Exam 4 Review
Exam 4 Review
Exam 4 Review
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Physics 2020 Summer 2011<br />
Richard Ingebretsen<br />
REVIEW FOR MIDTERM 4<br />
1. A small 2.00 g plastic ball suspended by a 20.0 cm long string (R) is in a uniform electric<br />
field (E = 10 3 N/C), as shown.<br />
A. If the ball is in equilibrium when the string makes a 15° angle with the vertical.<br />
What is the net charge on the ball?<br />
B. If the charge on the ball were doubled, what would be the new angle that it<br />
hangs at, relative to the vertical? [Hint: It is not 30°.]<br />
2. A. Positive charges are situated at three corners of a rectangle as<br />
shown. Find the magnitude and direction of the electric field at the<br />
fourth corner. (Give the direction relative to the x-axis.)<br />
3. A small drop of water is suspended in air by a uniform electric field. The field is directed upward with a<br />
magnitude of 8480.0 N/C. The mass of the water drop is 3.5 × 10 -9 kg. Neglect the buoyant force acting on<br />
the drop.<br />
(a)<br />
(b)<br />
Is the excess charge on the water drop positive or negative. Show all work.<br />
How many excess electrons or protons reside on the drop? The magnitude of an electron (proton)<br />
charge is 1.60 × 10 -19 C. Show all work.<br />
4. A point charge Q of !0.70 :C is fixed to one corner of a square. An identical charge is fixed to the<br />
diagonally opposite corner. A point charge q is fixed to each of the remaining corners. The net force acting<br />
on either of the charges (q) is zero. Find the magnitude and algebraic sign of q.<br />
5. Two identidal small plastic balls (mass = 2.00 g) are suspended by 20.0 cm<br />
long strings. If the balls are in equilibrium when the strings make a 15.0°<br />
angle with the vertical, what is the charge on the balls?<br />
k = 8.99 × 10 9 N@m 2 /C 2
6. A. A parallel plate capacitor has an area of 5.00 cm 2 , and the plates are separated by 1.00 cm with air<br />
between them. It stores a charge of .004 :C. [dielectric constant of air is 1.0; permittivity of free<br />
space , o = 8.85 × 10 !12 C 2 /(N@m 2 )]<br />
(a)<br />
(b)<br />
What is the potential difference across the plates of the capacitor?<br />
What is the magnitude of the uniform electric field in the region between the plates?<br />
B. Calculate the speed of an electron that is accelerated from rest through a potential difference of<br />
120 V.<br />
electron mass = 9.11 × 10 !31 kg;<br />
electron charge = 1.60 × 10 !19 C<br />
7. A. A 5.00 g charged insulating ball hangs on a 30.0 cm long string in a uniform<br />
horizontal electric field as shown. If the charge on the ball is 1.00 :C, find the<br />
strength of the field.<br />
8. Four point charges are fixed at the corners of a square with sides of length d.<br />
(a)<br />
(b)<br />
Find the direction and magnitude of the net electrostatic force exerted on the point charge q 3 . Let<br />
q = +2.4 :C and d = 33 cm.<br />
Now, the length d is doubled. Find the direction and magnitude of the<br />
net electrostatic force exerted on the point charge q 3 .<br />
q 1 = +q<br />
q 2 = -2.0 q<br />
q 3 = -3.0 q<br />
q 4 = -4.0 q<br />
9. A. An object with a charge of -3.6 :C and a mass of 0.012 kg experiences an upward electric force,<br />
due to a uniform electric field which is equal in magnitude to its weight.<br />
(a)<br />
(b)<br />
Find the direction and magnitude of the electric field.<br />
If the electric charge on the object is doubled while its mass remains the same, find the<br />
direction and magnitude of its acceleration.<br />
B. A small object of mass 0.025 kg and charge 3.1 :C hangs from the ceiling by a thread. A second<br />
small object, with a charge of 4.2 :C, is placed 1.5 m vertically below the first charge.<br />
(a)<br />
(b)<br />
Find the electric field at the position of the upper charge due to the lower charge.<br />
Calculate the tension in the thread.<br />
10. A small plastic ball with mass 8.00 × 10 -3 kg and charge +0.200 :C is suspended<br />
from an insulating thread and hangs between the plates of a capacitor as shown in<br />
the drawing. The ball is in equilibrium, with the thread making an angle of 30.0°<br />
with respect to the vertical. The area of each plate is 0.020 m 2 and the distance<br />
between the plates is 1.00 × 10 -4 m.. There is air between the plates (dielectric<br />
constant of air = 1.0). Permittivity of free space = 8.85 × 10 -12 C 2 /(NAm 2 ).<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
(e)<br />
What is the magnitude of the charge on each plate?<br />
What is the capacitance of this capacitor?<br />
Find the potential difference between the two plates.<br />
How much energy is stored by the capacitor?<br />
Replace the air between the plates with argon (dielectric constant = 1.5). Would the angle<br />
decrease, increase or stay the same? Explain. You may use equations if you find them helpful.
11. A -15 :C charge with a mass of 2 × 10 -3 kg is fixed in place on the x-axis at x = - 2.0 m. A second charge of<br />
+12 :C with a mass of 4 × 10 -3 kg is fixed in place on the x-axis at x = 3.0 m. [k = 8.99 × 10 9 NAm 2 /c 2 ]<br />
(a)<br />
(b)<br />
(c)<br />
At what point along the x-axis is the net electric field zero?<br />
Find a point along the x-axis where the electric potential is zero.<br />
If the +12 :C charge were not fixed in place, what would the initial acceleration be (magnitude<br />
and direction)?<br />
12. The drawing shows six point charges arranged in a rectangle. The<br />
value of q is 5.0 :C, and the distance, d, is 0.20 m. Find the total<br />
electric potential at location p, which is at the center of the rectangle.<br />
[k = 8.99 × 10 9 NAm 2 /c 2 ]<br />
13. Two charges, q 1 = +10.0 :C at x 1 = -5.0 cm, and q 2 = +10.0 :C at x 2 = -6.0 cm, are located on the x-axis.<br />
Two other charges, q 3 = -5.0 :C at y 3 = -5.0 cm and q 4 = +6.0 :C at y 4 = +6.0 cm, are located on the y-axis.<br />
[k = 8.99 × 10 9 NAm 2 /c 2 ]<br />
(a)<br />
(b)<br />
(c)<br />
Find the magnitude of the net electric field at the origin.<br />
Find the direction (the acute angle measured with respect to the x-axis) of the net electric field at<br />
the origin.<br />
You add a fifth charge, +8 :C. What would be the x and y coordinates of it’s position in order to<br />
make the field at the origin zero?<br />
14. Two small plastic balls, each with mass 4.00 × 10 -3 kg and charge<br />
+0.200 nC, are suspended from insulating threads (R = 5 × 10 -5 m) and<br />
hang between the plates of a capacitor (see drawing). The balls are in<br />
equilibrium. Each thread makes an angle of 50.0/ with respect to the<br />
vertical. The area of each plate is 0.030 m 2 and the distance between<br />
the plates is 1.00 × 10 -4 m. There is air between the plates (dielectric<br />
constant of air = 1.0). Permittivity of free space = 8.85 × 10 -12<br />
C 2 /(Nm 2 ); k = 8.99 × 10 9 Nm 2 /C 2 ; 1 nC = 10 -9 C<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
(e)<br />
What is the magnitude of the charge on each plate?<br />
What is the capacitance of this capacitor?<br />
Find the potential difference between the two plates.<br />
How much energy is stored by the capacitor?<br />
Replace the air between the plates with argon (dielectric constant = 1.5). Would the angle<br />
decrease, increase or stay the same? Explain. You may use equations if you find them helpful<br />
15. A -15 :C charge with a mass of 3 grams is fixed in place on the x axis at x = - 2.0 m. A +8 :C charge is<br />
fixed in a different place on the x-axis. The net electric field at the origin is zero. k = 8.99 × 10 9 Nm 2 /C 2<br />
(a) What is the position of the +8 :C charge?<br />
(b) Find a point along the x-axis where the electric potential is zero.<br />
(c) If the -15 :C charge was not fixed in place, what would the initial acceleration be (magnitude<br />
and direction)?<br />
16. The drawing shows three point charges arranged in a triangle. The<br />
value of q is 5.0 :C, and d = 0.15 m. k = 8.99 × 10 9 Nm 2 /C 2<br />
(a)<br />
(b)<br />
Find the total potential at point P. Assume the potential of<br />
a point charge is zero at infinity.<br />
What is the electric potential energy of the 3 charge<br />
system, relative to its value when they are infinitely far<br />
away?<br />
17. Four charges are arranged on an x-y coordinate system as follows:
Charge<br />
Position<br />
-20 :C (-0.2m,0.0m)<br />
+5 :C (0.0m, 0.0m)<br />
-15 :C (0.0m, 0.5m)<br />
+10 :C (0.3m, -0.3m)<br />
k = 8.99 × 10 9 Nm 2 /C 2<br />
(a)<br />
(b)<br />
Find the net electric force (magnitude and direction) acting on the charge at the origin.<br />
A fifth charge of -25 :C is added. What is the position of the fifth charge so that the charge<br />
located at the origin feels a net electric force of zero?<br />
18. A. A charge particle enters a region of uniform magnetic field and follows a<br />
circular path as shown in the drawing.<br />
(a)<br />
(b)<br />
Is the particle positively or negatively charge?<br />
The magnetic field has a magnitude of 0.30 T. The particle has a<br />
speed of 6.0 × 10 6 m/s. The radius of the path is 80.0 cm. What is<br />
the mass of the particle which has a charge of magnitude 2.00 × 10 -19<br />
C?<br />
B. A step-up transformer has 25 turns on the primary coil and 500 turns on the secondary coil. If this<br />
transformer is to produce an output of 4800 V with a 20 mA current, what input current voltage are<br />
needed?<br />
19. A. A special mass spectrometer with 3 detectors (labeled A, B and C)<br />
is shown in the drawing. A uniform magnetic field of 0.01 T is<br />
present everywhere inside the spectrometer as shown. The<br />
dimensions are 0.2 m on each side with the detectors being located<br />
at the middle of each side. A proton, neutron and electron are sent<br />
into the spectrometer. m e = 9.109 × 10 -31 kg; m n = 1.674 × 10 -27 kg;<br />
m p = 1.672 × 10 -27 kg; e = 1.602 × 10 -19 C<br />
(a)<br />
(b)<br />
If the proton and electron make it to a detector, what are<br />
their initial speeds?<br />
Assuming each particle makes it to a detector:<br />
a proton goes to detector<br />
a neutron goes to detector<br />
an electron goes to detector<br />
B. A neon sign requires 12,000 V for its operation. It operates from a 220 V receptacle.<br />
(a)<br />
(b)<br />
(c)<br />
[3 pts.] What type of transformer, step-up or step-down, is needed?<br />
[3 pts.] What is the turns ratio N s /N p of the transformer?<br />
[3 pts.] The sign has an equivalent resistance of 1.44 × 10 6 S. Find the current leaving<br />
the receptacle, assuming 100% efficiency of the transformer.
20. A A positively charged oil drop is allowed to fall through the electric field created by the plates as<br />
shown in the drawing. In order to give the oil drop a straight trajectory, a magnetic field should be<br />
established with field lines pointing<br />
(a) left to right (c) out of the page<br />
(b) right to left (d) into the page<br />
B. A positively charged particle is moving through a magnetic field of strength B as shown in the<br />
drawing. The force experienced by the particle due to the magnetic<br />
field is<br />
(a) to the right (c) into the page<br />
(b) to the left (d) equal to zero<br />
C. Which combination of units can be used to express the magnetic field.?<br />
(a) kg @ m 2 /C (d) kg/(C @ s)<br />
(b) kg @ s/C 2 (e) kg @ m/(C@s 2 )<br />
(c) N @ m 2 /C<br />
D. An electron is moving with a speed of 3.5 × 10 5 m/s when it encounters a magnetic field of 0.60 T.<br />
The direction of the magnetic field makes an angle of 60.0° with respect to the velocity of the<br />
electron. What is the magnitude of the magnetic force on the electron? [e = 1.60 × 10 -19 C]<br />
(a) 4.0 × 10 -13 N (d) 3.4 × 10 -14 N<br />
(b) 3.2 × 10 -13 N (e) 2.9 × 10 -14 N<br />
(c) 1.7 × 10 -13 N<br />
E. A long, straight wire is in the same plane as a rectangular, conducting loop.<br />
The wire carries a constant current I as shown in the figure. Which one of<br />
the following statements is true if the wire is suddenly moved toward the<br />
loop?<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
(e)<br />
There will be no induced emf and no induced current.<br />
There will be an induced emf, but no induced current.<br />
There will be an induced current that is clockwise around the loop.<br />
There will be an induced current that is counterclockwise around the loop.<br />
There will be an induced electric field that is clockwise around the loop.<br />
F. Two conducting loops carry equal currents I in the same direction as shown in the figure. If the<br />
current in the upper loop suddenly drops to zero, what will happen to the current in the lower loop<br />
according to Lenz’s law?<br />
(a)<br />
(b)<br />
(c)<br />
(d)<br />
(e)<br />
The current in the lower loop will decrease.<br />
The current in the lower loop will increase.<br />
The current in the lower loop will not change.<br />
The current in the lower loop will also drop to zero.<br />
The current in the lower loop will reverse its direction
21. Three long straight wires, each of length 3.0 m, are arranged in a<br />
rectangular configuration as shown in cross section. The current in<br />
wire A is 1.3 A, the current in wire B is 0.6 A, and the current in wire<br />
C is 2.5 A. The direction of the current flow is also indicated in the<br />
drawing.<br />
(a)<br />
(b)<br />
What is the magnitude and direction of the magnetic field at<br />
point P?<br />
What is the magnitude and direction of the net force acting on<br />
wire C?<br />
22. The two conducting rails in the drawing are tilted upward so they each<br />
make an angle of 30° with respect to the ground. The vertical magnetic<br />
field has a magnitude of 0.046 T. The 0.24 kg copper rod (length R = 1.6<br />
m) slides without friction down the rails at a constant velocity of 2.5 m/s.<br />
(a)<br />
(b)<br />
What is the magnitude and direction (indicate into the page or out<br />
of the page as seen from the side view) of the current flowing<br />
through the bar?<br />
What is the resistance of the copper rod? Assume the resistance<br />
of the conducting rails is negligible.<br />
23. A. A generating station is producing 1.5 × 10 6 W of power that is to be sent to a small town located<br />
9.0 km away. Each of the two wires that compromise the transmission line has a resistance per<br />
kilometer of length 5.0 × 10 -2 S/km.<br />
(a) Find the power used to heat the wires if the power is transmitted at 1200 V.<br />
(b) A 450:5 step-up transformer is used to raise the voltage before the power is transmitted.<br />
How much power is now used to heat the wires?<br />
B. For each of the three sheets of polarizing material<br />
shown in the drawing, the orientation of the<br />
transmission axis is labeled relative to the vertical.<br />
The incident beam of light is unpolarized and has an<br />
intensity of 1150 W/m 2 .<br />
(a)<br />
(b)<br />
What is the intensity of the beam<br />
transmitted through the three sheets when<br />
1 = 20.0°, 2 = 60.0°, and 3 = 30.0°?<br />
A fourth sheet of polarizing material with a<br />
transmission axis aligned with the vertical is<br />
inserted into the above configuration immediately after the second polarizer while leaving<br />
everything else the same. What is the new intensity of the transmitted beam?
24. A An electron is moving through a magnetic field whose magnitude is 9.00 × 10 !4 T. The electron<br />
experiences only a magnetic force and has an acceleration of magnitude 3.20 × 10 14 m/s 2 . At a<br />
certain instant, it has a speed of 7.00 × 10 6 m/s. Determine the angle 2 (less than 90°) between the<br />
electron's velocity and the magnetic field. [m e = 9.11 × 10 !31 kg]<br />
B. A !6.00 :C charge is moving with a speed of 6.60 × 10 4 m/s parallel to a very long, straight wire.<br />
The wire is 5.00 cm from the charge and carries a current of 76.5 A in a direction opposite to that<br />
of the moving charge. Find the magnitude and direction of the force on the charge.<br />
C. Two astronauts are 10.0 m apart in their spaceship. One speaks to the other. The conversation is<br />
transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343<br />
m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to<br />
travel to the earth. How far away from the<br />
earth is the spaceship?<br />
D. Unpolarized light whose intensity is 1.10<br />
W/m 2 is incident on the polarizer in the<br />
figure. If the analyzer is set at an angle of<br />
2 = 72° with respect to the polarizer, what<br />
is the intensity of the light that reaches the<br />
photocell?<br />
25. A. A positively charged particle of mass 7.60 × 10 -8 kg is traveling due east with a speed of 30 m/s<br />
and enters a 0.45 T uniform magnetic field. The particle moves through one-quarter of a circle in a<br />
time of 6.40 × 10 -3 s, at which time it leaves the field heading due south. All during the motion the<br />
particle moves perpendicular to the magnetic field.<br />
(a) What is the magnitude of the magnetic force acting on the particle?<br />
(b) What is the magnitude of the charge of the particle?<br />
B. A rectangular current loop is located near a long,<br />
straight wire that carries a current of I W = 14 A (see<br />
drawing). The current in the loop is I L = 22 A.<br />
Determine the magnitude and direction of the net<br />
magnetic force that acts on the loop.
26. A. Two conducting rails are 1.6 m apart and are parallel to<br />
the ground at the same height. As the drawing shows, a<br />
0.20-kg aluminum rod is lying on top of the rails, and a<br />
0.50 T magnetic field points upward, perpendicular to the<br />
ground. There is a current I in the rod, directed as in the<br />
drawing. The coefficient of static friction between the rod<br />
and each rail is : s = 0.5. How much current is needed to<br />
make the rod begin moving, and in which direction will it<br />
move?<br />
B B B <br />
B. A loop of a wire has the shape shown in the drawing. The<br />
top part of the wire is bent into a semicircle of radius<br />
qr = 0.19 m. The normal to the plane of the loop is<br />
parallel to a constant magnetic field (N = 0°) of magnitude<br />
0.88 T. The resistor has a resistance of 3 S. What is the<br />
induced current in the loop when, starting with the position<br />
shown in the drawing, the semicircle is rotated through<br />
half a revolution in 0.05 s? Does the current flow<br />
clockwise or counterclockwise?<br />
27. A. A circular coil (650 turns, radius = 0.185 m) is rotating in a uniform magnetic field. At t = 0 s, the<br />
normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle<br />
of N = 30° with the field because the coil has made one-sixth of a revolution. An average emf of<br />
magnitude 0.075 V is induced in the coil. What is the magnitude of the magnetic field at the<br />
location of the coil?<br />
B. Two long straight wires, oriented perpendicular to the page,<br />
carry currents of I left = 10.0 A and I right = 25.0 A. I left is into the<br />
page and I right is coming out of the page. The wires are<br />
separated by a distance of 20.0 cm. Somewhere along an<br />
extended line though the two wires the net magnetic field is<br />
zero. How far away is this point from the left wire? Is it to<br />
the right or the left of the left wire?<br />
28. A. An electron is moving through a magnetic field whose magnitude is 7.80 × 10 -4 T. The electron<br />
experiences only a magnetic force and has an acceleration of magnitude 3.60 × 10 14 m/s 2 . At a<br />
certain instant, it has a speed of 6.50 × 10 6 m/s. Determine the angle 2 (less than 90°) between the<br />
electron's velocity and the magnetic field.<br />
B. A -6.00 :C charge is moving with a speed of 6.60 × 10 4 m/s parallel to a very long, straight wire.<br />
The wire is 5.00 cm from the charge and carries a current of 76.5 A in a direction opposite to that<br />
of the moving charge. Find the magnitude and direction (clearly specify direction) of the force on<br />
the charge.<br />
C. Two astronauts are 10.0 m apart in their spaceship. One speaks to the other. The conversation is<br />
transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343<br />
m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to<br />
travel to the earth. How far away from the earth is the spaceship?<br />
D. A beam of polarized light has an average intensity of 16 W/m 2 and is sent through a polarizer. The<br />
transmission axis makes an angle of 33° with respect to the direction of polarization. Determine<br />
the rms value of the electric field of the transmitted beam.
29. A. A magnetic field has a magnitude of 1.20 × 10 -3 T, and an electric field has a magnitude of 4.00 ×<br />
10 3 N/C. The fields point in opposite directions. A positive 1.8 :C charge moves at a speed of<br />
3.20 × 10 6 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the<br />
net force that acts on the charge.<br />
B. A beam of protons moves in a circle of radius 0.1 m. The protons move perpendicular to a 0.30 T<br />
magnetic field. Determine the magnitude of the centripetal force that acts on each proton.<br />
C. A rectangular loop of wire is moving toward the bottom of the page with a constant<br />
speed of 0.021 m/s (see the drawing). The loop is leaving a region in which a 2.1 T<br />
magnetic field exists; the magnetic field outside this region is zero. During a time<br />
of 2.0 s, what is the magnitude of the change in the magnetic flux?<br />
30. A. A circular coil (800 turns, radius = 0.045 m) is rotating in a uniform magnetic field. At t = 0 s, the<br />
normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle<br />
of 2 = 60° with the field because the coil has made one-twelfth of a revolution. An average emf of<br />
magnitude 0.075 V is induced in the coil. What is the magnitude of the uniform magnetic field at<br />
the location of the coil?<br />
B. A rectangular current loop is located near two long,<br />
straight wires that carry a current of I W = 10 A (see the<br />
drawing). The current in the loop is I L = 26 A.<br />
Determine the magnitude of the net magnetic force that<br />
acts on the loop.<br />
31. A. A 300 turn solenoid with a length of 20.0 cm and a radius of 2.50 cm carries a current of 5.0<br />
Amps. A square with sides 1.00 cm and made of 4 turns is placed inside the solenoid so that the<br />
flux is maximal. The square has a resistance of 2.00 S.<br />
1. Find the magnitude of the average induced current in the square when the current in the<br />
solenoid decreases to 2.00 Amps in a period of 0.0900 seconds.<br />
2. Does the current in the square flow the same direction or opposite direction as the current<br />
in the solenoid?<br />
B. Two long straight wires, oriented perpendicular to the page, carry<br />
currents of I left = 10.0 A and I right = 25.0 A. I left is into the page and I right<br />
is coming out of the page. The wires are separated by a distance of<br />
20.0 cm. Somewhere along an extended line though the two wires the<br />
net magnetic field is zero. Is it to the right or the left of the left wire<br />
(circle one)? How far away is this point from the left wire?<br />
32. A. An electron is moving through a magnetic field whose magnitude is 8.10 × 10 -4 T. The electron<br />
experiences only a magnetic force and has an acceleration of magnitude 3.80 × 10 14 m/s 2 . At a<br />
certain instant, it has a speed of 5.90 × 10 6 m/s. Determine the angle 2 (less than 90/) between the<br />
electron's velocity and the magnetic field. [m e = 9.11 × 10 -31 kg; q e = 1.6 × 10 -19 C]<br />
T<br />
B. The 1200-turn coil in a dc motor has a radius per turn of 6.9 cm. The design for the motor<br />
specifies that the magnitude of the maximum torque is 5.6 N A m when the coil is placed in a 0.18<br />
magnetic field. What is the maximum current in the coil?<br />
C. At a certain location, the horizontal component of the earth's magnetic field is 4.0 × 10 -5 T, due<br />
north. A 3.0 × 10 -9 kg particle with charge 7 :C moves eastward with just the right speed, so the<br />
magnetic force on it balances its weight. Find the speed of the particle.
D. The wingspan (tip-to-tip) of a Boeing 747 jetliner is 59 m. The plane is flying horizontally at a<br />
speed of 240 m/s. The vertical component of the earth's magnetic field is 5.0 × 10 -6 T. Find the<br />
emf induced between the wing tips.<br />
33. A. Two very long, rigid wires are oriented parallel to each other and to the ground. The wires carry<br />
the same current in the same direction. The mass density of each wire is 0.114 kg/m. One wire is<br />
held in place 1 m above the ground, and the other floats beneath it at a distance of 8.2 × 10 -3 m.<br />
Determine the current in the wires.<br />
B. The magnetic field produced by a 2 m long solenoid in a magnetic resonance imaging (MRI)<br />
system designed for measurements on whole human bodies has a field strength of 4.0 T and a<br />
current of 2.5 × 10 2 A. The solenoid is now compressed to 1.5 m with a current of 1.9 × 10 2 A.<br />
Find the strength of the magnetic field produced by the solenoid.<br />
C. The coil within an ac generator has an area per turn of 1.2 × 10 -2 m 2 and consists of 500 turns. The<br />
coil is situated in a 0.20 T magnetic field. The emf induced in the coil at the instant when the<br />
normal to the loop makes an angle of 35° with respect to the direction of the magnetic field is<br />
23.4 V. What is the angular speed of the loop in revolutions per minute?<br />
34. A. A 5.0 m long and narrow rectangular loop of wire is moving<br />
toward the bottom of the page with a constant speed of 2.4 m/s. The<br />
loop is just starting to leave a region in which a 3.2 T magnetic field<br />
exists; the magnetic field outside this region is zero. The loop has a<br />
resistance of 2 S. During a time of 1.7 s, what is the magnitude of the<br />
induced current? The current flows CLOCKWISE or<br />
COUNTERCLOCKWISE (circle one)?<br />
B. The drawing shows an end-view of three wires. They are<br />
long, straight, and perpendicular to the plane of the paper.<br />
Their cross sections lie at the corners of a rectangle. The<br />
current in wire 1 is 2 amps and it is directed into the paper.<br />
The net magnetic field at the empty corner is zero. The<br />
current in wire 2 is also into the page and the current in wire<br />
3 is directed out of the page. What are the currents in wires<br />
2 and 3?<br />
35. A. Two long straight wires, oriented perpendicular to the<br />
page, carry currents of I left = 50.0 A and I right = 15.0 A.<br />
The wires are separated by a distance of 12.0 cm.<br />
Suppose a third wire carrying a 4.00 A current is<br />
situated perpendicular to the plane of the page and passes through point P. The current<br />
flowing in this wire goes into the plane of the page. What magnetic force, magnitude<br />
and direction, does a 20.0 cm length of this wire feel?<br />
B. A single loop of a wire has the shape shown in the drawing. The<br />
top part of the wire is bent into a semicircle of radius r = 0.19 m.<br />
The normal to the plane of the loop is parallel to a constant<br />
magnetic field of magnitude 0.88 T. The resistor has a resistance<br />
of 3 S. What is the average induced current in the loop when,<br />
starting with the position shown in the drawing, the semicircle is<br />
rotated through half a revolution in 0.05 s? Does the current flow<br />
clockwise or counterclockwise (circle one)?
36. A. A -6.00 μC charge is moving with a speed of 6.60 × 10 4 m/s parallel to a very long,<br />
straight wire. The wire is 5.00 cm from the charge and carries a current of 76.5 A in a<br />
direction opposite to that of the moving charge. Find the force on the charge ( magnitude<br />
and direction) and clearly specify direction.<br />
B. The coil within an ac generator has an area per turn of 1.2 × 10 -2 m 2 and consists of 500<br />
turns. The coil is situated in a 0.20 T magnetic field. The emf induced in the coil, at the<br />
instant when the normal to the loop makes an angle of 35° with respect to the direction of<br />
the magnetic field, is 23.4 V. What is the angular speed of the loop?<br />
C. A magnetic field has a magnitude of 1.20 × 10 -3 T, and an electric field has a magnitude<br />
of 5.40 × 10 3 N/C. Both fields point in the same direction. A positive 1.8 µC charge<br />
moves at a speed of 3.60 × 10 6 m/s in a direction that is perpendicular to both fields.<br />
Determine the magnitude of the net force that acts on the charge.<br />
D. Solar wind is a thin, hot gas given off by the sun. Charged particles in this gas enter the<br />
magnetic field of the earth and can experience a magnetic force. Suppose an electron<br />
traveling with a speed of 9.00 × 10 6 m/s encounters the earth's magnetic field at an<br />
altitude where the field has a magnitude of 1.40 × 10 -7 T. Assuming that the electron's<br />
velocity makes a 37.0° angle with respect to the magnetic field, find the radius of the<br />
circular path on which the electron would move.<br />
37. A. Two long straight wires carry currents of I 1 = 30.0 A<br />
and I 2 = 12.0 A and are oriented perpendicular to the<br />
page as shown. Suppose a third wire carrying a 6.00<br />
A current is situated perpendicular to the plane of the<br />
page and passes through point P. The current flowing<br />
in the third wire goes into the plane of the page.<br />
What is the magnitude of the magnetic force on a<br />
40.0 cm length of the third wire?<br />
B. A circular coil (650 turns, radius = 0.02 m) is rotating in a uniform magnetic field. At<br />
t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the<br />
normal makes an angle of θ = 30° with the field since the coil has made one-sixth of a<br />
revolution. An average emf of magnitude 0.04 V is induced in the coil. What is the<br />
magnitude of the magnetic field at the location of the coil?<br />
38. A. A piece of copper wire has a resistance per unit length of 6.20 × 10 -3 Ω/m. The wire is<br />
wound into a thin, flat coil of many turns that has a radius of 0.200 m. The ends of the<br />
wire are connected to a 12.0 V battery. Find the magnetic field strength at the center of<br />
the coil.<br />
B. A particle with a charge of 14 μC experiences a force of 2.2 × 10 -4 N when it moves at<br />
right angles to a magnetic field with a speed of 23 m/s. What force does this particle<br />
experience when it moves with a speed of 6.8 m/s at an angle of 25° relative to the<br />
magnetic field?
C. Two isotopes of carbon, carbon-12 and carbon-13, have masses of<br />
19.93 × 10 -27 kg and 21.59 × 10 -27 kg, respectively. These two isotopes are singly<br />
ionized (+e) and each is given a speed of 6.00 × 10 5 m/s. The ions then enter the<br />
bending region of a mass spectrometer where the magnetic field is 0.8500 T.<br />
Determine the spatial separation between the two isotopes after they have traveled<br />
through a half-circle.<br />
39. A. A 2500 turn solenoid with a length of 30.0 cm and a radius of 2.5 cm carries an initial<br />
current of 5.0 Amps. A small circular coil of radius 1.5 cm and made of 3 turns is placed<br />
inside the solenoid so that the flux is maximal. The circular coil has a resistance of<br />
3.00 Ω.<br />
1. Find the magnitude of the average induced current in the circular coil when the<br />
current in the solenoid increases to 7.0 Amps in 0.080 seconds.<br />
2. Does the current in the circular coil flow the same direction or opposite direction<br />
as the current in the solenoid?<br />
B. Two long straight wires, oriented perpendicular to<br />
the page, carry currents of I left = 10.0 A and I right =<br />
25.0 A. The wires are separated by a distance of<br />
20.0 cm. Somewhere along an extended line though<br />
the two wires the net magnetic field is zero. Is it in Region I, Region II, or Region III<br />
(circle one)? How far away is this point from the left wire?<br />
40. A. An electron is moving through a magnetic field whose magnitude is 9.00 × 10 -4 T. The<br />
electron experiences only a magnetic force and has an acceleration of magnitude<br />
3.20 × 10 14 m/s 2 . At a certain instant, the angle between the electron’s velocity and the<br />
magnetic field is 20.1°. Determine the speed of the electron.<br />
B. A -6.00 μC charge is moving with a speed of 5.60 × 10 4 m/s parallel to a very long,<br />
straight wire. The wire is 4.00 cm from the charge and carries a current of 76.5 A in a<br />
direction opposite to that of the moving charge. Find the magnitude and direction<br />
(clearly specify direction) of the force on the charge.<br />
C. In 1996, NASA performed an experiment called the Tethered Satellite experiment. In<br />
this experiment a 1.80 × 10 4 m length of wire was let out by the space shuttle Atlantis to<br />
generate a motional emf. The shuttle had an orbital speed of 7.70 × 10 3 m/s, and the<br />
magnitude of the earth's magnetic field at the location of the wire was 5.40 × 10 -5 T. If<br />
the wire was moved perpendicular to the earth's magnetic field, what was the motional<br />
emf generated between the ends of the wire?<br />
D. A 0.88 m length of wire is formed in to a double-turn, square loop in which there is a<br />
current of 10 A. The loop is placed in a magnetic field of 0.20 T. What is the maximum<br />
torque that the loop can experience?
41. A. For each of the three sheets of polarizing<br />
material shown in the drawing, the<br />
orientation of the transmission axis is labeled<br />
relative to the vertical. The incident beam of<br />
light is unpolarized and has an intensity of<br />
1200 W/m 2 .<br />
1. What is the intensity of the beam<br />
transmitted through the three sheets<br />
when θ 1 = 30°, θ 2 = 60° and θ 3 = 90°?<br />
2. A fourth sheet of polarizing material with a transmission axis aligned with the<br />
vertical is inserted into the above configuration immediately after the second<br />
polarizer while leaving everything else the same. What is the new intensity of<br />
the transmitted beam?<br />
B. Two long straight wires, oriented perpendicular to the page,<br />
carry currents of I left = 10.0 A and I right = 25.0 A. I left is into the<br />
page and I right is coming out of the page. The wires are separated<br />
by a distance of 20.0 cm. Somewhere along an extended line<br />
though the two wires the magnetic field created by each wire is<br />
the same in magnitude and points in the same direction.<br />
1. Is this point to the right or the left of the left wire (circle one)? RIGHT LEFT<br />
2. How far away is this point from the left wire?<br />
42. A. The coil within an ac generator has an area per turn of 1.2 × 10 -2 m 2 and consists of 500<br />
turns. The coil is situated in a 0.20 T magnetic field. The emf induced in the coil at the<br />
instant when the normal to the loop makes an angle of 35° with respect to the direction of<br />
the magnetic field is 23.4 V. What is the angular speed of the loop in revolutions per<br />
minute?<br />
B. The resistances of the primary and secondary coils of a transformer are 47 and 15 Ω,<br />
respectively. Both coils are made from lengths of the same copper wire. The circular<br />
turns of each coil have the same diameter. Find the turns ratio N s /N p .<br />
C. Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10 -27 kg and<br />
21.59 × 10 -27 kg, respectively. These two isotopes are singly ionized (+e) and each is<br />
given a speed of 6.50 × 10 5 m/s. The ions then enter the bending region of a mass<br />
spectrometer where the magnetic field is 0.8800 T. Determine the spatial separation<br />
between the two isotopes after they have traveled through a half-circle.<br />
43. A. A solenoid has a radius of 5.60 cm, consists of 600 turns per meter, and carries a current<br />
of 2.1 A. A 10 turn circular loop of radius 2.00 cm is placed inside the solenoid so that<br />
the flux is maximal. The resistance of the loop is 1.7 Ω. Suddenly, a switch is opened,<br />
and the current in the solenoid dies to zero in a time of 0.14 s.<br />
Find the average current induced in the loop.<br />
B. Three long straight wires, each of length 4.0 m, are arranged in a<br />
rectangular configuration as shown in cross section. The<br />
current in wire A is 1.7 A, the current in wire B is 0.6 A, and the<br />
current in wire C is 2.5 A. The direction of the current flow is<br />
also indicated in the drawing. What is the magnitude and<br />
direction of the net force acting on wire C?
44. A. In a certain region, the earth's magnetic field has a magnitude of 5.50 × 10 -5 T and is<br />
directed north at an angle of 52° below the horizontal. An electrically charged bullet is<br />
fired north and 11° above the horizontal, with a speed of 657 m/s. The magnetic force on<br />
the bullet is 2.60 × 10 -10 N, directed due east. Determine the bullet's electric charge,<br />
including its algebraic sign (+ or −)<br />
B. A -6.00 μC charge is moving with a speed of 5.60 × 10^4 m/s parallel to a very<br />
long, straight wire. The wire is 4.00 cm from the charge and carries a current of<br />
76.5 A in the same direction as that of the moving charge. Find the magnitude<br />
and direction (clearly specify direction) of the force on the charge.<br />
C. In 1996, NASA performed an experiment called the Tethered Satellite experiment. In<br />
this experiment a 1.80 × 10 4 m length of wire was let out by the space shuttle Atlantis to<br />
generate a motional emf. The shuttle had an orbital speed of 7.70 × 10 3 m/s, and the<br />
magnitude of the earth's magnetic field at the location of the wire was 5.40 × 10 -5 T. I f<br />
the wire had moved perpendicular to the earth's magnetic field, what would have been the<br />
motional emf generated between the ends of the wire?<br />
D. The maximum torque experienced by a coil in a 0.55 T magnetic field is 8.4 × 10 -4 N · m.<br />
The coil is circular and consists of only one turn. T he current in the coil is 3.3 A. What<br />
is the length of the wire from which the coil is made?<br />
45. A. A 0.3 m long solenoid has a radius of 5.60 cm, consists of 500 turns , and carries a<br />
current of 1.3 A. A 10 turn square loop of side 2.00 cm is placed inside the solenoid so<br />
t-+hat the flux is maximal. The resistance of the loop is 1.3 Ω. Suddenly, a switch is<br />
opened, and the current in the solenoid dies to zero in a time of 0.12 s. Find the average<br />
current induced in the loop during the 0.12 s.<br />
B. The drawing shows four insulated wires overlapping one another,<br />
forming a square with 0.050-m sides. All four wires are much longer<br />
than the sides of the square. The net magnetic field at the center of<br />
the square is 74.5 µT. Calculate the current I.<br />
46. A. The maximum strength of the earth's magnetic field is about 6.9 × 10 -5 T near the south<br />
magnetic pole. In principle, this field could be used with a rotating coil to generate<br />
60.0-Hz ac electricity. What is the minimum number of turns (area per turn = 0.080 m 2 )<br />
that the coil must have to produce an rms voltage of 120 V?<br />
B. T transformer consisting of two coils wrapped around an<br />
iron core is connected to a generator and a resistor, as<br />
shown in the drawing. There are 11 turns in the primary<br />
coil and 18 turns in the secondary coil. The peak voltage<br />
across the resistor is 73.3 V. What is the peak emf of the<br />
generator?
C. When beryllium-7 ions (m = 1.165 × 10 -26 kg) pass<br />
through a mass spectrometer, a uniform magnetic field of<br />
0.3465 T curves their path directly to the center of the<br />
detector (see figure below). For the same accelerating<br />
potential difference, what magnetic field should be used<br />
to send beryllium-10 ions (m = 1.663 × 10 -26 kg) to the<br />
same location in the detector? Both types of ions are<br />
singly ionized (q = +e).<br />
47. A. For each of the three sheets of polarizing<br />
material shown in the drawing, the<br />
orientation of the transmission axis is<br />
labeled relative to the vertical. The<br />
incident beam of light is vertically<br />
polarized and has an intensity of<br />
1500 W/m 2 .<br />
1. What is the intensity of the<br />
beam transmitted through the<br />
three sheets when θ 1 = 0°, θ 2 = 30° and θ 3 = 15°?<br />
2. A fourth sheet of polarizing material with a transmission axis aligned<br />
perpendicular to that of the third polarizer is inserted into the above configuration<br />
immediately after the second polarizer while leaving everything else the same.<br />
What is the new intensity of the transmitted beam?<br />
B. Three long straight wires, each of length 7.0 m, are arranged in<br />
a rectangular configuration as shown in cross section. The<br />
current in wire A is 1.3 A, the current in wire B is 1.8 A, and<br />
the current in wire C is 2.5 A. The direction of the current<br />
flow is also indicated in the drawing. What is the magnitude<br />
and direction of the net force acting on wire C?