5 charges, q, are arranged in a regular pentagon, as shown. What is the E field at the center? <img src ="./images/5charges.png" align="center" style="width: 250px";/> 1. Zero 2. Non-zero 3. Really need trig and a calculator to decide Note: CORRECT ANSWER: A

### Announcements * Help Session 1420 BPS (4-5pm) * Starts this week! * We will use GitHub Classroom for [digital submissions of homework](https://dannycab.github.io/phy482msu/assignments/homework1.html) * Create a [GitHub account](https://github.com/join) * Download [GitHub Desktop](https://desktop.github.com/) * Review [Piazza post on usage](https://piazza.com/msu/spring2017/phy482/home) * Come to help session (or my office) if you need/want help

<img src ="./images/zappa.jpeg" align="right" style="width: 100px";/> 1 of the 5 charges has been removed, as shown. What’s the E field at the center? <img src ="./images/4charges.png" align="center" style="width: 400px";/> 1. $+(kq/a^2)\hat{y}$ 2. $-(kq/a^2)\hat{y}$ 3. 0 4. Something entirely different! 5. This is a nasty problem which I need more time to solve Note: CORRECT ANSWER: B Superposition!

To find the E-field at P from a thin line (uniform charge density $\lambda$): <img src ="./images/linecharge.png" align="right" style="width: 400px";/> $$ \mathbf{E}(\mathbf{r}) = \dfrac{1}{4\pi\varepsilon_0}\int \dfrac{\lambda dl'}{\mathfrak{R}^2}\hat{\mathfrak{R}}$$ What is $\mathfrak{R}$? 1. $x$ 2. $y'$ 3. $\sqrt{dl'^2 + x^2}$ 4. $\sqrt{x^2+y'^2}$ 5. Something else Note: CORRECT ANSWER: D

What do you expect to happen to the field as you get really far from the rod? $$E_x = \dfrac{\lambda}{4\pi\varepsilon_0\}\dfrac{L}{x\sqrt{x^2+L^2}}$$ 1. $E_x$ goes to 0. 2. $E_x$ begins to look like a point charge. 3. $E_x$ goes to $\infty$. 4. More than one of these is true. 5. I can't tell what should happen to $E_x$. Note: CORRECT ANSWER: D (A and B)

Given the location of the little bit of charge ($dq$), what is $|\vec{\mathfrak{R}}|$? <img src ="./images/sphereintegrate.png" align="left" style="width: 300px";/> 1. $\sqrt{z^2+r'^2}$ 2. $\sqrt{z^2+r'^2-2zr'\cos\theta}$ 3. $\sqrt{z^2+r'^2+2zr'\cos\theta}$ 4. Something else Note: CORRECT ANSWER: B

Which of the following are vectors? (I) Electric field, (II) Electric flux, and/or (III) Electric charge 1. I only 2. I and II only 3. I and III only 4. II and III only 5. I, II, and II Note: * CORRECT ANSWER: A

A positive point charge $+q$ is placed outside a closed cylindrical surface as shown. The closed surface consists of the flat end caps (labeled A and B) and the curved side surface (C). What is the sign of the electric flux through surface C? <img src="./images/ABC_cylinder.png" align="center" style="width: 600px";/> 1. positive 2. negative 3. zero 4. not enough information given to decide Note: * CORRECT ANSWER: B * This is meant to be hard to visualize, next slide illustrates it better.

Let's get a better look at the side view. <img src="./images/ABC_cylinder_side.png" align="center" style="width: 350px";/>

Which of the following two fields has zero divergence? | I | II | |:-:|:-:| | <img src ="./images/cq_left_field.png" align="center" style="width: 400px";/> | <img src ="./images/cq_right_field.png" align="center" style="width: 400px";/> | 1. Both do. 2. Only I is zero 3. Only II is zero 4. Neither is zero 5. ??? Note: * CORRECT ANSWER: B * Think about dE/dx and dE/dy * Fall 2016: 7 [34] 13 43 3; (Asked them to consider dvx/dx and dvy/dy) 3 [90] 3 4 0

What is the value of: $$\int_{-\infty}^{\infty} x^2 \delta(x-2)dx$$ 1. 0 2. 2 3. 4 4. $\infty$ 5. Something else Note: * CORRECT ANSWER: C

A point charge ($q$) is located at position $\mathbf{R}$, as shown. What is $\rho(\mathbf{r})$, the charge density in all space? <img src ="./images/pt_charge_at_R.png" align="right" style="width: 300px";/> 1. $\rho(\mathbf{r}) = q\delta^3(\mathbf{R})$ 2. $\rho(\mathbf{r}) = q\delta^3(\mathbf{r})$ 3. $\rho(\mathbf{r}) = q\delta^3(\mathbf{R}-\mathbf{r})$ 4. $\rho(\mathbf{r}) = q\delta^3(\mathbf{r}-\mathbf{R})$ 5. Something else?? Note: * CORRECT ANSWER: E * This one is a curious one because a delta function is always positive, both C and D are correct. * Expect most everyone to pick C

<img src ="./images/dipole_gauss.png" align="right" style="width: 300px";/> An electric dipole ($+q$ and $–q$, small distance $d$ apart) sits centered in a Gaussian sphere. What can you say about the flux of $\mathbf{E}$ through the sphere, and $|\mathbf{E}|$ on the sphere? 1. Flux = 0, E = 0 everywhere on sphere surface 2. Flux = 0, E need not be zero *everywhere* on sphere 3. Flux is not zero, E = 0 everywhere on sphere 4. Flux is not zero, E need not be zero... Note: * CORRECT ANSWER: B * Think about Q enclosed; what can we say about E though?

Which of the following two fields has zero curl? | I | II | |:-:|:-:| | <img src ="./images/cq_left_field.png" align="center" style="width: 400px";/> | <img src ="./images/cq_right_field.png" align="center" style="width: 400px";/> | 1. Both do. 2. Only I is zero 3. Only II is zero 4. Neither is zero 5. ??? Note: * CORRECT ANSWER: C * Think about paddle wheel * Fall 2016: 9 0 [89] 3 0

<img src ="./images/zappa.jpeg" align="right" style="width: 100px";/> Can superposition be applied to electric potential, $V$? $$V_{tot} \stackrel{?}{=} \sum_i V_i = V_1 +V_2 + V_3 + \dots$$ 1. Yes 2. No 3. Sometimes Note: As long as the zero potential is the same for all measurements.

<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. ???

A point charge $+q$ sits outside a **solid neutral conducting copper sphere** of radius $A$. The charge q is a distance $r > A$ from the center, on the right side. What is the E-field at the center of the sphere? (Assume equilibrium situation). <img src="./images/copper_1.png" align="left" style="width: 300px";/> 1. $|E| = kq/r^2$, to left 2. $kq/r^2 > |E| > 0$, to left 3. $|E| > 0$, to right 4. $E = 0$ 5. None of these Note: * CORRECT ANSWER: D * Net electric field inside of a metal in static equilibrium is zero * Talk about the net field versus the field due to the charges on the metal.

A neutral copper sphere has a spherical hollow in the center. A charge $+q$ is placed in the center of the hollow. What is the total charge on the outside surface of the copper sphere? (Assume Electrostatic equilibrium.) <img src="./images/coppersphere_hole_and_charge.png" align="left" style="width: 350px";/> 1. Zero 2. $-q$ 3. $+q$ 4. $0 < q_{outer} < +q$ 5. $-q < q_{outer} < 0$