The potential is zero at some point in space. You can conclude that: 1. The E-field is zero at that point 2. The E-field is non-zero at that point 3. You can conclude nothing at all about the E-field at that point

The potential is constant everywhere along a line in space. You can conclude that: 1. The E-field has a constant magnitude along the line. 2. The E-field is zero along that line. 3. You can conclude nothing at all about the magnitude of $\mathbf{E}$ along that line.

<img src="./images/charged_shell.png" align="right" style="width: 200px";/> A spherical *shell* has a uniform positive charge density on its surface. (There are no other charges around.) What is the electric field *inside* the sphere? 1. $\mathbf{E}=0$ everywhere inside 2. $\mathbf{E}$ is non-zero everywhere in the sphere 3. $\mathbf{E}=0$ only that the very center, but non-zero elsewhere inside the sphere. 4. Not enough information given

<img src="./images/graph_shell.png" align="center" style="width: 400px";/> Could this be a plot of $\left|\mathbf{E}(r)\right|$? Or $V(r)$? (for SOME physical situation?) 1. Could be $E(r)$, or $V(r)$ 2. Could be $E(r)$, but can't be $V(r)$ 3. Can't be $E(r)$, could be $V(r)$ 4. Can't be either 5. ???