How to Prove ∇^2 (1/r) = 0 in Cartesian Coordinates?

[johnaphun]

Homework Statement

Write down an expression for ∇^2 in Cartesian co-ordinates and, by expressing the displacement vector r in Cartesians show that:

∇^2 ⎛ 1/r ⎞ = 0 for r > 0.

Homework Equations

I can do the first part of the question and i know how to show that ∇^2 ⎛ 1/r ⎞ = 0 in spherical polars but i think I'm missing something here.

The Attempt at a Solution

I tried differentiating the x component of 1/r twice w.r to x and likewise with the y and z components but I'm not getting zero.

 

[tiny-tim]

hi johnaphun! welcome to pf!

(try using the X² icon just above the Reply box )

I tried differentiating the x component of 1/r twice w.r to x and likewise with the y and z components but I'm not getting zero.

it should add up to zero …

show us your full calculations, and then we'll see what went wrong

 

[johnaphun]

Thanks for the quick response and apologies for my slow one!

Don't worry i manage to solve it in the end, silly miscalculations on my part.

Thank you for the help anyway!