A point charge + q rests halfway between two steady streams of positive charge of equal charge per unit length (, moving opposite directions and each at c / 3 relative to point charge. With equal electric forces on the point charge, it would remain at rest. Consider the situation from a frame moving right at c / 3 . (a) Find the charge per unit length of each stream in this frame. (b) Calculate the electric force and the magnetic force on the point charge in this frame, and explain why they must be related the way they are. (Recall that the electric field of a line of charge is λ / 2 π ε 0 r , that the magnetic field of a long wire is μ 0 I / 2 π r , and that the magnetic force is q v × B . You will also need to relate ( and the current I.)
A point charge + q rests halfway between two steady streams of positive charge of equal charge per unit length (, moving opposite directions and each at c / 3 relative to point charge. With equal electric forces on the point charge, it would remain at rest. Consider the situation from a frame moving right at c / 3 . (a) Find the charge per unit length of each stream in this frame. (b) Calculate the electric force and the magnetic force on the point charge in this frame, and explain why they must be related the way they are. (Recall that the electric field of a line of charge is λ / 2 π ε 0 r , that the magnetic field of a long wire is μ 0 I / 2 π r , and that the magnetic force is q v × B . You will also need to relate ( and the current I.)
A point charge
+
q
rests halfway between two steady streams of positive charge of equal charge per unit length (, moving opposite directions and each at
c
/
3
relative to point charge. With equal electric forces on the point charge, it would remain at rest. Consider the situation from a frame moving right at
c
/
3
. (a) Find the charge per unit length of each stream in this frame. (b) Calculate the electric force and the magnetic force on the point charge in this frame, and explain why they must be related the way they are. (Recall that the electric field of a line of charge is
λ
/
2
π
ε
0
r
, that the magnetic field of a long wire is
μ
0
I
/
2
π
r
, and that the magnetic force is
q
v
×
B
. You will also need to relate ( and the current I.)
How can you tell which vowel is being produced here ( “ee,” “ah,” or “oo”)? Also, how would you be able to tell for the other vowels?
You want to fabricate a soft microfluidic chip like the one below. How would you go about
fabricating this chip knowing that you are targeting a channel with a square cross-sectional
profile of 200 μm by 200 μm. What materials and steps would you use and why? Disregard the
process to form the inlet and outlet.
Square Cross Section
1. What are the key steps involved in the fabrication of a semiconductor device.
2. You are hired by a chip manufacturing company, and you are asked to prepare a silicon wafer
with the pattern below. Describe the process you would use.
High Aspect
Ratio
Trenches
Undoped Si Wafer
P-doped Si
3. You would like to deposit material within a high aspect ratio trench. What approach would you
use and why?
4. A person is setting up a small clean room space to carry out an outreach activity to educate high
school students about patterning using photolithography. They obtained a positive photoresist, a
used spin coater, a high energy light lamp for exposure and ordered a plastic transparency mask
with a pattern on it to reduce cost. Upon trying this set up multiple times they find that the full
resist gets developed, and they are unable to transfer the pattern onto the resist. Help them
troubleshoot and find out why pattern of transfer has not been successful.
5. You are given a composite…
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