# Max and min functions in spherical expansions

• snatchingthepi
In summary, the conversation is about solving the vector potential of a solid rotating sphere with a constant charge density. The final integral involves the use of ##r_>## and ##r_<## functions, with different interpretations for inside and outside the sphere. The correctness of the integral has not been confirmed, but the correct interpretation of the functions has been clarified.
snatchingthepi
Homework Statement
Finding the vector potential inside and outside of a rotating homogenous solid sphere.
Relevant Equations
## r_< = min(r,r') ##
##r_> = max(r,r') ##
I'm trying to solve the vector potential of a solid rotating sphere with a constant charge density. I'm at a point where I'm performing the final integral that looks like

$$-\left( \frac {\mu_0 i} {3} \right) \sqrt{\frac 3 {2\pi}} \frac {q\omega}{R^3} Y_{1,1} \int_0^R (r')^3 \frac {r_<} {r_>^2} dr'$$I'm thinking that outside the sphere ##r_> = r## and ##r_< = r'##, and vice-versa for inside the sphere. Is this correct? I've never seen those functions before, and am unsure if I'm interpretating them correctly.

Last edited:
Delta2
Your interpretation of ##r_>## and ##r_<## is correct. I have not checked the correctness of the the integral.

snatchingthepi
Not a problem. My concern was with the min and max functions. Thank you.

## What is a max function in spherical expansions?

A max function in spherical expansions is a mathematical function that calculates the maximum value of a given set of data points. It is commonly used in spherical expansions to determine the maximum value of a function at a specific point on the sphere.

## What is a min function in spherical expansions?

A min function in spherical expansions is a mathematical function that calculates the minimum value of a given set of data points. It is commonly used in spherical expansions to determine the minimum value of a function at a specific point on the sphere.

## How are max and min functions used in spherical expansions?

Max and min functions are used in spherical expansions to determine the maximum and minimum values of a function at specific points on the sphere. This information is important in understanding the behavior of the function and its overall shape on the sphere.

## What are some examples of max and min functions in spherical expansions?

Examples of max and min functions in spherical expansions include the maximum and minimum values of temperature at different points on the Earth's surface, the maximum and minimum values of atmospheric pressure at different points in the atmosphere, and the maximum and minimum values of ocean depth at different points in the ocean.

## How can max and min functions be optimized in spherical expansions?

In order to optimize max and min functions in spherical expansions, various mathematical techniques such as gradient descent or linear programming can be used to find the optimal values of the function at specific points on the sphere. Additionally, computer algorithms and simulations can also be used to efficiently determine the maximum and minimum values of the function.

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