$$\mathbf{E}_{dip}(\mathbf{r}) = \dfrac{p}{4 \pi \varepsilon_0 r^3}\left(2 \cos \theta\;\hat{\mathbf{r}} + \sin \theta\;\hat{\mathbf{\theta}}\right)$$ <img src="./images/small_dipole.png" align="right" style="width: 200px";/> For the dipole $\mathbf{p} = q\mathbf{d}$ shown, what does the formula predict for the direction of $\mathbf{E}(\mathbf{r})$ for $\theta =0$ and $\theta=\pi/2$? Consider $r$ to be large compared to $d$. 1. $+z$; $+x$ 2. $-z$; $+x$ 3. $-z$; $+z$ 4. $+z$; $-z$ 5. Some other pair of directions Note: * CORRECT ANSWER: D
## Announcements * Exam 2 is coming up (2 weeks from today) * BPS 1415 (this room), 7pm-9pm, Nov 6th * Same format as Exam 1 * Details next week
### Ideal vs. Real dipole <img src="./images/dipole_animation.gif" align="center" style="width: 450px";/>
$$\mathbf{p} = \sum_i q_i \mathbf{r}_i$$ What is the magnitude of the dipole moment of this charge distribution? <img src="./images/2q_dipole.png" align="right" style="width: 200px";/> 1. qd 2. 2qd 3. 3qd 4. 4qd 5. It's not determined Note: * CORRECT ANSWER: B
$$\mathbf{p} = \sum_i q_i \mathbf{r}_i$$ <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