Download Practice Problems without Answers Part 2 rev 4

Practice Problems – Part 2
TF: Widagdo Setiawan, [email protected]
1. Logic problem
a. Write down the truth table
b. Write down the Boolean expression for H(A,B)
2. Give the Boolean expression for the following circuits
3. Write down the Boolean expression for the following truth table
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
F(A,B,C)
1
0
0
0
1
1
0
1
G(A,B,C)
0
0
0
1
0
1
1
1
4. Write and XOR in terms of AND, OR, and NOT
5. Parity bits
We would like to create a device that takes three inputs, 𝐴, 𝐵, 𝐶 and gives one output, 𝑃, the parity
of the inputs. In other words, the output is one if there are an odd number of ones among the
inputs, and zero otherwis
a. Write down the truth table for this device
b. Draw a logic diagram showing an implementation of the parity bit generator
6. A mass spectrometer accelerates doubly ionized atoms over a potential difference 𝑉 before they
enter a uniform magnetic field 𝐵 which is perpendicular to the direction of motion of the ions. If 𝑑 is
the radius of the ions’ path in the magnetic field, what is the mass of one ion?
7. A current 𝐼 goes through a rectangular wire in the direction shown with the arrows in the figure. The
dimensions of the rectangle are 𝑎 and 𝑏 as shown. A uniform magnetic field of strength 𝐵 is in a
direction perpendicular to the paper as shown in the picture. What is the torque on the rectangular
loop?
8. Same as previous problem, but this time, the magnetic field is pointing to the left.
9. Charged particle velocity selector
An electron with velocity 𝑣 to the right enters a parallel plate capacitor with separation between the
plates 𝑑 (see picture below). At the capacitor, there is magnetic field going out of the page with
magnitude 𝐵. The capacitor is connected to a battery. What battery voltage 𝜀 do we have to use so
that the electron can travel through the capacitor without being deflected?
10. True or false questions:
⃑⃑ force
a. Charged particles in a magnetic field cannot experience an acceleration due to the 𝑣⃑ × 𝐵
⃑⃑ force
b. Charged particles in a magnetic field cannot change speed due to the 𝑣⃑ × 𝐵
c. A positive charge and a negative charge turn in the opposite direction under uniform magnetic
field
d.
e.
f.
g.
Magnetic field lines start at the north pole of a magnet, and end at the south pole of the magnet
The magnetic south pole of the earth is located near the earth’s north pole
Magnetic field lines go from the south pole to the north pole inside a magnet.
NASA’s tether experiment generated electric power by moving a very long conducting wire
(attached to the shuttle) through the Earth’s magnetic field. The electric energy that was
generated was at the expense of the kinetic energy (thus speed) of the shuttle.
h. When a magnetic flux through a conducting loop is zero, there cannot be an induced EMF in that
loop
11. An electron is traveling with a constant velocity 𝑣 as shown in the picture below. The electron enters
a region with uniform magnetic field 𝐵. Which of the following trajectories best describes the
electron’s motion in this region
12. An electron is traveling with a constant velocity 𝑣 as shown in the picture below. The electron enters
a region with uniform magnetic field 𝐵. Which of the following trajectories best describes the
electron’s motion in this region
13. Two wires, each carrying current of 10 𝐴 in the same direction are separated by 1 𝑚. Calculate the
force per unit length on these wires.
14. Electromagnetic pump on molten metal. (Irodov 3.261)
In an electromagnetic pump designed for transferring molten metals, a pipe section with molten
metal inside is located in a uniform magnetic field 𝐵. A current 𝐼 is made to flow across this pipe
section in the direction perpendicular both to the vector 𝐵 and to the axis of the pipe. Find the
pressure difference produced by the pump. 𝐵 = 0.1𝑇, 𝐼 = 100 𝐴, 𝑎 = 2 𝑐𝑚.
15. Rail Gun
Consider the following setup
A pair of conducting rails with negligible resistance is placed horizontally. A bar of mass 𝑀 = 1 𝑘𝑔
with resistance = 10 Ω , and length 𝐿 = 2 𝑚, that can freely move is placed on top of these rails,
initially at rest. A magnetic field of magnitude 𝐵 = 5 𝑇 is applied on the entire setup with the
direction shown on the picture above. A battery with voltage 𝜀 = 1000 𝑉 is then connected to the
rails as shown in the figure. Ignore Faraday’s law in this problem. Assume that there is no friction.
Ignore the magnetic field generated by the rails and the bar.
a) What happen with the bar qualitatively after the battery is connected?
b) What is the initial acceleration of the bar just after the battery is connected?
c) Write down the relevant differential equation to describe the system above involving the
position of the bar
d) Calculate the position of the bar as a function of time
e) Calculate the velocity of the bar as a function of time
f) How long does the rail have to be in order for the bar to escape the earth’s gravitational field?
16. Rail gun with Faraday’s law.
Same problem as before, but this time, you cannot neglect Faraday’s effect. You can still neglect the
induced magnetic field. This problem captures a lot of things that you learn for the past few weeks:
current, voltage, magnetic field, magnetic force, EMF. The math is similar to the capacitor charging
problem. This could be a nice but extremely hard exam problem.
a) What happen with the bar qualitatively after the battery is connected?
b) What is the initial acceleration of the bar just after the battery is connected?
c) Write down the relevant differential equation to describe the system above involving the
position of the bar
d) What is the terminal velocity of the bar?
e) Calculate the velocity of the bar as a function of time
f) Calculate the position of the bar as a function of time
g) Can the bar ever escape the earth’s gravitational field? If yes, what is the minimum length of the
rail? If not, what parameter should you change (and to what value), such that the bar can
escape the earth’s gravitational field.
17. A simple electric generator (as shown below) is rotating about the y-axis with a frequency of 𝑓.
There is a uniform magnetic field 𝐵 in the +𝑧 direction. The rotor consists of a coil of 𝑁 windings
each with an area of 𝑆. The generator, through slipping contacts, is powering a light bulb whose
resistance is 𝑅 (see the figure). The ohmic resistance of the coil is negligibly small compared to that
of the light bulb. You may also assume here, for simplicity, that the self-inductance of the coil is
negligibly small.
a. What is the maximum value magnetic flux?
b. What is the maximum value 𝐼𝑚𝑎𝑥 of the induced current? (Note that the current
changes as a function of time). Also indicate in the figure one of the two positions of the
coil when this maximum current occurs.
18. A Conducting bar of length D rotates with angular frequency 𝜔 about a pivot P at one end of the bar
(see the figure). The other end of the bar is in slipping contact with a stationary conducting wire in
the shape of a circle (we only show a smaller part of that circle to keep the drawing simple).
Between point P and the circular wire, there is a resistor R as shown. Thus the bar, the resistor and
the arc form a closed conducting loop. The resistance of the bar and the circular wire are negligibly
small. There is a uniform magnetic field B everywhere, it is perpendicular to the plane of the paper
as indicated.
What is the induced current in the loop? Express your answer in terms of 𝐷, 𝜔, 𝑅, and 𝐵.
19. In the figure below, a uniform magnetic field points into the page. (The magnetic field vectors are
indicated by the ⨂’s ). Four particles with the same mass and different electric charges follow the
paths shown as they pass through this magnetic field with identical, constant speed. Ranks the
charges from the least to the greatest? (Remember, any negative number is smaller than any
positive number)
20. MRI Concept questions:
a. What is Larmor frequency?
b. How do you select the plane that you want to image?
c. When should we turn the 𝐵0 on/off?
d. When should we turn the 𝐵1 on/off?
e. What is the oscillation frequency of 𝐵0 ?
f. What is the oscillation frequency of 𝐵1 ?
g. What particle does typical MRI machine image?
h. What are the differences between MRI imaging and x-ray imaging?
21. Spherical Mirror (Past exam)
An object is placed on the axis of a spherical mirror. The radius of curvature of the mirror is 𝑅. As a
function of the distance 𝑥 from the mirror to the object,
a. Sketch the distance 𝑦𝑖 from the image position to the mirror. Indicate the meaning of any
relevant signs. Indicate on the plot the focal point and the role of the radius R, and show where
𝑦𝑖 = 𝑥
b. Sketch the magnification of the image. Indicate the meaning of any relevant signs. Indicate on
the plot the focal points and the role of the radius 𝑅. Label any points where the magnification is
1, 0, or −1.
22. Mirascope
Mirascope, can be purchased for $6.83 at amazon.com) is constructed by having two concave mirror
facing each other as shown in the figure above (shiny sides are on the inside). We then put an object
on the bottom of this device (represented by the purple arrow). The two mirrors create images
sequentially, creating the final image above the mirascope itself represented by the green arrow.
The final image is inverted. We also know that the two mirrors have the same curvature. Finally, we
also know that the image looks weird but awesome.
a.
b.
c.
d.
Is the image real or virtual?
Which one is the first mirror and which one is the second mirror?
What is the focal length of the two mirrors given the information that we have?
Is this a hologram?
23. Light sail
Consider a mirror with mass 𝑚 = 1 gram floating in space initially at rest (it’s not mounted to
anything). A 100 Watt laser beam shines at the mirror. How long do we have to wait until the mirror
reach 100 𝑘𝑚/ℎ𝑜𝑢𝑟? Note that the mirror reflects the laser beam.
24. Slowing down atom
A Sodium atom moves at 1500 m/s. We shine a laser beam at 589 nm from the opposite side to slow
down this atom.
a. How many photons does the atom need to absorb until the atom does not move anymore?
b. If the atom can absorb 6 million photons per second, how long does it take to slow down this
atom?
c. How far does the atom travel during the slowing process?
25. Photodiode
You have a photo diode which is a device that converts photon into electron. You shine 1 mW laser
beam at 589 nm on the photodiode. What current do you measure coming out of the photodiode?
26. Photoelectric effect
Consider a setup shown in figure above. We shine a laser on the bottom plate. We then measure the
current on the Ampere meter.
a. Set V=0. You have 2 lasers, one at 300 nm and one at 900 nm (both are invisible). You do not
know which one is which. Let’s call the laser A and B. You shine laser A, then you measure the
current. The current is zero. When you shine laser B however, you measure some current. What
wavelength is laser A?
b. You shine laser B on the bottom plate and you measure some current. What do you have to do
with V to make the current goes to zero? (apply negative V or positive V)?
c. You increase the magnitude of V slowly while measuring the current. When the magnitude of V
is exactly 1 V, you see the current goes to zero. What is the work function of the bottom plate?