$$\mathbf{E}_{dip}(\mathbf{r}) = \dfrac{p}{4 \pi \varepsilon_0 r^3}\left(2 \cos \theta\;\hat{\mathbf{r}} + \sin \theta\;\hat{\mathbf{\theta}}\right)$$
<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