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i) In three dimensions, show that f(x, y, z) = 1/r satisfies Laplace's equation. Show this first in Cartesian coordinates and then in spherical polar coordinates.

i) In three dimensions, show that f(x, y, z) = 1/r satisfies Laplace's equation. Show this first in Cartesian coordinates and then in spherical polar coordinates.

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i) In three dimensions, show that f(x, y, z) = 1/r satisfies Laplace's equation. Show this first in Cartesian coordinates and then in spherical polar coordinates. ii) If a point has spherical coordinates (4,0, 7), what are its Cartesian coordi- nates? Draw a picture. iii) A fellow student claims that the curl in spherical polar coordinates has the form 1 V x A= (sin 0A,) – (40) £ r sin 0 \a0 1 (A,) sin 0 dø (rA6))0+ (r Ae) (rA,)) . - Or Use dimensional arguments to find their error.
Transcribed Image Text:i) In three dimensions, show that f(x, y, z) = 1/r satisfies Laplace's equation. Show this first in Cartesian coordinates and then in spherical polar coordinates. ii) If a point has spherical coordinates (4,0, 7), what are its Cartesian coordi- nates? Draw a picture. iii) A fellow student claims that the curl in spherical polar coordinates has the form 1 V x A= (sin 0A,) – (40) £ r sin 0 \a0 1 (A,) sin 0 dø (rA6))0+ (r Ae) (rA,)) . - Or Use dimensional arguments to find their error.
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