Question

A. The component of flux, given flux density F, crossing the surface dsu F.ûdsu OB. In spherical coordinates the following is true for any point, r= Rsin o cos 6î + Rsin o sin oſ + R cos and de =R c. The gradient in the u, v, w coordinates is 1 0 1 0 V= ü+T V .hu du h, du + 1 0 hw dw Then, the component of flux, given flux density F, crossing the surface, dSu, Fuh, dvdw.

MARK WHICH OF THE FOLLOWING ARE TRUE/FALSE

Answer 1

& given. flux density = F Surface area = dsu. flux component is - (p = f.ûd su this is true then the ③ In spesical coordinates for any point. 8= Rsing cose i TR sind Sino ŷ TR cosa  - and dr = R This is True] © The gradient in the u, uw coordinates as the component affilux Foûdsu = (fuê tfuütfw w). ûndsu Flûdsa : fudsu = fuhuhududw So given that So I fu hududeo] is FALSE this

given hen the divergence of a vector f in spherical the Coordinates as - R² sine JR . den this is TRUE Graven the gradient in terms of Spherical coordinates. P = R S + 2 Jous to lose This is TFALSE I © Griven in spherical coordinate for any point &= R sind coso ê te sind sino ŷ TR cos& À and or = Rsino This is FALSE] do = R sind ê this is true 29 flux is the change in the amount of Stuff per unit area across a surface flowing A This as ETRUE given a position vector r(s) which is a function of a&c length then drogen bang This is [TRUE su

0 for transfered coordinates u,uw area of a face in dsu= hu hududw This is [TRUE o The divergence of the gradient of a function is known as the laplacian. Deve et 2221 go to the 22 This is [TRUE