Have you taken CMSE 201?
1. I have taken CMSE 201.
2. I am currently taking CMSE 201.
3. I have not taken CMSE 201, but I plan to.
4. I have not taken CMSE 201, and don't plan to.
## Help Sessions (1300 BPS)
- Wednesdays 7:15-8:30
- Thursdays 6:30-8:30
Either Danny or Bryan will be there for about one hour.
In a typical Cartesian coordinate system, vector $\mathbf{A}$ lies along the $+\hat{x}$ direction and vector $\mathbf{B}$ lies along the $-\hat{y}$ direction. What is the direction of $\mathbf{A} \times \mathbf{B}$?
1. $-\hat{x}$
2. $+\hat{y}$
3. $+\hat{z}$
4. $-\hat{z}$
5. Can't tell
Note:
* Correct Answer: D
* Use the right-hand rule
* Fall 2016: 0 0 23 [77]
In a typical Cartesian coordinate system, vector $\mathbf{A}$ lies along the $+\hat{x}$ direction and vector $\mathbf{B}$ lies along the $-\hat{y}$ direction. What is the direction of $\mathbf{B} \times \mathbf{A}$?
1. $-\hat{x}$
2. $+\hat{y}$
3. $+\hat{z}$
4. $-\hat{z}$
5. Can't tell
Note:
* Correct Answer: C
* Use right-hand rule; means $\mathbf{A} \times \mathbf{B} = - \mathbf{B} \times \mathbf{A}$
* Fall 2016: 0 0 [94] 6 0
<img src ="./images/cq_spherical.png" align="right" style="width: 350px";/>
### You derive it
Consider the radial unit vector ($\hat{r}$) in the spherical coordinate system as shown in the figure to the right.
Determine the $z$ component of this unit vector in the Cartesian $(x,y,z)$ system as a function of $r,\theta,\phi$.
Note:
This demonstrates that the r unit vector is a curious thing, in fact in contains all the information that is needed to define where you on the unit sphere. The other vectors can be though of as defined relative to that.
Altered for F2017 to be shorter, only work on z component
<img src ="./images/cq_vector_in_cylindrical.png" align="right" style="width: 350px";/>
In cylindrical (2D) coordinates, what would be the correct description of the position vector $\mathbf{r}$ of the point P shown at $(x,y) = (1, 1)$?
1. $\mathbf{r} = \sqrt{2} \hat{s}$
2. $\mathbf{r} = \sqrt{2} \hat{s} + \pi/4 \hat{\phi}$
3. $\mathbf{r} = \sqrt{2} \hat{s} - \pi/4 \hat{\phi}$
4. $\mathbf{r} = \pi/4 \hat{\phi}$
5. Something else entirely
Note:
* CORRECT ANSWER: A
* Fall 2016: [6] 90 3 0 1; Second vote (discussion and hint about units): [54] 35 4 1 4
How is the vector $\mathfrak{R}_{12}$ related to $\mathbf{r}_1$ and $\mathbf{r}_2$?
<img src ="./images/cq_r1r2.png" align="right" style="width: 350px";/>
1. $\mathfrak{R}_{12} = \mathbf{r}_1 +\mathbf{r}_2$
1. $\mathfrak{R}_{12} = \mathbf{r}_1 - \mathbf{r}_2$
1. $\mathfrak{R}_{12} = \mathbf{r}_2 - \mathbf{r}_1$
4. None of these
Note:
* CORRECT ANSWER: C
* Fall 2016: 6 1 [91] 1 0
Coulomb's Law: $\mathbf{F} = \frac{k q_1 q_2}{\left|\mathfrak{R}\right|^2}\hat{\mathfrak{R}}$ where $\mathfrak{R}$ is the relative position vector. In the figure, $q_1$ and $q_2$ are 2 m apart. Which arrow **can** represent $\hat{\mathfrak{R}}$?
<img src ="./images/cq_unit_r.png" align="center" style="width: 550px";/>
1. A
2. B
3. C
4. More than one (or NONE) of the above
5. You can't decide until you know if $q_1$ and $q_2$ are the same or opposite charges
Note:
* CORRECT ANSWER: D
* A unit vector has no units; so it's length is meaningless on a picture with units.
* Fall 2016 (hint given while still open): 14 10 9 [44] 23; students wanted to discuss E
You are trying to compute the work done by a force, $\mathbf{F} = a\hat{x} + x\hat{y}$, along the line $y=2x$ from $\langle 0,0 \rangle$ to $\langle 1,2 \rangle$. What is $d\mathbf{l}$?
1. $dl$
2. $dx\;\hat{x}$
3. $dy\;\hat{y}$
4. $2dx\;\hat{x}$
5. Something else
Note:
* CORRECT ANSWER: E
* It's $dx\;\hat{x}+dy\;\hat{y}$.
* Fall 2016 (given right at the end of class): 8 6 8 58 [20]; 5 0 3 38 [54]
You are trying to compute the work done by a force, $\mathbf{F} = a\hat{x} + x\hat{y}$, along the line $y=2x$ from $\langle 0,0 \rangle$ to $\langle 1,2 \rangle$. Given that $d\mathbf{l} = dx\;\hat{x}+dy\;\hat{y}$, which of the following forms of the integral is correct?
1. $\int_0^1 a\;dx + \int_0^2 x\;dy$
2. $\int_0^1 (a\;dx + 2x\;dx)$
3. $\frac{1}{2} \int_0^2 (a\;dy + y\;dy)$
4. More than one is correct
Note:
* CORRECT ANSWER: D
* All are correct forms, but B and C are ready to integrate.
* Fall 2016: 7 3 0 [90] 0