208 Electric Potential

This report should adhere to a more formal lab report structure. You can see what that entails here.

Report Question: Potential Plots

It can be shown that the analytical prediction for the potential in between the two conducting rings will be described by the expression: $$ \begin{equation} V(r) = A \ln \left( \frac{r}{r_a} \right) \label{eq:potentialfunction} \end{equation} $$ where $A$ is a constant determined by the actual potential difference between the two rings.

1. Prepare a plot of your Potential vs. Position data using the averages for the voltage measurements at various positions. It should resemble a log function.

2. Also plot $V$ vs. $\ln(r)$. This should be a straight line.

3. Use the above to establish a value for the constant $A$. What units should it have?

Report Question: Electric Field

The relation between fields and potential is given by: $$ \begin{equation} E_x = - \frac{\Delta V}{\Delta x} \label{eq:fieldgradpot} \end{equation} $$

3. Use equation \eqref{eq:fieldgradpot} and \eqref{eq:potentialfunction} to obtain an expression for the electric field.

4. Make an analytical plot of the electric field as a function of position between the rings, $E(r)$

Report Question: Visualization

5. On the sheet provided here, draw the equipotential lines corresponding to 1, 2, 3, and 4 V at approximately the correct locations based on your data and understanding of equation \eqref{eq:potentialfunction}.

6. Also draw several field lines indicating the direction of the electric field between the rings.

Submit this visualization along with the rest of the lab write-up.