Question

Calculate a) the components of (ar) in spherical polar coordinates, b) Ver , (Ver). Vxer , Vep, V x ee in spherical polar coordinates, c) the components of VX (a x r) in cylindrical coordinates (a =const.).

Answer 1

9. let 2= 0, 1 ta tag i r = ng + BÊ - .1= Qim tegy + dyz In eherical coordinate system I1 = r since las på y = nsino sing garlos Jo . ū= der Sin 0610+ 0 1 Sin Osind + er beso - 1/2.7) = În scan) + êo J (@??) + ep (ar) CZ, Jr Do Job = ên (d, sino Cosp + a, sino sin ø + d3 690) + êo fyn Geso Gasif + agr Groding-cgarsino) US B tiep (-0,9 Sinosing + og de sino caso) In spherical Co-ordinate system hal, hy = r , hy = rsino - So Components of 7 (2.2) are & Singles6+& Sino sing ta, caso, a, conocos off, Grosing Taago de Sindg-dising to cont.

- 2rsino Pode a tu 3. (4,49") i (1410) ,05] - they have inte at have ever 06. 2) = 0 (43) = , 19) +300)+ê? (2.) = @MED Dxe = then he lo ha te t h e cathe (-26) ² Sino sesino Thillu helle) 5101 7.6 Care Center) + ssime crear un ) = 0 tua [2 (660) *: (4,14,(69) + 3; (hik01) La Chies) a fos) 23

TX G = he he he I thing o hi ha una ? J*****!°/thy plache] t o [o to th sino ép 1 1 ssino Leo 3-dzy) + (ogn=d, 3) + (017-4; 4) r In cylindrical co-ordinate systema, If are replaced by ên, &o , & and a= scoso, y = rsinde z=z then 2 x 2 = 1 % z - dersino) ent(&greso-d, 3) et (a, s sino-agricose) iz Jo XX (2x2) = 1 her to be 1

In cylindrical condimenteystem th= 1, 6,=1, p = So vx laxa) = lê soo (@ So v* (***) The , Song Jy / Lirsino ar logo = ( 012 69 0 tegasin o + ) +56 (9,-,sin0 44,650) 46; (3,698 44, aande = (0,696 + y line to ') € +(3:1-6, asi0 +3:1 (aro) @ +(03 698 (1+x Please like and comment: