What is the definition of a function being spherically symmetric?

[Taylor_1989]

Homework Statement

Hi guys, having problem trying to understand what this question wants.

the question I am stuck with is 7.3.

Homework Equations

The Attempt at a Solution

So for a) I converted to spherical co-ordinates:
$log(r^2sin^\theta cos^2\phi+r^2sin^2\theta sin^2\phi+r^2 cos^2\theta)$ which simplifies to $log(r^2)=2log(r)$
is this correct?

for b) I am not quite sure what it wants. Could someone please advise. Thanks in advance

 

[blue_leaf77]

is this correct?

You forgot the 1 inside the log argument.

b) I am not quite sure what it wants. Could someone please advise.

You can try calculating its gradient $\nabla f(r)$ and then the directional derivative in an arbitrary direction perpendicular to the radial unit vector $\hat r$.

 

[LCKurtz]

@Taylor_1989 : What is your definition of a function being spherically symmetric?

 

[Taylor_1989]

@LCKurtz Well looking at the above function, wid the 1 in. It will have to go from the center of the axis because the way i see it each side about the center will have the same volume, but if you say move it to the left one side will have a larger volume that the other.

 

[LCKurtz]

@Taylor_1989 : What is your definition of a function being spherically symmetric?

@LCKurtz Well looking at the above function, wid the 1 in. It will have to go from the center of the axis because the way i see it each side about the center will have the same volume, but if you say move it to the left one side will have a larger volume that the other.

You were asked to show a certain function is spherically symmetric. How can you expect to do that if you don't know what being spherically symmetric is? That should have been included in the homework template under "relevant equations", which you left blank. Look in your text, find the definition, and quote it here. Then we might be able to help you.