- #1
Reshma
- 749
- 6
I worked out this problem from Griffith's book. The problem is to find the general expression for [tex]\nabla(r^n)[/tex]. This is how I worked it out:
If [tex]\vec r = \hat x x+\hat y y+\hat z z [/tex]
r is the separation vector whose magnitude is given by [tex]\sqrt{x^2+y^2+z^2}[/tex]
Hence [tex]r^n = (x^2+y^2+z^2)^\frac{n}{2}[/tex]
I applied the [tex]\nabla[/tex] operator to it and this is solution I got:
[tex]\nabla(r^n) = n(r^2)^\frac{2n-2}{2}\vec r[/tex]
Is this the right way to find the solution or is there another generalised solution?
If [tex]\vec r = \hat x x+\hat y y+\hat z z [/tex]
r is the separation vector whose magnitude is given by [tex]\sqrt{x^2+y^2+z^2}[/tex]
Hence [tex]r^n = (x^2+y^2+z^2)^\frac{n}{2}[/tex]
I applied the [tex]\nabla[/tex] operator to it and this is solution I got:
[tex]\nabla(r^n) = n(r^2)^\frac{2n-2}{2}\vec r[/tex]
Is this the right way to find the solution or is there another generalised solution?