I feel that Exam 2 was a fair assessment.

1. Strongly Agree
2. Agree
3. Neither Agree/Disagree
4. Disagree
5. Strongly Disagree

I feel that Exam 2 was aligned with what we have been doing (in class and on homework).

1. Strongly Agree
2. Agree
3. Neither Agree/Disagree
4. Disagree
5. Strongly Disagree

I felt better prepared for Exam 2 than Exam 1.

1. Strongly Agree
2. Agree
3. Neither Agree/Disagree
4. Disagree
5. Strongly Disagree

A proton (speed $v$) enters a region of uniform $\mathbf{B}$. $v$ makes an angle $\theta$ with $\mathbf{B}$. What is the subsequent path of the proton?

1. Helical
2. Straight line
3. Circular motion, $\perp$ to page. (plane of circle is $\perp$ to $\mathbf{B}$)
4. Circular motion, $\perp$ to page. (plane of circle at angle $\theta$ w.r.t. $\mathbf{B}$)
5. Impossible. $\mathbf{v}$ should always be $\perp$ to $\mathbf{B}$

In the first stage of the mass spectrometer, with $\mathbf{E} = E_0 \hat{z}$ (pointing upward) and $\mathbf{B} = B_0 \hat{x}$ (pointing out of the page), which particles travel through in a straight line?

1. All particles regardless of speed
2. Particles with speed $B_0/E_0$
3. Particles with speed $E_0/B_0$
4. Can't tell without knowing $q$ and/or $m$

You may assume all particles move exclusively in the +y direction.

If we place a physical filter (i.e., a piece of metal with a thin slot that is a bit larger than the beam width to avoid diffraction) at the end of the first stage, which particles (assume they are all positively charged) hit the upper-part of the filter? Which hit the lower part?

1. Fast moving particles hit the upper part; slow ones hit the lower part
2. Slow moving particles hit the upper part; fast ones hit the lower part
3. It's not possible to tell without $q$ and/or $m$

Can we use the same mass spectrometer set up for negatively and positively charged particles? That is, will our set up distinguish between particles of a given mass and differently-signed charges?

1. Yes
2. No

For our velocity selector where $\mathbf{E}=E_0\hat{z}$ and $\mathbf{B} = B_0 \hat{x}$ and we start particles from rest, we end up with the following coupled equations of motion,

$$m\dot{v}_y = q v_z B_0$$ $$m\dot{v}_z = q E_0 - q v_y B_0$$

How might we solve them for $y(t)$ and $z(t)$?

1. Just integrate the equations of motion
2. Guess the general solution
3. Take the time derivative of one and plug into the other
4. Give up???