors ê, ê, in terms of the Cartesian unit vectors
✰, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas,
giving ✰, ŷ, 2 in terms of f, 0, $ (and 0, $). Calculate af/00 and af/ap, and
express them in terms of spherical unit vectors.
(b) Express the cylindrical unit vectors ŝ, , 2 in terms of the Cartesian unit vec-
tors î, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse
formulas, giving x, ŷ, 2 in terms of ŝ, $, 2 (and ). Show that af/0 = $.
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