- #1

- 117

- 17

- Homework Statement
- Need help with setting up the first part of the problem.

- Relevant Equations
- See solution.

Problem:

Solution:

When I looked at an example problem, they started writing the potential in terms of the Legendre polynomials.

The example problem:

This is what I did:

$$V_0 \alpha P_2 (\cos(\theta)) \Rightarrow \frac{\alpha 3 \cos ^2 (\theta)}{2} - \frac{\alpha}{2} \Rightarrow \frac{\alpha 3}{2} - \frac{\alpha}{2}= 1 \Rightarrow \alpha = 1$$

Hence,

$$V(\theta) = V_0 P_2 (\cos(\theta)).$$

Have I done right?

Solution:

When I looked at an example problem, they started writing the potential in terms of the Legendre polynomials.

The example problem:

This is what I did:

$$V_0 \alpha P_2 (\cos(\theta)) \Rightarrow \frac{\alpha 3 \cos ^2 (\theta)}{2} - \frac{\alpha}{2} \Rightarrow \frac{\alpha 3}{2} - \frac{\alpha}{2}= 1 \Rightarrow \alpha = 1$$

Hence,

$$V(\theta) = V_0 P_2 (\cos(\theta)).$$

Have I done right?