Summer 2011

REVIEW FOR MIDTERM 4

1.

A small 2.00 g plastic ball suspended by a 20.0 cm long string (R) is in a uniform electric field (E = 103 N/C), as shown. A. B.

If the ball is in equilibrium when the string makes a 15° angle with the vertical. What is the net charge on the ball? If the charge on the ball were doubled, what would be the new angle that it hangs at, relative to the vertical? [Hint: It is not 30°.]

2.

A.

3.

A small drop of water is suspended in air by a uniform electric field. The field is directed upward with a magnitude of 8480.0 N/C. The mass of the water drop is 3.5 × 10-9 kg. Neglect the buoyant force acting on the drop. (a) (b)

Positive charges are situated at three corners of a rectangle as shown. Find the magnitude and direction of the electric field at the fourth corner. (Give the direction relative to the x-axis.)

Is the excess charge on the water drop positive or negative. Show all work. How many excess electrons or protons reside on the drop? The magnitude of an electron (proton) charge is 1.60 × 10-19 C. Show all work.

4.

A point charge Q of !0.70 :C is fixed to one corner of a square. An identical charge is fixed to the diagonally opposite corner. A point charge q is fixed to each of the remaining corners. The net force acting on either of the charges (q) is zero. Find the magnitude and algebraic sign of q.

5.

Two identidal small plastic balls (mass = 2.00 g) are suspended by 20.0 cm long strings. If the balls are in equilibrium when the strings make a 15.0° angle with the vertical, what is the charge on the balls? k = 8.99 × 109 N@m2/C2

6.

A.

A parallel plate capacitor has an area of 5.00 cm2, and the plates are separated by 1.00 cm with air between them. It stores a charge of .004 :C. [dielectric constant of air is 1.0; permittivity of free space ,o = 8.85 × 10!12 C2/(N@m2)] (a) (b)

B.

What is the potential difference across the plates of the capacitor? What is the magnitude of the uniform electric field in the region between the plates?

Calculate the speed of an electron that is accelerated from rest through a potential difference of 120 V. electron mass = 9.11 × 10!31 kg;

electron charge = 1.60 × 10!19 C

7.

A.

8.

Four point charges are fixed at the corners of a square with sides of length d. (a) (b)

A 5.00 g charged insulating ball hangs on a 30.0 cm long string in a uniform horizontal electric field as shown. If the charge on the ball is 1.00 :C, find the strength of the field.

Find the direction and magnitude of the net electrostatic force exerted on the point charge q3. Let q = +2.4 :C and d = 33 cm. Now, the length d is doubled. Find the direction and magnitude of the net electrostatic force exerted on the point charge q3. q1 = +q q2 = -2.0 q q3 = -3.0 q q4 = -4.0 q

9.

A.

An object with a charge of -3.6 :C and a mass of 0.012 kg experiences an upward electric force, due to a uniform electric field which is equal in magnitude to its weight. (a) (b)

B.

A small object of mass 0.025 kg and charge 3.1 :C hangs from the ceiling by a thread. A second small object, with a charge of 4.2 :C, is placed 1.5 m vertically below the first charge. (a) (b)

10.

Find the direction and magnitude of the electric field. If the electric charge on the object is doubled while its mass remains the same, find the direction and magnitude of its acceleration.

Find the electric field at the position of the upper charge due to the lower charge. Calculate the tension in the thread.

A small plastic ball with mass 8.00 × 10-3 kg and charge +0.200 :C is suspended from an insulating thread and hangs between the plates of a capacitor as shown in the drawing. The ball is in equilibrium, with the thread making an angle of 30.0° with respect to the vertical. The area of each plate is 0.020 m2 and the distance between the plates is 1.00 × 10-4 m.. There is air between the plates (dielectric constant of air = 1.0). Permittivity of free space = 8.85 × 10-12 C2/(NAm2). (a) (b) (c) (d) (e)

What is the magnitude of the charge on each plate? What is the capacitance of this capacitor? Find the potential difference between the two plates. How much energy is stored by the capacitor? Replace the air between the plates with argon (dielectric constant = 1.5). Would the angle 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 +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 × 109 NAm2/c2] (a) (b) (c)

At what point along the x-axis is the net electric field zero? Find a point along the x-axis where the electric potential is zero. If the +12 :C charge were not fixed in place, what would the initial acceleration be (magnitude and direction)?

12.

The drawing shows six point charges arranged in a rectangle. The value of q is 5.0 :C, and the distance, d, is 0.20 m. Find the total electric potential at location p, which is at the center of the rectangle. [k = 8.99 × 109 NAm2/c2]

13.

Two charges, q1 = +10.0 :C at x1 = -5.0 cm, and q2 = +10.0 :C at x2 = -6.0 cm, are located on the x-axis. Two other charges, q3 = -5.0 :C at y3 = -5.0 cm and q4 = +6.0 :C at y4 = +6.0 cm, are located on the y-axis. [k = 8.99 × 109 NAm2/c2] (a) (b) (c)

14.

Two small plastic balls, each with mass 4.00 × 10-3 kg and charge +0.200 nC, are suspended from insulating threads (R = 5 × 10-5 m) and hang between the plates of a capacitor (see drawing). The balls are in equilibrium. Each thread makes an angle of 50.0/ with respect to the vertical. The area of each plate is 0.030 m2 and the distance between the plates is 1.00 × 10-4 m. There is air between the plates (dielectric constant of air = 1.0). Permittivity of free space = 8.85 × 10-12 C2/(Nm2 ); k = 8.99 × 109 Nm2/C2; 1 nC = 10-9C (a) (b) (c) (d) (e)

15.

What is the position of the +8 :C charge? Find a point along the x-axis where the electric potential is zero. If the -15 :C charge was not fixed in place, what would the initial acceleration be (magnitude and direction)?

The drawing shows three point charges arranged in a triangle. The value of q is 5.0 :C, and d = 0.15 m. k = 8.99 × 109 Nm2 /C2 (a) (b)

17.

What is the magnitude of the charge on each plate? What is the capacitance of this capacitor? Find the potential difference between the two plates. How much energy is stored by the capacitor? Replace the air between the plates with argon (dielectric constant = 1.5). Would the angle decrease, increase or stay the same? Explain. You may use equations if you find them helpful

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 fixed in a different place on the x-axis. The net electric field at the origin is zero. k = 8.99 × 109 Nm2 /C2 (a) (b) (c)

16.

Find the magnitude of the net electric field at the origin. Find the direction (the acute angle measured with respect to the x-axis) of the net electric field at the origin. You add a fifth charge, +8 :C. What would be the x and y coordinates of it’s position in order to make the field at the origin zero?

Find the total potential at point P. Assume the potential of a point charge is zero at infinity. What is the electric potential energy of the 3 charge system, relative to its value when they are infinitely far away?

Four charges are arranged on an x-y coordinate system as follows:

Charge

Position

-20 :C

(-0.2m,0.0m)

+5 :C

(0.0m, 0.0m)

-15 :C

(0.0m, 0.5m)

+10 :C

(0.3m, -0.3m)

k = 8.99 × 109 Nm2 /C2

18.

(a) (b)

Find the net electric force (magnitude and direction) acting on the charge at the origin. A fifth charge of -25 :C is added. What is the position of the fifth charge so that the charge located at the origin feels a net electric force of zero?

A.

A charge particle enters a region of uniform magnetic field and follows a circular path as shown in the drawing. (a) (b)

19.

Is the particle positively or negatively charge? The magnetic field has a magnitude of 0.30 T. The particle has a speed of 6.0 × 106 m/s. The radius of the path is 80.0 cm. What is the mass of the particle which has a charge of magnitude 2.00 × 10-19 C?

B.

A step-up transformer has 25 turns on the primary coil and 500 turns on the secondary coil. If this transformer is to produce an output of 4800 V with a 20 mA current, what input current voltage are needed?

A.

A special mass spectrometer with 3 detectors (labeled A, B and C) is shown in the drawing. A uniform magnetic field of 0.01 T is present everywhere inside the spectrometer as shown. The dimensions are 0.2 m on each side with the detectors being located at the middle of each side. A proton, neutron and electron are sent into the spectrometer. me = 9.109 × 10-31 kg; mn = 1.674 × 10-27 kg; e = 1.602 × 10-19 C mp = 1.672 × 10-27 kg; (a) (b)

B.

If the proton and electron make it to a detector, what are their initial speeds? Assuming each particle makes it to a detector: a proton goes to detector a neutron goes to detector an electron goes to detector

A neon sign requires 12,000 V for its operation. It operates from a 220 V receptacle. (a) (b) (c)

[3 pts.] What type of transformer, step-up or step-down, is needed? [3 pts.] What is the turns ratio Ns/Np of the transformer? [3 pts.] The sign has an equivalent resistance of 1.44 × 106 S. Find the current leaving 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 shown in the drawing. In order to give the oil drop a straight trajectory, a magnetic field should be established with field lines pointing (a) (b)

B.

(c) (d)

into the page equal to zero

kg @ m2/C kg @ s/C2 N @ m2/C

(d) (e)

kg/(C @ s) kg @ m/(C@s2)

4.0 × 10-13 N 3.2 × 10-13 N 1.7 × 10-13 N

(d) (e)

3.4 × 10-14 N 2.9 × 10-14 N

A long, straight wire is in the same plane as a rectangular, conducting loop. The wire carries a constant current I as shown in the figure. Which one of the following statements is true if the wire is suddenly moved toward the loop? (a) (b) (c) (d) (e)

F.

to the right to the left

An electron is moving with a speed of 3.5 × 105 m/s when it encounters a magnetic field of 0.60 T. The direction of the magnetic field makes an angle of 60.0° with respect to the velocity of the electron. What is the magnitude of the magnetic force on the electron? [e = 1.60 × 10-19 C] (a) (b) (c)

E.

out of the page into the page

Which combination of units can be used to express the magnetic field.? (a) (b) (c)

D.

(c) (d)

A positively charged particle is moving through a magnetic field of strength B as shown in the drawing. The force experienced by the particle due to the magnetic field is

(a) (b) C.

left to right right to left

There will be no induced emf and no induced current. There will be an induced emf, but no induced current. There will be an induced current that is clockwise around the loop. There will be an induced current that is counterclockwise around the loop. There will be an induced electric field that is clockwise around the loop.

Two conducting loops carry equal currents I in the same direction as shown in the figure. If the current in the upper loop suddenly drops to zero, what will happen to the current in the lower loop according to Lenz’s law? (a) (b) (c) (d) (e)

The current in the lower loop will decrease. The current in the lower loop will increase. The current in the lower loop will not change. The current in the lower loop will also drop to zero. 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 rectangular configuration as shown in cross section. The current in wire A is 1.3 A, the current in wire B is 0.6 A, and the current in wire C is 2.5 A. The direction of the current flow is also indicated in the drawing. (a) (b)

22.

The two conducting rails in the drawing are tilted upward so they each make an angle of 30° with respect to the ground. The vertical magnetic field has a magnitude of 0.046 T. The 0.24 kg copper rod (length R = 1.6 m) slides without friction down the rails at a constant velocity of 2.5 m/s. (a)

(b)

23.

What is the magnitude and direction of the magnetic field at point P? What is the magnitude and direction of the net force acting on wire C?

A.

What is the magnitude and direction (indicate into the page or out of the page as seen from the side view) of the current flowing through the bar? What is the resistance of the copper rod? Assume the resistance of the conducting rails is negligible.

A generating station is producing 1.5 × 106 W of power that is to be sent to a small town located 9.0 km away. Each of the two wires that compromise the transmission line has a resistance per kilometer of length 5.0 × 10-2 S/km. (a) (b)

B.

Find the power used to heat the wires if the power is transmitted at 1200 V. A 450:5 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now used to heat the wires?

For each of the three sheets of polarizing material shown in the drawing, the orientation of the transmission axis is labeled relative to the vertical. The incident beam of light is unpolarized and has an intensity of 1150 W/m2. (a)

(b)

What is the intensity of the beam transmitted through the three sheets when 1 = 20.0°, 2 = 60.0°, and 3 = 30.0°? A fourth sheet of polarizing material with a transmission axis aligned with the vertical is inserted into the above configuration immediately after the second polarizer while leaving everything else the same. What is the new intensity of the transmitted beam?

24.

25.

A

An electron is moving through a magnetic field whose magnitude is 9.00 × 10!4 T. The electron experiences only a magnetic force and has an acceleration of magnitude 3.20 × 1014 m/s2. At a certain instant, it has a speed of 7.00 × 106 m/s. Determine the angle 2 (less than 90°) between the electron's velocity and the magnetic field. [me = 9.11 × 10!31 kg]

B.

A !6.00 :C charge is moving with a speed of 6.60 × 104 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 76.5 A in a direction opposite to that of the moving charge. Find the magnitude and direction of the force on the charge.

C.

Two astronauts are 10.0 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth. How far away from the earth is the spaceship?

D.

Unpolarized light whose intensity is 1.10 W/m2 is incident on the polarizer in the figure. If the analyzer is set at an angle of 2 = 72° with respect to the polarizer, what is the intensity of the light that reaches the photocell?

A.

A positively charged particle of mass 7.60 × 10-8 kg is traveling due east with a speed of 30 m/s and enters a 0.45 T uniform magnetic field. The particle moves through one-quarter of a circle in a time of 6.40 × 10-3 s, at which time it leaves the field heading due south. All during the motion the particle moves perpendicular to the magnetic field. (a) What is the magnitude of the magnetic force acting on the particle? (b) What is the magnitude of the charge of the particle?

B.

A rectangular current loop is located near a long, straight wire that carries a current of IW = 14 A (see drawing). The current in the loop is IL = 22 A. Determine the magnitude and direction of the net magnetic force that acts on the loop.

26.

27.

28.

B

B

B

A.

Two conducting rails are 1.6 m apart and are parallel to the ground at the same height. As the drawing shows, a 0.20-kg aluminum rod is lying on top of the rails, and a 0.50 T magnetic field points upward, perpendicular to the ground. There is a current I in the rod, directed as in the drawing. The coefficient of static friction between the rod and each rail is :s = 0.5. How much current is needed to make the rod begin moving, and in which direction will it move?

B.

A loop of a wire has the shape shown in the drawing. The top part of the wire is bent into a semicircle of radius qr = 0.19 m. The normal to the plane of the loop is parallel to a constant magnetic field (N = 0°) of magnitude 0.88 T. The resistor has a resistance of 3 S. What is the induced current in the loop when, starting with the position shown in the drawing, the semicircle is rotated through half a revolution in 0.05 s? Does the current flow clockwise or counterclockwise?

A.

A circular coil (650 turns, radius = 0.185 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle of N = 30° with the field because the coil has made one-sixth of a revolution. An average emf of magnitude 0.075 V is induced in the coil. What is the magnitude of the magnetic field at the location of the coil?

B.

Two long straight wires, oriented perpendicular to the page, carry currents of Ileft = 10.0 A and Iright = 25.0 A. Ileft is into the page and Iright is coming out of the page. The wires are separated by a distance of 20.0 cm. Somewhere along an extended line though the two wires the net magnetic field is zero. How far away is this point from the left wire? Is it to the right or the left of the left wire?

A.

An electron is moving through a magnetic field whose magnitude is 7.80 × 10-4 T. The electron experiences only a magnetic force and has an acceleration of magnitude 3.60 × 1014 m/s2. At a certain instant, it has a speed of 6.50 × 106 m/s. Determine the angle 2 (less than 90°) between the electron's velocity and the magnetic field.

B.

A -6.00 :C charge is moving with a speed of 6.60 × 104 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 76.5 A in a direction opposite to that of the moving charge. Find the magnitude and direction (clearly specify direction) of the force on the charge.

C.

Two astronauts are 10.0 m apart in their spaceship. One speaks to the other. The conversation is transmitted to earth via electromagnetic waves. The time it takes for sound waves to travel at 343 m/s through the air between the astronauts equals the time it takes for the electromagnetic waves to travel to the earth. How far away from the earth is the spaceship?

D.

A beam of polarized light has an average intensity of 16 W/m2 and is sent through a polarizer. The transmission axis makes an angle of 33° with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam.

29.

30.

31.

A.

A magnetic field has a magnitude of 1.20 × 10-3 T, and an electric field has a magnitude of 4.00 × 103 N/C. The fields point in opposite directions. A positive 1.8 :C charge moves at a speed of 3.20 × 106 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net force that acts on the charge.

B.

A beam of protons moves in a circle of radius 0.1 m. The protons move perpendicular to a 0.30 T magnetic field. Determine the magnitude of the centripetal force that acts on each proton.

C.

A rectangular loop of wire is moving toward the bottom of the page with a constant speed of 0.021 m/s (see the drawing). The loop is leaving a region in which a 2.1 T magnetic field exists; the magnetic field outside this region is zero. During a time of 2.0 s, what is the magnitude of the change in the magnetic flux?

A.

A circular coil (800 turns, radius = 0.045 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle of 2 = 60° with the field because the coil has made one-twelfth of a revolution. An average emf of magnitude 0.075 V is induced in the coil. What is the magnitude of the uniform magnetic field at the location of the coil?

B.

A rectangular current loop is located near two long, straight wires that carry a current of IW = 10 A (see the drawing). The current in the loop is IL = 26 A. Determine the magnitude of the net magnetic force that acts on the loop.

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 Amps. A square with sides 1.00 cm and made of 4 turns is placed inside the solenoid so that the flux is maximal. The square has a resistance of 2.00 S. 1. 2.

32.

Find the magnitude of the average induced current in the square when the current in the solenoid decreases to 2.00 Amps in a period of 0.0900 seconds. Does the current in the square flow the same direction or opposite direction as the current in the solenoid?

B.

Two long straight wires, oriented perpendicular to the page, carry currents of Ileft = 10.0 A and Iright = 25.0 A. Ileft is into the page and Iright is coming out of the page. The wires are separated by a distance of 20.0 cm. Somewhere along an extended line though the two wires the net magnetic field is zero. Is it to the right or the left of the left wire (circle one)? How far away is this point from the left wire?

A.

An electron is moving through a magnetic field whose magnitude is 8.10 × 10-4 T. The electron experiences only a magnetic force and has an acceleration of magnitude 3.80 × 1014 m/s2. At a certain instant, it has a speed of 5.90 × 106 m/s. Determine the angle 2 (less than 90/) between the electron's velocity and the magnetic field. [me = 9.11 × 10-31 kg; qe = 1.6 × 10-19 C]

B.

The 1200-turn coil in a dc motor has a radius per turn of 6.9 cm. The design for the motor specifies that the magnitude of the maximum torque is 5.6 N A m when the coil is placed in a 0.18 magnetic field. What is the maximum current in the coil?

C.

At a certain location, the horizontal component of the earth's magnetic field is 4.0 × 10-5 T, due north. A 3.0 × 10-9 kg particle with charge 7 :C moves eastward with just the right speed, so the magnetic force on it balances its weight. Find the speed of the particle.

T

33.

34.

D.

The wingspan (tip-to-tip) of a Boeing 747 jetliner is 59 m. The plane is flying horizontally at a speed of 240 m/s. The vertical component of the earth's magnetic field is 5.0 × 10-6 T. Find the emf induced between the wing tips.

A.

Two very long, rigid wires are oriented parallel to each other and to the ground. The wires carry the same current in the same direction. The mass density of each wire is 0.114 kg/m. One wire is held in place 1 m above the ground, and the other floats beneath it at a distance of 8.2 × 10-3 m. Determine the current in the wires.

B.

The magnetic field produced by a 2 m long solenoid in a magnetic resonance imaging (MRI) system designed for measurements on whole human bodies has a field strength of 4.0 T and a current of 2.5 × 102 A. The solenoid is now compressed to 1.5 m with a current of 1.9 × 102 A. Find the strength of the magnetic field produced by the solenoid.

C.

The coil within an ac generator has an area per turn of 1.2 × 10-2 m2 and consists of 500 turns. The coil is situated in a 0.20 T magnetic field. The emf induced in the coil at the instant when the normal to the loop makes an angle of 35° with respect to the direction of the magnetic field is 23.4 V. What is the angular speed of the loop in revolutions per minute?

A.

A 5.0 m long and narrow rectangular loop of wire is moving toward the bottom of the page with a constant speed of 2.4 m/s. The loop is just starting to leave a region in which a 3.2 T magnetic field exists; the magnetic field outside this region is zero. The loop has a resistance of 2 S. During a time of 1.7 s, what is the magnitude of the induced current? The current flows CLOCKWISE or COUNTERCLOCKWISE (circle one)?

35.

B.

The drawing shows an end-view of three wires. They are long, straight, and perpendicular to the plane of the paper. Their cross sections lie at the corners of a rectangle. The current in wire 1 is 2 amps and it is directed into the paper. The net magnetic field at the empty corner is zero. The current in wire 2 is also into the page and the current in wire 3 is directed out of the page. What are the currents in wires 2 and 3?

A.

Two long straight wires, oriented perpendicular to the page, carry currents of Ileft = 50.0 A and Iright = 15.0 A. The wires are separated by a distance of 12.0 cm. Suppose a third wire carrying a 4.00 A current is situated perpendicular to the plane of the page and passes through point P. The current flowing in this wire goes into the plane of the page. What magnetic force, magnitude and direction, does a 20.0 cm length of this wire feel?

B.

A single loop of a wire has the shape shown in the drawing. The top part of the wire is bent into a semicircle of radius r = 0.19 m. The normal to the plane of the loop is parallel to a constant magnetic field of magnitude 0.88 T. The resistor has a resistance of 3 S. What is the average induced current in the loop when, starting with the position shown in the drawing, the semicircle is rotated through half a revolution in 0.05 s? Does the current flow clockwise or counterclockwise (circle one)?

36.

37.

38.

A.

A -6.00 μC charge is moving with a speed of 6.60 × 104 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 76.5 A in a direction opposite to that of the moving charge. Find the force on the charge ( magnitude and direction) and clearly specify direction.

B.

The coil within an ac generator has an area per turn of 1.2 × 10-2 m2 and consists of 500 turns. The coil is situated in a 0.20 T magnetic field. The emf induced in the coil, at the instant when the normal to the loop makes an angle of 35° with respect to the direction of the magnetic field, is 23.4 V. What is the angular speed of the loop?

C.

A magnetic field has a magnitude of 1.20 × 10-3 T, and an electric field has a magnitude of 5.40 × 103 N/C. Both fields point in the same direction. A positive 1.8 µC charge moves at a speed of 3.60 × 106 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net force that acts on the charge.

D.

Solar wind is a thin, hot gas given off by the sun. Charged particles in this gas enter the magnetic field of the earth and can experience a magnetic force. Suppose an electron traveling with a speed of 9.00 × 106 m/s encounters the earth's magnetic field at an altitude where the field has a magnitude of 1.40 × 10-7 T. Assuming that the electron's velocity makes a 37.0° angle with respect to the magnetic field, find the radius of the circular path on which the electron would move.

A.

Two long straight wires carry currents of I1 = 30.0 A and I2 = 12.0 A and are oriented perpendicular to the page as shown. Suppose a third wire carrying a 6.00 A current is situated perpendicular to the plane of the page and passes through point P. The current flowing in the third wire goes into the plane of the page. What is the magnitude of the magnetic force on a 40.0 cm length of the third wire?

B.

A circular coil (650 turns, radius = 0.02 m) is rotating in a uniform magnetic field. At t = 0 s, the normal to the coil is perpendicular to the magnetic field. At t = 0.010 s, the normal makes an angle of θ = 30° with the field since the coil has made one-sixth of a revolution. An average emf of magnitude 0.04 V is induced in the coil. What is the magnitude of the magnetic field at the location of the coil?

A.

A piece of copper wire has a resistance per unit length of 6.20 × 10-3 Ω/m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.200 m. The ends of the wire are connected to a 12.0 V battery. Find the magnetic field strength at the center of the coil.

B.

A particle with a charge of 14 μC experiences a force of 2.2 × 10-4 N when it moves at right angles to a magnetic field with a speed of 23 m/s. What force does this particle experience when it moves with a speed of 6.8 m/s at an angle of 25° relative to the magnetic field?

39.

C.

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10-27 kg and 21.59 × 10-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 6.00 × 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.8500 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle.

A.

A 2500 turn solenoid with a length of 30.0 cm and a radius of 2.5 cm carries an initial current of 5.0 Amps. A small circular coil of radius 1.5 cm and made of 3 turns is placed inside the solenoid so that the flux is maximal. The circular coil has a resistance of 3.00 Ω. 1. 2.

40.

Find the magnitude of the average induced current in the circular coil when the current in the solenoid increases to 7.0 Amps in 0.080 seconds. Does the current in the circular coil flow the same direction or opposite direction as the current in the solenoid?

B.

Two long straight wires, oriented perpendicular to the page, carry currents of Ileft = 10.0 A and Iright = 25.0 A. The wires are separated by a distance of 20.0 cm. Somewhere along an extended line though the two wires the net magnetic field is zero. Is it in Region I, Region II, or Region III (circle one)? How far away is this point from the left wire?

A.

An electron is moving through a magnetic field whose magnitude is 9.00 × 10-4 T. The electron experiences only a magnetic force and has an acceleration of magnitude 3.20 × 1014 m/s2. At a certain instant, the angle between the electron’s velocity and the magnetic field is 20.1°. Determine the speed of the electron.

B.

A -6.00 μC charge is moving with a speed of 5.60 × 104 m/s parallel to a very long, straight wire. The wire is 4.00 cm from the charge and carries a current of 76.5 A in a direction opposite to that of the moving charge. Find the magnitude and direction (clearly specify direction) of the force on the charge.

C.

In 1996, NASA performed an experiment called the Tethered Satellite experiment. In this experiment a 1.80 × 104 m length of wire was let out by the space shuttle Atlantis to generate a motional emf. The shuttle had an orbital speed of 7.70 × 103 m/s, and the magnitude of the earth's magnetic field at the location of the wire was 5.40 × 10-5 T. If the wire was moved perpendicular to the earth's magnetic field, what was the motional emf generated between the ends of the wire?

D.

A 0.88 m length of wire is formed in to a double-turn, square loop in which there is a current of 10 A. The loop is placed in a magnetic field of 0.20 T. What is the maximum torque that the loop can experience?

41.

A.

For each of the three sheets of polarizing material shown in the drawing, the orientation of the transmission axis is labeled relative to the vertical. The incident beam of light is unpolarized and has an intensity of 1200 W/m2. 1. 2.

B.

Two long straight wires, oriented perpendicular to the page, carry currents of Ileft = 10.0 A and Iright = 25.0 A. Ileft is into the page and Iright is coming out of the page. The wires are separated by a distance of 20.0 cm. Somewhere along an extended line though the two wires the magnetic field created by each wire is the same in magnitude and points in the same direction. 1. 2.

42.

43.

What is the intensity of the beam transmitted through the three sheets when θ1 = 30°, θ2 = 60° and θ3 = 90°? A fourth sheet of polarizing material with a transmission axis aligned with the vertical is inserted into the above configuration immediately after the second polarizer while leaving everything else the same. What is the new intensity of the transmitted beam?

Is this point to the right or the left of the left wire (circle one)? How far away is this point from the left wire?

RIGHT LEFT

A.

The coil within an ac generator has an area per turn of 1.2 × 10-2 m2 and consists of 500 turns. The coil is situated in a 0.20 T magnetic field. The emf induced in the coil at the instant when the normal to the loop makes an angle of 35° with respect to the direction of the magnetic field is 23.4 V. What is the angular speed of the loop in revolutions per minute?

B.

The resistances of the primary and secondary coils of a transformer are 47 and 15 Ω, respectively. Both coils are made from lengths of the same copper wire. The circular turns of each coil have the same diameter. Find the turns ratio Ns/Np.

C.

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10-27 kg and 21.59 × 10-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 6.50 × 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.8800 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle.

A.

A solenoid has a radius of 5.60 cm, consists of 600 turns per meter, and carries a current of 2.1 A. A 10 turn circular loop of radius 2.00 cm is placed inside the solenoid so that the flux is maximal. The resistance of the loop is 1.7 Ω. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time of 0.14 s. Find the average current induced in the loop.

B.

Three long straight wires, each of length 4.0 m, are arranged in a rectangular configuration as shown in cross section. The current in wire A is 1.7 A, the current in wire B is 0.6 A, and the current in wire C is 2.5 A. The direction of the current flow is also indicated in the drawing. What is the magnitude and direction of the net force acting on wire C?

44.

45.

46.

A.

In a certain region, the earth's magnetic field has a magnitude of 5.50 × 10-5 T and is directed north at an angle of 52° below the horizontal. An electrically charged bullet is fired north and 11° above the horizontal, with a speed of 657 m/s. The magnetic force on the bullet is 2.60 × 10-10 N, directed due east. Determine the bullet's electric charge, including its algebraic sign (+ or −)

B.

A -6.00 μC charge is moving with a speed of 5.60 × 10^4 m/s parallel to a very long, straight wire. The wire is 4.00 cm from the charge and carries a current of 76.5 A in the same direction as that of the moving charge. Find the magnitude and direction (clearly specify direction) of the force on the charge.

C.

In 1996, NASA performed an experiment called the Tethered Satellite experiment. In this experiment a 1.80 × 104 m length of wire was let out by the space shuttle Atlantis to generate a motional emf. The shuttle had an orbital speed of 7.70 × 103 m/s, and the magnitude of the earth's magnetic field at the location of the wire was 5.40 × 10-5 T. I f the wire had moved perpendicular to the earth's magnetic field, what would have been the motional emf generated between the ends of the wire?

D.

The maximum torque experienced by a coil in a 0.55 T magnetic field is 8.4 × 10-4 N · m. The coil is circular and consists of only one turn. T he current in the coil is 3.3 A. What is the length of the wire from which the coil is made?

A.

A 0.3 m long solenoid has a radius of 5.60 cm, consists of 500 turns , and carries a current of 1.3 A. A 10 turn square loop of side 2.00 cm is placed inside the solenoid so t-+hat the flux is maximal. The resistance of the loop is 1.3 Ω. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time of 0.12 s. Find the average current induced in the loop during the 0.12 s.

B.

The drawing shows four insulated wires overlapping one another, forming a square with 0.050-m sides. All four wires are much longer than the sides of the square. The net magnetic field at the center of the square is 74.5 µT. Calculate the current I.

A.

The maximum strength of the earth's magnetic field is about 6.9 × 10-5 T near the south magnetic pole. In principle, this field could be used with a rotating coil to generate 60.0-Hz ac electricity. What is the minimum number of turns (area per turn = 0.080 m2) that the coil must have to produce an rms voltage of 120 V?

B.

T transformer consisting of two coils wrapped around an iron core is connected to a generator and a resistor, as shown in the drawing. There are 11 turns in the primary coil and 18 turns in the secondary coil. The peak voltage across the resistor is 73.3 V. What is the peak emf of the generator?

47.

C.

When beryllium-7 ions (m = 1.165 × 10-26 kg) pass through a mass spectrometer, a uniform magnetic field of 0.3465 T curves their path directly to the center of the detector (see figure below). For the same accelerating potential difference, what magnetic field should be used to send beryllium-10 ions (m = 1.663 × 10-26 kg) to the same location in the detector? Both types of ions are singly ionized (q = +e).

A.

For each of the three sheets of polarizing material shown in the drawing, the orientation of the transmission axis is labeled relative to the vertical. The incident beam of light is vertically polarized and has an intensity of 1500 W/m2. 1. 2.

B.

What is the intensity of the beam transmitted through the three sheets when θ1 = 0°, θ2 = 30° and θ3 = 15°? A fourth sheet of polarizing material with a transmission axis aligned perpendicular to that of the third polarizer is inserted into the above configuration immediately after the second polarizer while leaving everything else the same. What is the new intensity of the transmitted beam?

Three long straight wires, each of length 7.0 m, are arranged in a rectangular configuration as shown in cross section. The current in wire A is 1.3 A, the current in wire B is 1.8 A, and the current in wire C is 2.5 A. The direction of the current flow is also indicated in the drawing. What is the magnitude and direction of the net force acting on wire C?