Question

Әf Əf HW: #1. Find the expressions for af of - and om I in terms of адх” ду дz. x = p sino cos 0; y = psin o sin 0; z = pcosø. , where do and of #2. Express V? f in spherical coordinates, where f(0,0,0) is a scalar function.

Answer 1

ny, 8 are function of Pid and o hone at he goes by Now Now xrind coso y = r sind sino z = rcos & r= Sx?r gh tgh cosa = 2 hence 989). Using basic differentiation. od a sing or = coso using these in o 2x 0 4 r posing 24 i By Similarly sind coso at + cose cose of using of simply putting values from above words more similarly 9 SNTO putting values from above e in an sina sino pote + caso su se

Similarly COS

Now, of die al title Using previous results, we get DE DE Now O 2.0 d (2 34 ) 941 ] +40 2342 ] Now =0; 18 = 0 =0) do 1= 6; Heb = idâ zo ; I ? =-sindh; do = cosod, it å = -sin o 7-10506; - Put this in sove equation & upon simplification Thus we'll get - obe same.

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