Hi. I need a bit of help with the following question:

Calculate the normal to the sphere of radius

*R *and centred at the origin, using the appropriate Jacobians and the spherical coordinates. Show that the normal is directed everywhere along the radial vector from the sphere centre, r = (*x, y, z*).

So initially I desrcibed the sphere using polar coordinates:

x = Rcos(phi)sin(phi) y = Rsin(phi)sin(phi)and z = Rcos(phi) ;

Then I got three jacobians:

Jx=d(y,z)/d(phi,z) Jy=d(z,x)/d(phi,z) Jz=d(x,y)/d(phi,z)

For this I got:

Jx=2Rsin(phi)cos(phi)

Jy=Rsin(phi)sin(phi)-Rcos(phi)cos(phi)

Jz=0

So N=2Rsin(phi)cos(phi)** i** + Rsin(phi)sin(phi)-Rcos(phi)cos(phi) **j**

Just wanted to know if I have done this coorectly, and how to do the final 'show that' part of the question.

Cheers.