SET 1
/msuphysicslib/type35/msu-prob05a.txt
1. [1pt]
The wavefunction of a harmonic wave on a string is y(x,t) = 0.005 sin(43.7x + 378.0t), where
x and y are in m
and t is in s. What is the speed of the wave taking positive to be in the +x direction and
negative to be in the
-x direction.
/msuphysicslib/type35/msu-prob05b.txt
2. [1pt]
What is the wavelength of the traveling wave?
msuphysicslib/type35/msu-prob05c.txt
3. [1pt]
What is the period of this wave?
/msuphysicslib/type35/msu-prob06.txt
4. [2pt]
A steel piano wire, of length 1.15 m and mass 4.2 g is stretched under a tension of 440.0 N.
What is the speed of transverse waves on the wire?
/msuphysicslib/type35/msu-prob20a.txt
5. [1pt]
The transverse displacement of a streched string from equilibrium as a function of time and
position is given by :
y=0.13cos(3x+27t). x and y are in m; t is in s .
(Select T-True, F-False, G-Greater than, L-Less than, E-Equal to, If the first is T and the rest
F, enter TFFF .)
A) The speed of the wave is ..... 10 m/s
B) The wavelength is ..... 1 m
C) The period is ..... 0.1 s
D) The wave travels in the negative x direction
Answers:
1) -8.65 m/s 2) 1.44E-01 m 3) 1.66E-02 s
4) 3.47E+02 m/s 5) LGGT
SET 2
/msuphysicslib/type35/msu-prob21a.txt
1. [1pt]
A typical steel B-string in a guitar resonates in its fundamental frequency at 240 Hertz. The
length of the
string is 0.680 m. What is the wave velocity along the string ?
/msuphysicslib/type35/msu-prob21b.txt
2. [1pt]
The tension in the above string is 84.0 N. Calculate the mass of a 3 m long piece of the steel
string.
/msuphysicslib/type35/msu-prob21c.txt
3. [1pt]
Find the wavelength of the third harmonic of the guitar string described in the problem before
last.
/msuphysicslib/type37/msu-prob01a.txt
4. [1pt]
The length of the B string on a certain guitar is 58.0 cm. It vibrates at a fundamental
frequency of 246.0 Hz.
What is the speed of the transverse waves on the string?
/msuphysicslib/type37/msu-prob01b.txt
5. [1pt]
If the linear mass density of the guitar string is 1.50 g/m what should the tension be when the
string is in tune?
Hints:
1) see (normal modes) for the various modes of a string fixed at 2 ends, and use that the
velocity is the frequency times the wavelength.
2) from the velocity of the wave and the tension we can find the mass per unit length.
The total mass is the mass per unit length times the length.
4+5) Standing waves on a string
Answers:
1) 3.26E+02 m/s 2) 2.37E-03 kg 3) 4.53E-01 m 4) 2.85E+02 m/s 5)1.22E+02 N
SET 3
/msuphysicslib/type38/msu-prob06.txt
1. [1pt]
John is listening to a horn. He knows the frequency of the horn is 300 Hz when both he and
the horn are at rest. If he hears a pitch of 330 Hz, there are clearly several possibilities. (Give
ALL correct answers, i.e., B,AC, BCD )...
A) Both cannot be moving in the same direction.
B) The distance between John and the horn is increasing (decreasing) with time.
C) Both can be moving and have different speeds.
D) Both can be moving, in opposite directions.
E) John is moving towards (away from) the horn at rest.
F) Both can be moving and have the same speed.
/msuphysicslib/type38/msu-prob10.txt
2. [1pt]
A person standing close to a railroad crossing hears the whistle of an approaching train. He
notes that the
pitch of the whistle drops as the train passes by and moves away from the crossing. The
frequency of the
approaching whistle is 553 Hz; it drops to 470 Hz after the train is well past the crossing.
What is the speed of the train? Use 340 m/s for the speed of sound in air.
/msuphysicslib/type38/msu-prob07.txt
3.[1pt]
A student in a parked car honks the horn, which has a `proper' frequency of 290 Hz. An
observer in an approaching vehicle measures the frequency of the sound to be 322 Hz.
Calculate the speed of the approaching vehicle. Use 340 m/s as the speed of sound in air.
/msuphysicslib/type38/msu-prob13.txt
4. [1pt]
A driver sounds the horn of her car as she accelerates steadily from rest. Her direction is
directly away from
an audio recorder which is stationary. The recorded frequency changes from 480.0 Hz to
456.0 Hz in 3.60
s. What is the acceleration of the car? Speed of sound = 340 m/s.
Hints:
2) Find the ratio of frequency of the whistle before and after the crossing. That ration
does not include the frequency of the train at rest.
3) Use the doppler equation for approaching source and observer (plus sign).
4) Use the Doppler Effect to tell you the final speed, then use your linear motion
equations for constant acceleration to get the acceleration given the change in speed
and the time elapsed. Assume that the time it takes for the sound to get to the recorder
is negligible.
Answers:
1) CDEF 2) 2.76E+01 m/s 3) 3.75 E+01 m/s 4) 4.97E+00 m/s^2
SET 4
/msuphysicslib/type51/msu-prob01a.txt
1. [1pt]
What is the total charge of the thorium nucleus? (The neutral thorium atom has 90 electrons.)
/msuphysicslib/type51/msu-prob01b.txt
2. [1pt]
What is the magnitude of its electric field at a distance of 1.7 x10-10 m from the nucleus?
/msuphysicslib/type51/msu-prob01c.txt
3. [1pt]
What is the magnitude of the force on an electron at that distance?
/msuphysicslib/type51/msu-prob02.txt
4. [1pt]
It is known that the electric force of repulsion between two electrons is much stronger than
the gravitational attraction. For two electrons a distance `R' apart, calculate the ratio of the
size of the repulsion to that of the attraction.
Data: Mass of electron =9.11x10-31 kg;
Charge of electron =-1.60 x10-19 Coulombs.
G=6.673x10-11 Nm2/kg2.
k=8.99x109 Nm2/C2.
/msuphysicslib/type51/msu-prob03a.txt
5. [1pt]
Three charges, Q1, Q2, and Q3 are located in a straight line. The position of Q2 is 0.246 m to
the right of Q1. Q3 is located 0.180 m to the right of Q2. The force on Q2 due to its interaction
with Q3 is directed to the (Give ALL correct answers, i.e., B, AC, BCD...)
A) right if the two charges are negative.
B) left if the two charges have opposite signs.
C) right if the two charges have opposite signs.
D) left if the two charges are negative.
E) left if the two charges are positive.
/msuphysicslib/type51/msu-prob03b.txt
6. [1pt]
In the above problem, Q1= 2.24x10-6 C, Q2=-2.65 x10-6 C, and Q3= 3.18 x10-6 C. Calculate
the total force on Q2. Give with the plus sign for a force directed to the right.
Answers:
1) 1.44e-17 C 2) 4.49e+12 V/m 3)7.19e-07 N 4) 4.156e+42 5) CDE
5) 1.46e+00 N
SET 5
1. [1pt]
Which of the following statements for electric field lines are true? (Give ALL correct
answers, i.e., B, AC, BCD...)
A) E-field lines point inward toward negative charges.
B) E-field lines may cross.
C) E-field lines do not begin or end in a charge-free region (except at infinity).
D) Where the E-field lines are dense the E-field must be weak.
E) E-field lines make circles around positive charges.
F) A point charge q, released from rest will initially move along an E-field line.
G) E-field lines point outward from positive charges.
2. [1pt]
Consider two uniformly charged parallel plates as shown above. The magnitudes of the
charges are equal. (For each statement select T True, F False).
A) If the plates are oppositely charged, there is no electric field at c.
B) If both plates are negatively charged, the electric field at a points towards the top of the
page.
C) If both plates are positively charged, there is no electric field at b.
3. [1pt]
As shown in the figure above, a ball of mass 1.050 g and positive charge q =38.1microC is
suspended on a string of negligible mass in a uniform electric field. We observe that the ball
hangs at an angle of theta=15.0° from the vertical. What is the magnitude of the electric field?
Answers: 1) ACFG 2)TFT 3) 7.24e+01 N/C
SET 6
1. [1pt]
A solid metal sphere of radius a= 1.30 cm is surrounded by a concentric spherical metal shell
of inner radius b= 2.00 cm and outer radius c= 2.50 cm. The inner sphere has net charge Q1=
4.60 microCoulombs, and the outer spherical shell has net charge Q2= -8.10 microCoulombs.
What is the radial component of the electric field Er at a point located at radius r= 1.70 cm,
i.e. between the two conductors? (Er is positive if E points outward, negative if E points
inward.)
2. [1pt]
What is Er at a point located at radius r= 2.90 cm, i.e. outside the outer shell?
3. [1pt]
What is the surface charge density, sigmab, on the inner surface of the outer spherical
conductor?
4. [1pt]
What is the surface charge density, sigmac, on the outer surface of the outer spherical
conductor?
5. [1pt]
Consider the following arrangement of two conducting hollow spheres with a point charge of
Q0 = 4.10muC at the center. The inner sphere has a radius of 0.011 m and carries a net charge
of Q1=-2.70muC. The outer sphere has a radius of 0.061 m and carries a net charge of Q2 =
6.10muC.
Calculate the magnitude of the electric field at point A located at a distance 0.021 m from the
center.
6. [1pt]
Calculate the surface charge density on the outer surface of the outer sphere. Neglect the
thickness of the sphere.
Answers:
1) 1.431E+08 N/C 2) -3.741E+07 N/C 3) -9.151E-04 C/m^2
4)-4.456E-04 C/m^2 5) 2.85E+07 N/C 6) 1.60E-04 C/m^2
SET 7
1. [1pt]
The figure below shows two points in an E-field:
Point 1 is at (X1,Y1) = (3,4) in m, and
Point 2 is at (X2,Y2) = (12,9) in m.
The Electric Field is constant, with a magnitude of 74 V/m, and is directed parallel to the +Xaxis. The potential at point 1 is 1100 V. Calculate the potential at point 2.
2. [1pt]
Calculate the work required to move a negative charge of Q = -516 microC from point 1 to
point 2.
Note, in problem 3 you have 10 trials only!
Also, the equipotential contour spacing is 1kV.
3. [1pt]
The lines show the equipotential contours in the plane of three point charges, Q1, Q2, and Q3.
The values of the potentials are in kV as indicated for the +5, 0, and -5 kV contours. The
positions of the charges are indicated by the dots. (Give ALL correct answers, i.e., B, AC,
BCD...)
The letters are on the equipotential contours.
A) Charge Q3 has the largest magnitude of all.
B) The force on a proton at g points to the bottom of the page.
C) The electric field at i is stronger than at j.
D) Charge Q2 is the largest negative charge.
E) Q1 is a negative charge.
F) The electric field at k is zero.
4. [1pt]
Calculate the work required to move a charge of -0.47x10-12 C from `i' to `b'.
5. [1pt]
Calculate the size of the electric field at `g' .
6. [1pt]
Calculate the size of Q3. The magnitudes of the three charges are in the exact ratios of 1 to 2
to 3.
Answers:
1) 4.340e+02 V 2) 3.437e-01 J 3) ACE 4) 2.82e-09 J 5) 2.24e+05 V/m
6) 8.51E-09 C
SET 8
1. [1pt]
A capacitor consists of two closely spaced metal conductors of large area,
separated by a thin insulating foil. It has an electrical capacity of
3400 uF and is charged to a potential difference of 90.0 V. Calculate the amount of energy
stored in the capacitor.
2. [1pt]
Calculate the charge on this capacitor when the electrical energy stored in the capacitor is
6.75 J.
3. [1pt]
If the two plates of the capacitor have their separation increased by a factor of 3 while the
charge on the plates remains constant, by what factor is the energy stored in the capacitor
increased?
Note, in problem 4 you have 10 trials only!
4. [1pt]
Which statements are true for two oppositely charged, isolated parallel plates:
(C=capacitance, U=stored energy, +Q and -Q = charge on the plates). Note: Isolated plates
can not lose their charge. (Give ALL correct answers, i.e., B, AC, BCD...)
A) Inserting a dielectric increases C.
B) When the distance is doubled, C increases.
C) Increasing the distance increases the Electric field.
D) When the distance is doubled, U increases.
E) Inserting a dielectric increases Q.
F) When the distance is halved, Q stays the same.
G) Inserting a dielectric decreases U.
Answers:
1) 1.38e+01 J 2) 2.14e-01 C 3) 3 4)ADFG
SET 9
Note, in problems 1 and 2 you have 10 trials only!
1. [1pt]
The picture shows a battery connected to two wires in parallel. Both wires are made of the
same material and are of the same length, but the diameter of wire A is twice the diameter of
wire B.
(For each statement select T True, F False).
A) The current through the battery is five times larger than the current through wire B.
B) The voltage drop across wire B is larger than the voltage drop across wire A.
C) The resistance of wire B is four times as large as the resistance of wire A.
D) The resistance of wire B is twice as large as the resistance of wire A.
E) The power dissipated in wire A is 16 times the power dissipated in wire B.
2. [1pt]
Consider the three circuits shown above. All the resistors and all the batteries are identical.
(For each statement select T True, F False).
A) The total power dissipated in circuit C is twice the total power dissipated in circuit B.
B) The current through a resistor is the same in circuits A and C.
C) The current through a resistor is the same in circuits A and B.
D) The power dissipated in circuit A is twice the power dissipated in circuit B.
E) The voltage across a single resistor in circuit C is twice the voltage across a single resistor
in circuit B.
From now on you have 25 trials!
3. [1pt]
What is the equivalent capacitance Cab? DATA: C1=0.5 uF. C2=C3=0.27 uF.
4. [1pt]
If a 6.0 V battery is connected across ab, what is the charge on C2?
Answers:
1) TFTFF 2) FTFTT 3) 2.60e-01 uF 4) 7.79e-01 uC
SET 10
Note, in problem 1 you have 10 trials only!
1. [1pt]
The circuit which was at position a for a long time is suddenly switched to position b at time
t=0.
(For each statement select T True, F False).
A) In the instant after the switch is thrown the voltage across the resistor is zero.
B) In the instant after the switch is thrown, the voltage across the capacitor is zero.
C) The current through the resistor equals the current through the capacitor at all times.
D) In the instant after the switch is thrown the current through the capapacitor is zero.
2. [1pt]
What is Vc at time t=2.0 milliseconds?
DATA: R=415 ohm,
C=4.0 uF,
Vb=2.45 V.
3. [1pt]
Using the same data as above, consider the case when the switch is in position
b for a long time, then switched to position a at time t=0. What is Vc at time t=2.0
milliseconds?
4. [1pt]
Which of the following statements are correct for the RC circuit shown? (Give ALL correct
answers, i.e., B, AC, BCD...)
A) Right after S is moved to the position b, following a long time in the position a, the
potential across C is nearly zero.
B) If S is in the position a for a long time, the current through R approaches zero.
C) Right after S is moved to the position b, following a long time in the position a, the current
through R is zero.
D) If S is in the position a for a long time, the charge on C approaches zero.
E) Right after S is moved to the position b, following a long time in the position a, the
potential across C is close to E.
F) Right after S is moved to the position b, following a long time in the position a, the current
through R is E/R.
G) Right after S is moved to the position a, following a long time in the position b, the current
through R is zero.
A) If S is in the position a for a long time, the current through R approaches E/R.
B) The longer S is kept in the position a, the lower is the energy stored in C.
C) After S is in the position b for a long time, the current through R becomes close to zero.
D) If S is in the position b for a long time, the charge on C approaches CE.
E) If S is in the position b for a long time, the current through R approaches E/R.
F) After S is moved to b, it takes a time tau= RC, for the charge on C to drop to 1/e of its
initial value.
G) If S is in the position a for a long time, the current through R approaches zero.
Answers:
1) FFTF 2) 0.73 V 3) 1.72 V 4) BEF , CFG
SET 11
1. [1pt]
The rectangular loop shown below, carrying the current I, is located in a uniform magnetic
field of 0.35 T pointing in the negative y direction.
DATA:
h=8.0 cm w=7.5 cm theta=33.0° I=5.5A What is the magnitude of the magnetic dipole
moment of the loop?
/msuphysicslib/type61/msu-prob08b.txt
2. [1pt]
Calculate the magnitude of the torque about the z-axis on the loop.
A thin metal film of length 2.40cm, width of 0.60cm, and thickness of 24.0micrometers is
used to measure the Hall effect. A current of 1.50A is maintained along the length of the
sample. The Hall voltage of 26.2microVolts is detected across its width, when a magnetic
field of 1.60 Tesla is applied normal to the film.
3. [1pt]
Calculate the drift velocity of the charge carriers.
4. [1pt]
Assuming the charge carriers are electrons, calculate their density.
5. [1pt]
By measuring the voltage drop along the sample, the resistivity of the metal was found to be
2.00E-08Ohms-m. Find the ratio of the Hall electric field to the electric field responsible for
maintaining the electric current through the sample.
6. [1pt]
Consider two parallel conducting wires along the direction of the z axis as shown below. Wire
1 crosses the x-axis at x = -1.10 cm and carries a current of 3.50 A out of the xy-plane of the
page. Wire 2 (right) crosses the x axis at x = 1.10 cm and carries a current of 6.30 A into the
xy plane.
At which value of x is the magnetic field zero? (Hint: Careful with sign)
Answers:
1) 3.30E-02 J/T 2) 9.69e-03 N*m 3) 2.73E-03 m/s 4) 2.39E+28 m^-3
5) 2.10E-02 6) -3.85E+00 cm
SET 12
A 1000-turn loop (radius = 0.039 m) of wire is connected to a (20 ohm) resistor as shown in
the figure. A magnetic field is directed perpendicular to the plane of the loop. The field points
into the paper and has a magnitude that varies in time as B=gt, where g=0.25 T/s. Neglect the
resistance of the wire.
1. [1pt]
What is the magnitude of the potential difference between points a and b?
2. [1pt]
What is the electrical energy dissipated in the resistor in 32 s?
A conducting rod is pulled horizontally with constant force F= 4.00 N along a set of rails
separated by d= 0.260 m. A uniform magnetic field B= 0.800 T is directed into the page.
There is no friction between the rod and the rails, and the rod moves with constant velocity v=
3.90 m/s.
3. [1pt]
Using Faraday's Law, calculate the induced emf around the loop in the figure that is caused by
the changing flux. Assign clockwise to be the positive direction for emf.
4. [1pt]
The emf around the loop causes a current to flow. How large is that current? (Again, use a
positive value for clockwise direction.)
5. [1pt]
From your previous results, what must be the electrical resistance of the loop? (The resistance
of the rails is negligible compared to the resistance of the rod, so the resistance of the loop is
constant.)
6. [1pt]
The rate at which the external force does mechanical work must be equal to the rate at which
energy is dissipated in the circuit. What is that rate of energy dissipation (power dissipated)?
Hints:
1) The induce EMF is proportional to the number of turns and the change in
magnetic flux per coil. Why is the magnetic flux changing? Is the area
changing?
2) Is the EMF induced in the coil constant? What is the relation between power
and energy?
3) When the magnetic field is uniform and normal to the plane of the loop, then
the flux is of the product of the field and the area. In this problem it is the
area that changes with time, not the field
4) Remember F=ma: since v is constant, a=0, so it must be true that the net force
on the rod is zero. The pulling force is compensating the force on the rod due
to the current through it and the magnetic field.
5) Use Ohms Law.
6) You can either calculate the mechanical power generated by the external
force, or the electrical power dissipation in the circuit. Do it both ways to
check your answer.
Answers:
1) 1.195e+00 V 2) 2.283e+00 J 3) -8.11E-01 V 4) -1.92E+01 A
6) 4.22E-02 Ohm 6) 1.56E+01 W
SET 13
1. [1pt]
The switch in the above diagram is closed after being open for a very long time, during which
the capacitor has lost all of its charge.
(For each statement select T True, F False).
A) In the instant after the switch is closed, the voltage across the inductor equals the voltage
across the battery.
B) A long time after the switch is closed, the current through the resistor is zero.
C) A long time after the switch is closed, the voltage across the capacitor equals the voltage
across the battery.
D) In the instant after the switch is closed, the voltage across the capacitor equals the voltage
across the battery.
A very long solenoid with a circular cross section and radius r1= 1.80 centimeters with ns=
290 turns/cm lies inside a short coil of radius r2= 3.50 centimeters and Nc= 47 turns.
2. [1pt]
If the current in the solenoid is ramped at a constant rate from zero to Is= 2.00 Amperes over a
time interval of 88.0 milliseconds, what is the magnitude of the emf in the outer coil while the
current in the solenoid is changing?
/msuphysicslib/type66/msu-prob05b.txt
3. [1pt]
What is the mutual inductance between the solenoid and the short coil?
/msuphysicslib/type66/msu-prob05c.txt
4. [1pt]
Now reverse the situation. If the current in the short coil is ramped up steadily from zero to
Ic= 3.30 Amperes over a time interval of 24.0 milliseconds, what is the magnitude of the emf
in the solenoid while the current in the coil is changing?
5. [1pt]
The switch S in the following circuit is closed after having been open for a very long time.
The current through the battery immediately after the switch is closed is i(t=0) and the value
after a very long time t is i(t->infinity). Calculate the ratio i(t=0)/i(t->infinity).
EMF = 3.0 V
R_1 = 80.0 ohm
R_2 = 20.0 ohm
L = 30.0 mH
Hints:
1) Non-ideal capacitors keep charge only for a limited time.
2) Use Faraday's Law.
3) Look up the definition of mutual inductance. You already did most of the
work in the previous problem.
4) The mutual inductance is the same both ways: M12=M21. You don't need to
start all over with Faraday's Law.
Answers:
1) TTTF 2) 3.96E-02 V 3) 1.74E-03 H 4) 2.40E-01 V 5) 8.00e-01