Subject: Engineering EM fields Q : Express the vector field W = (x² – y²)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q = 60, z= -4). (b) Spherical coordinate at P(r=4, 0 = 30, q = 120).

Answered: Q : Express the vector field W = (x² –…

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Subject: Engineering EM fields

Q : Express the vector field W = (x² – y²)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q = 60, z
= -4). (b) Spherical coordinate at P(r=4, 0 = 30, q = 120).

Expert Solution

(a) Cylindrical coordinate

W = (x²-y²)a_y + (xz)a_z

in cylindrical coordinate,

W = (W. $a_{ρ}$ ) $a_{ρ}$ + (W. $a_{ϕ}) a_{ϕ}$ + (W. $a_{z})$ $a_{z}$

= (x²-y²)sin $ϕ$ $a_{ρ}$ + (x²-y²)cos $ϕ$ $a_{ϕ}$ + xza_z

= -9 $\sqrt{3}$ $a_{ρ}$ - 9 $a_{ϕ}$ -12a_z

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Q : Express the vector field W = (x² – y²)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q = 60, z = -4). (b) Spherical coordinate at P(r=4, 0 = 30, q = 120).