PHYS 251 FINAL EXAM 7/7/06 Dr. Holmes NAME
DO ALL FIFTEEN PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED BESIDE THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT. USE MKS UNITS IN ALL ANSWERS UNLESS OTHERWISE SPECIFIED.
For problems 1 through 3, consider the following situation: point C located
at (+9 m, 0 m);
qA = 7 mC located
at (0 m, +2 m); qB = -5 mC located at ( 0 m, -6 m).
1) a) What is the magnitude and direction of the force on qA due to the presence of qB ?
magnitude: 4.92 x 10-3 Nt.
direction: down, or 270 degrees, or -y.
b) Is the magnitude of the force on qB due to the presence of qA [smaller than, the same as, or larger than] the magnitude of the force on qA due to the presence of qB ?
same.
c) Is the direction of the force on qB due to the presence of qA [the same as, opposite to, or other than] the direction of the force on qA due to the presence of qB ?
opposite.
2) a) What is the magnitude and direction of the electric field at point C due to qA ONLY ?
magnitude: 741.2 Nt/Coul.
direction: -12.5 degrees.
b) What is the magnitude and direction of the total electric field at point C due to both qA and qB ?
magnitude: 550.3 Nt/Coul.
direction: -42.8 degrees.
c) What would be the magnitude and direction of the electric force on an electron placed at position C ?
magnitude: 8.8 x 10-17 Nt.
direction: 137.2 degrees.
3) Consider the same two charges at the same locations as in prob #1.
a) What is the voltage at the point C due to the presence of the two charges qA and qB (assuming that the voltage at infinity is zero) ?
2,673 volts.
b) How much energy would it take to bring a third charge of -4 nCoul from very far away and place it at the point C ?
-1.07 x 10-5 Joules.
c) Would this process take energy or would it give up energy?
Give up energy.
For problems 4 and 5, consider the following situation: two parallel plates, each of area 36 cm2 (6 cm x 6 cm) are separated by 5 mm with vacuum initially between the plates. One plate is directly above the other plate. A voltage of 40 volts is placed across the two plates with the top plate having the higher voltage.
4. a) What will the electric field be 4 mm above the bottom plate (1 mm below the top plate)?
magnitude: 8,000 Nt/Coul.
direction: down, or toward the bottom plate.
b) Will the electric field get [stronger, weaker, or stay the same in magnitude] as you approach the top plate (go from 4 mm above the bottom plate to more than 4 mm above the bottom plate)?
same.
c) What is the electric field at a distance of 1 mm above the top plate?
magnitude: zero.
direction: (none).
5) a) How much charge is on the top plate?
2.55 x 10-10 C.
b) Does the top plate or does the bottom plate have the positive charge?
top.
c) What is the capacitance of this parallel plate system?
6.37 pF.
d) How much energy does this capacitor store with this charge and voltage on it?
5.09 x 10-9 Joules.
6) Consider three resistors, the first two are connected in series and this combination is connected to a third in parallel. The resistors have resistances of: R1 = 2 ohms, R2 = 6 ohms, and R3 = 12 ohms.
a) What is the effective resistance of these three connected in this way?
4.80 ohms.
b) ) If the resistors
were replaced by capacitors with C1 = 2 nF, C2 = 6 nF and
C3 = 12 nF, what would the effective capacitance of the three
capacitors be for this hookup?
13.5 nF.
7) Consider the
situation to the right: The resistor
has a resistance of 8,500 ohms and the capacitor has a capacitance of 35 nF,
and the battery has a voltage of 40 volts.
a) How long will it take the capacitor to lose half (50%) of its charge after the switch to the battery is opened?
2.06 x 10-4 sec.
b) How long will it take for the capacitor to lose 95% of its charge (have 5% left)?
8.91 x 10-4 sec.
c) If the capacitance were increased, would the times for parts a and b above [increase, stay the same, or decrease]?
increase;
IN ALL CASES INVOLVING DIRECTIONS, EXPRESS YOUR ANSWER AS ONE OF THE FOLLOWING: {UP, DOWN, NORTH, EAST, SOUTH, OR WEST}. (DO NOT EXPRESS IT AS INTO THE PAPER OR OUT OF THE PAPER!)
USE MKS UNITS IN YOUR ANSWERS UNLESS OTHERWISE SPECIFIED.
8) a) A electron is moving toward the West with a speed of 5 x 104 m/s in a magnetic field of strength 0.44 T directed down. What is the magnetic force on the electron:
magnitude: 3.52 x 10-15 Nt.
direction: North.
b) If the particle were an proton moving at the given speed in the same magnetic field, would the magnetic force on the proton be more (>), the same (=), or less (<) in magnitude than on the electron?
= (same).
c) Would the direction of the magnetic force on the proton be the same or different (if different, specify the new direction) than on the electron?
opposite (South).
d) Assuming the field were constant, the electron would: [move in a straight line and begin to go faster, move in a straight line and start to slow down, move in a circle with the same radius as the proton, move in a circle with a smaller radius than the proton, move in a circle with a bigger radius than the proton]?
move in a circle with a smaller radius than the proton.
9) A solenoid has a length of 20 cm,
a radius of 3 cm, and 2,400 windings wound around it. A current of 1.2 amps flows
through the solenoid.
a) What is the magnitude of the
magnetic field at the center of the solenoid?
.0181 Teslas (aprox) or
.0173 Teslas (exact)
b) Is this an "exact" or
"approximate" calculation?
c) Is the "approximate" value
higher, the same, or lower than the
"exact" value?
Higher.
d) In this case, by what percent does
the "approximate" value
differ from the "exact" value?
4% .
10) A rectangular loop of wire of width («) 8 cm and length (b) 5 cm is placed horizontally in a region where the magnetic field is .034 Teslas in strength (the North pole of the magnet is on the West side of the loop and South pole of the magnet is on the East side). A current of 1.7 Amps flows counter-clockwise (as viewed from above) through the wire. Use the direction convention indicated on the first page (N, E®, S¯, W¬, up¤, downÄ) .
a) What will be the magnetic force on the North side of the loop?
Magnitude: zero;
Direction: none
b) What will be the magnetic force on the East side of the loop?
Magnitude: .0029 Nt;
Direction: down Ä
c) Will the force on the West side be equal and opposite to that on the East side (yes or no)?
Yes.
d) Which direction will the TOTAL magnetic FORCE on the rectangular current loop be? (specify direction or answer none if force is zero)
none.
e) Which direction will the total magnetic TORQUE on the rectangular current loop be? (specify direction or answer none if torque is zero)
North.
11) DESIGN an electric generator that will provide an rms voltage of 1,000 volts. Both DRAW A DIAGRAM and indicate the values for all parameters.
12) Clearly draw in the direction of the induced current in each of the
three diagrams, or write NONE if there is no induced current.
13 ) Consider a series LRC circuit with an oscillating voltage source of 20 volts (rms) at 1,200 Hz. The resistance is 15 W, the capacitance is 3 mF, and the inductance is 7 mH. What is the:
a) capacitive reactance (XC)?
44.21 ohms;
b) inductive reactance (XL)?
52.78 ohms;
c) impedance (Z) of the circuit?
17.27 ohms;
d) rms current in the circuit?
1.16 A;
e) What is the rms voltage across the capacitor (V-rms)?
51.2 volts.
14) a) Given that the intensity of a sound wave of frequency 285 Hz is 4.0 x 10-6 W/m² , what will its intensity be if the frequency of the sound wave is increased by a factor of 6 and the amplitude stays constant:
in Watts/m2 1.44 x 10-4 W/m2;
in dB: 81.6 dB.
b) Given that the intensity of a sound wave of frequency 85 Hz is 85 dB at a distance of 2 meters from the speaker, what will its intensity be at a distance of 9 meters from the speaker::
in Watts/m2 1.56 x 10-5 W/m2;
in dB: 71.9 dB.
15) ) Assume the speed of sound in this room is 345 m/s. Consider a speaker that produces a sound of frequency 5,000 Hz. (In parts a and b, consider the air to be still ‑ no wind.)
a) Suppose that the speaker is held stationary, and you head toward the speaker at a speed of 35 m/s. What frequency will you measure for the sound?
5,507.2 Hz.
b) Suppose that you are stationary and the speaker goes toward you at a speed of 22 m/s. What frequency will you now measure for the sound?
5,340.6 Hz.
c) Suppose that the speaker of frequency 5,000 Hz is mounted on a train that is leaving the station going North at 22 m/s, you are approaching the station (and the train) going South at a speed of 35 m/s, and there is a wind blowing North (from the South) at a speed of 12 m/s (relative to the station). What will you measure for the frequency of the sound [you must be precise: answer to the closest Hz]?
5,850.8 Hz.