$\mathbf{E}(\mathbf{r}) = \int \dfrac{\lambda dl'}{4\pi\varepsilon_0\mathfrak{R}^3}\vec{\mathfrak{R}}$, so: $E_x(x,0,0) = \dfrac{\lambda}{4\pi\varepsilon_0}\int \dots$ <img src ="./images/linecharge_coords.png" align="right" style="width: 400px";/> 1. $\int \dfrac{dy'x}{x^3}$ 2. $\int \dfrac{dy' x}{(x^2 + y'^2)^{3/2}}$ 3. $\int \dfrac{dy' y'}{x^3}$ 4. $\int \dfrac{dy' y'}{(x^2+y'^2)^{3/2}}$ 5. Something else Note: CORRECT ANSWER: B

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)

**Activity:** You determine that a particular electrostatics problem cannot be integrated analytically. How do you instruct a computer to do it for you? Work with those around you to come up with a series of instructions (in plain words) to tell the computer to do it.

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