$$\mathbf{p} = \sum_i q_i \mathbf{r}_i$$ <img src="./images/dipole_2q_and_q.png" align="right" style="width: 200px";/> What is the dipole moment of this system? (BTW, it is NOT overall neutral!) 1. $q\mathbf{d}$ 2. $2q\mathbf{d}$ 3. $\frac{3}{2}q\mathbf{d}$ 4. $3q\mathbf{d}$ 5. Someting else (or not defined) Note: * CORRECT ANSWER: B

$$\mathbf{p} = \sum_i q_i \mathbf{r}_i$$ <img src="./images/dipole_2q_and_q_shift.png" align="right" style="width: 200px";/> What is the dipole moment of this system? (Same as last question, just shifted in $z$.) 1. $q\mathbf{d}$ 2. $2q\mathbf{d}$ 3. $\frac{3}{2}q\mathbf{d}$ 4. $3q\mathbf{d}$ 5. Someting else (or not defined) Note: * CORRECT ANSWER: C

You have a physical dipole, $+q$ and $-q$ a finite distance $d$ apart. When can you use the expression: $$V(\mathbf{r}) = \dfrac{1}{4 \pi \varepsilon_0}\dfrac{\mathbf{p}\cdot \hat{\mathbf{r}}}{r^2}$$ 1. This is an exact expression everywhere. 2. It's valid for large $r$ 3. It's valid for small $r$ 4. No idea... Note: * CORRECT ANSWER: B

You have a physical dipole, $+q$ and $-q$ a finite distance $d$ apart. When can you use the expression: $$V(\mathbf{r}) = \dfrac{1}{4 \pi \varepsilon_0}\sum_i \dfrac{q_i}{\mathfrak{R}_i}$$ 1. This is an exact expression everywhere. 2. It's valid for large $r$ 3. It's valid for small $r$ 4. No idea... Note: * CORRECT ANSWER: A

Which charge distributions below produce a potential that looks like $\frac{C}{r^2}$ when you are far away? <img src="./images/multipole_charge_configs_1.png" align="center" style="width: 600px";/> E) None of these, or more than one of these! (For any which you did not select, how DO they behave at large r?) Note: * CORRECT ANSWER: E (Both C and D)

Which charge distributions below produce a potential that looks like $\frac{C}{r^2}$ when you are far away? <img src="./images/multipole_charge_configs_2.png" align="center" style="width: 600px";/> E) None of these, or more than one of these! (For any which you did not select, how DO they behave at large r?) Note: * CORRECT ANSWER: E (Both B and D)

In terms of the multipole expansion $V(r) = V(mono) + V(dip) + V(quad) + \dots$, the following charge distribution has the form: <img src="./images/multipole_charge_configs_3.png" align="center" style="width: 600px";/> 1. $V(r) = V(mono) + V(dip) +\;$ higher order terms 2. $V(r) = V(dip) +\;$ higher order terms 3. $V(r) = V(dip)$ 4. $V(r) =\;$ only higher order terms than dipole 5. No higher terms, $V(r) = 0$ for this one. Note: * CORRECT ANSWER: D