<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 Note: * Correct Answer: A
### Exam 1 Information * Exam 1 on Wednesday, October 3rd (BCH 101) - Next to BPS (Wilson side) * 7pm-9pm - Arrive on time! - Put one seat between you and the next person * I will provide a formula sheet (posted on Slack already) * You can bring one-side of a sheet of paper with your own notes. * 5 questions - True/False, Essay, Code, Graphing, Short Calculations
### What's on Exam 1? * Identify whether conceptual statements about $\mathbf{E}$, $V$, $\rho$, and/or numerical integration are true or false. * Sketch and discuss delta functions in relation to charge density, $\rho$ * Explain the process for using a computational alogrithm for predicting $\mathbf{E}$ and write the necessary code to illustrate how it works for a given example * Calculate the electric field, $\mathbf{E}$, inside and outside a continuous distribution of charge and sketch the results * Calculate the electric potential, $V$, for a specific charge distribution and discuss what happens in limiting cases
We are trying to compute the the electric potential $V(\mathbf{r})$ for a line of charge at the location $\langle x,0,z \rangle$. What is $|\mathfrak{R}|$ in this case? 1. $x$ 2. $z$ 3. $\sqrt{x^2+z^2}$ 4. Something else Note: Correct Answer D (needs to have z')
We derived the potential for this short rod to be $V(x,z) = \dfrac{\lambda}{4\pi\varepsilon_0}\log\left[\dfrac{L+z+\sqrt{x^2+(L+z)^2}}{L-z+\sqrt{x^2+(L-z)^2}}\right]$ The associated electric field at $\langle x,0,z\rangle$ location can have the following components: 1. only x 2. only y 3. only z 4. x, y, and z 5. Something else
<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 Note: * Correct Answer: A
We derived the electric potential outside ($r>R$) the charged shell to be $$V(r) = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}$$ What is it for $r<R$? 1. Zero 2. Constant 3. It changes but I don't know how yet 4. Something else Note: * Correct Answer: B
<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. ??? Note: * Correct Answer: B