Unformatted text preview: of a stream function by 2 1 1 , . sin sin r u u r r r θ ψ ∂ ∂ = = ∂ ∂ (a) Find an explicit expression for ( ) sin . E r = ∇× u ( E is to be considered as a differential operator.) (b) The stream function satisfies 2 E = and, for the flow past a sphere, ( ) ( ) 2 , sin . r f r = Show that ( ) 4 4 2 4 8 8 0. r f r f rf f ′′ ′+= 3. A vector field is defined by cos cos cos sin sin . x z y z z F z F z a a a λ = + + = + F i j k e k Use the divergence theorem to calculate the flux of F through the closed surface bounded by the cylinders a = and 2 a = and the planes 2. z a π = ±...
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 Fall '11
 MacDonald
 Current, Work, Magnetic Field, Fundamental physics concepts

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