Exam Rewrites

• Circled grade is the grade you will earn if you do the rewrite
• To earn the circled grade:
  • Complete the parts that you didn't earn full credit
  • Write one paragraph per problem (max 4 paragraphs) about what you didn't understand at the time of the exam, what you did to correct that understanding, and how that relates to the solution you've written up.

Laplace's Equation

A region of space contains no charges. What can I say about $V$ in the interior?

1. Not much, there are lots of possibilities for $V(r)$ in there
2. $V(r)=0$ everywhere in the interior.
3. $V(r)=$constant everywhere in the interior

A region of space contains no charges. The boundary has V=0 everywhere. What can I say about $V$ in the interior?

1. Not much, there are lots of possibilities for $V(r)$ in there
2. $V(r)=0$ everywhere in the interior.
3. $V(r)=$constant everywhere in the interior

For the 1D Laplace problem ($\nabla^2 V = \partial^2 V/\partial x^2 = 0$), we can choose the following ansatz:

1. $k_0\,x$
2. $k_0\,x+k_1$
3. $k_0\,x^2+k_1\,x+k_2$
4. Can't tell

If you put a positive test charge at the center of this cube of charges, could it be in stable equilibrium?

1. Yes
2. No
3. ???