Deck 6: The Magnetic Field

Question 1

An electron is traveling horizontally east in the magnetic field of Earth near the equator. The direction of the force on the electron is

A) zero
B) north
C) south
D) upward
E) downward

Answer 1

downward

Question 2

The SI unit of magnetic field is the tesla (T). This is equivalent to

A) N · s/(C · m)
B) N · C/(s · m)
C) N · m/s²
D) C/(A · s)
E) None of these is correct.

Answer 2

N · s/(C · m)

Question 3

The left diagram shows a positively charged particle is moving with velocity v in a magnetic field B. Using the right diagram, the direction of the magnetic force on the particle is

A) 1
B) 2
C) 3
D) 4
E) 5

Answer 3

1

Question 4

A wire 30 cm long with an east-west orientation carries a current of 3.0 A eastward. There is a uniform magnetic field perpendicular to this wire. If the force on the wire is 0.18 N upward, what are the direction and magnitude of the magnetic field?

A) 0.20 T up
B) 0.20 T north
C) 0.20 T south
D) 2.0 *10^-3 T north
E) 2.0 *10^-3 T up

Question 5

The phenomenon of magnetism is best understood in terms of

A) the existence of magnetic poles.
B) the magnetic fields associated with the movement of charged particles.
C) gravitational forces between nuclei and orbital electrons.
D) electrical fluids.
E) None of these is correct.

Question 6

The magnetic force on a charged particle

A) depends on the sign of the charge on the particle.
B) depends on the velocity of the particle.
C) depends on the magnetic field at the particle's instantaneous position.
D) is at right angles to both the velocity and the direction of the magnetic field.
E) is described by all of these.

Question 7

A straight wire segment 3.0 m long makes an angle of 28º with a uniform magnetic field of 1.0 T. The magnitude of the force on the wire if it carries a current of 1.5 A is approximately

A) 2.1 N
B) 4.0 N
C) 1.4 N
D) 0.70 N
E) 4.7 N

Question 8

A rectangular loop of wire (0.10 m by 0.20 m) carries a current of 5.0 A in a counterclockwise direction. The loop is oriented as shown in a uniform magnetic field of 1.5 T. The force acting on the upper 0.10-m side of the loop is

A) 1.5 N
B) 0.75 N
C) 0.50 N
D) 0.15 N
E) zero

Question 9

The region of space around a moving proton contains

A) a gravitational field only.
B) a magnetic field only.
C) an electric field only.
D) both an electric and a magnetic field.
E) neither an electric nor a magnetic field.

Question 10

Which of the following statements is false?

A) Electric field lines due to an electric dipole and magnetic field lines due a magnetic dipole have similar configuration.
B) Electric field starts from a positive charge and ends at a negative charge.
C) Magnetic field starts at the north pole and ends at the south pole.
D) Magnetic poles always occur in pairs.
E) Magnetic fields result from the flow of charges.

Question 11

A straight wire of length 20 cm floats in a horizontal perpendicular to a magnetic field of 1.5 T when a current of 1.3 A passes through the wire in a perpendicular direction to the magnetic field. Find the mass per unit length of the wire. (The wire is connected to a battery by ultra light flexible leads.)

A) 0.40 kg/m
B) 0.20 kg/m
C) 20 g/m
D) 40 g/m
E) none of the above

Question 12

A long straight wire parallel to the y axis carries a current of 6.3 A in the positive y direction. There is a uniform magnetic field = 1.5 T . The force per unit length on the wire is approximately

A) 6.3 N/m
B) -9.5 N/m
C)-6.3 N/m
D) 9.5 N/m
E) 1.5 N/m

Question 13

A positively charged particle is moving northward in a magnetic field. The magnetic force on the particle is toward the northeast. What is the direction of the magnetic field?

A) up
B) west
C) south
D) down
E) This situation cannot exist.

Question 14

One Tesla is equal to

A) 10 G
B) 100 G
C) 1000 G
D) 10000 G
E) 10^-4 G

Question 15

A proton with a charge +e is moving with a speed v at 50º to the direction of a magnetic field . The component of the resulting force on the proton in the direction of is

A) evB sin 50º cos 50º
B) evB cos 50º
C) zero
D) evB sin 50º
E) None of these is correct.

Question 16

If the magnetic field vector is directed toward the north and a positively charged particle is moving toward the east, what is the direction of the magnetic force on the particle?

A) up
B) west
C) south
D) down
E) east

Question 17

A current I flows in a wire that is oriented as shown. The vector representing the magnetic field that results in a maximum force on the wire is

A)
B)
C)
D)
E)

Question 18

A charged particle is moving horizontally westward with a velocity of 3.5* 10⁶ m/s in a region where there is a magnetic field of magnitude 5.6 * 10^-5 T directed vertically downward. The particle experiences a force of 7.8 * 10^-16 N northward. What is the charge on the particle?

A) +4.0 *10^-18 C
B) -4.0 * 10^-18 C
C) +4.9 * 10^-5 C
D) -1.2 *10^-14 C
E) +1.4 * 10^-11 C

Question 19

An electron is traveling east with an instantaneous velocity of 3.3 * 10⁵ m/s when it enters a uniform magnetic field of 0.25 T that points X degrees north of east. (Take east as to the right of the paper and north as towards the top of the paper, i.e. both in the plane of the paper.) If the magnitude of the force on the electron is 5.5*10^-15 N, then calculate the angle X and whether the electron moves up out of or down into the plane of the page, or otherwise.

A) 26° and up out of the page
B) 65° and down into the page
C) 26° and down into the page
D) 65° and up out of the page
E) 65° and south in the plane of the paper

Question 20

The left diagram shows a force F on a negatively charged particle moving a magnetic field B. Using the right diagram, the direction of the velocity of the particle is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 21

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional to

A) the particle's charge.
B) the particle's momentum.
C) the particle's energy.
D) the flux density of the field.
E) All of these are correct.

Question 22

When a cathode-ray tube with its axis horizontal is placed in a magnetic field that is directed vertically upward, the electrons emitted from the cathode follow one of the dashed paths to the face of the tube. The correct path is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 23

Use the diagram for the next three problems. Electrons traveling at a speed of v₀ = 3 * 10⁷ m/s pass through the deflection plates. The electric field between the plates is E = 5000 V/m and spans a distance of
x₁ = 5 cm. The electrons then travel a further distance of x₂ = 40 cm along the x-axis.

-With the magnetic field turned off, the total deflection in the y direction is

A) 1.22 * 10^-3 m
B) 1.95 * 10^-2 m
C) 2.07 * 10^-2 m
D) 9.50 * 10^-3 m
E) 1.38 * 10^-2 m

Question 24

A doubly ionized oxygen atom ¹⁶O²⁺ is moving in the same uniform magnetic field as an alpha particle. The velocities of both particles are at right angles to the magnetic field. The paths of the particles have the same radius of curvature. The ratio of the energy of the alpha particle to that of the ¹⁶O²⁺ ion is

A) E _$\alpha$ /E_O = 1/1
B) E _$\alpha$ /E_O = 1/4
C) E _$\alpha$ /E_O = 1/16
D) E _$\alpha$ /E_O = 4/1
E) None of these is correct.

Question 25

A deuteron is moving with a speed of 2.0 *10⁶ m/s at right angles to a magnetic field. The field is uniform, with magnitude B = 0.40 T. The mass and charge of a deuteron are 3.3 * 10^-27 kg and 1.6 * 10^-19 C, respectively. The radius of the deuteron orbit is approximately

A) 0.21 m
B) 1.8 m
C) 6.3 m
D) 10 cm
E) 27 cm

Question 26

The radius of curvature of the path of a charged particle moving perpendicular to a magnetic field is given by

A) qE/m
B) Bm/(qv)
C) Bv/(qm)
D) mv/(qB)
E) Bq/(mv)

Question 27

Use the diagram for the next three problems. Electrons traveling at a speed of v₀ = 3 * 10⁷ m/s pass through the deflection plates. The electric field between the plates is E = 5000 V/m and spans a distance of
x₁ = 5 cm. The electrons then travel a further distance of x₂ = 40 cm along the x-axis.

-What should the strength of the magnetic field be for the electrons to land at a?

A) 1.67 G
B) 3.33 G
C) 6000 G
D) 3000 G
E) 12000 G

Question 28

A particle with charge q and mass m is moving with speed v in the +x direction enters a magnetic field of strength B pointing in the +y direction. The work done by the magnetic force on the particle as it travels one semi-circle is

A) $\pi$ mqvB
B) $\pi$ mv²
C) $\pi$ qvB
D) zero
E) $\pi$ mv/qB

Question 29

All of the charged particles that pass through crossed electric and magnetic fields without deflection have the same

A) mass.
B) speed.
C) momentum.
D) energy.
E) charge-to-mass ratio.

Question 30

An electron is accelerated from rest by an electric field. After the acceleration, the electron is injected into a uniform magnetic field of 1.27 * 10^-3 T. The velocity of the electron and the magnetic field lines are perpendicular to one another. The electron remains in the magnetic field for 5.00 * 10^-9 s. The angle between the initial electron velocity and the final electron velocity is

A) 1.1 rad
B) 5.8 * 10^-2 rad
C) 8.68* 10^-2 rad
D) 6.5 * 10^-2 rad
E) 2.3 rad

Question 31

Use the diagram for the next three problems. Electrons traveling at a speed of v₀ = 3 * 10⁷ m/s pass through the deflection plates. The electric field between the plates is E = 5000 V/m and spans a distance of
x₁ = 5 cm. The electrons then travel a further distance of x₂ = 40 cm along the x-axis.

-In which direction should the magnetic field be applied so that the electron lands undeflected at a?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 32

A cyclotron

A) accelerates particles electrically.
B) accelerates particles magnetically.
C) guides particles magnetically.
D) gives the same period to all particles with the same charge-to-mass ratio.
E) is described by all of these.

Question 33

An alpha particle of charge +2e and mass 4(1.66 * 10^-27) kg, and an ¹⁶O nucleus of charge +8e and mass 16(1.66 *10^-27) kg have been accelerated from rest through the same electric potential. They are then injected into a uniform magnetic field , where both move at right angles to the field. The ratio of the radius of the path of the alpha particle to the radius of the path of the nucleus ¹⁶O is

A) r _$\alpha$ /r_O = 1/1
B) r _$\alpha$ /r_O = 1/4
C) r _$\alpha$ /r_O = 1/8
D) r _$\alpha$ /r_O = 1/2
E) None of these is correct.

Question 34

A beam of electrons is undeflected when it passes simultaneously through an electric field of 10 N/C perpendicular to its path and a magnetic field of 2 *10^-4 T perpendicular both to its path and to the electric field. The speed of the electrons is approximately

A) 2 * 10^-4 m/s
B) 1 * 10⁴ m/s
C) 5 * 10^-4 m/s
D) 2* 10⁴ m/s
E) 5*10⁴ m/s

Question 35

An electron passes through a region where there is an electric field E = 4.0 * 10⁵ V/m and a magnetic field B = 0.090 T. The directions of the electric field, the magnetic field, and the electron velocity are mutually perpendicular. If the electron is not deflected from its straight-line path through these fields, its velocity must be

A) 3.6*10⁴ m/s
B) 5.0* 10⁵ m/s
C) 2.2 *10^-7 m/s
D) 1.2 * 10⁴ m/s
E) 4.4 *10⁶ m/s

Question 36

The apparatus in the figure consists of two parallel plates (shown on edge) and a large magnet (not shown). The field of the magnet is uniform, perpendicular to the electric field between the plates, and directed into the plane of the paper. The magnitude of is 0.40 T. Charged particles with speeds of 5.0 *10⁵ m/s enter this region through the slit at the left and emerge through the exit slit at the right. What magnitude and direction must the field have so that positively charged particles entering from the left will traverse to the exit slit undeviated?

A) 2.0 *10⁵ V/m up
B) 2.0* 10⁵ V/m down
C) 1.2 * 10⁶ V/m down
D) 1.2 *10⁶ V/m up
E) 2.4 * 10⁶ V/m down

Question 37

An electric field and a magnetic field are at right angles to each other and to the direction of a beam of electrons. There is no deflection of the beam when the magnitudes of the fields are 30 *10⁴ V/m and 2.0 *10^-3 T, respectively. The velocity of the electrons must be approximately

A) 0.60 km/s
B) 6.7 * 10^-8 m/s
C) 2.3 * 10¹⁶ m/s
D) 1.5 * 10⁸ m/s
E) 1.5* 10^-8 m/s

Question 38

An electron moving with velocity v enters a region where there is a uniform magnetic field B . As the electron moves through this region, it is

A) deflected in the positive y direction.
B) deflected in the positive z direction.
C) deflected in the negative y direction.
D) deflected in the negative z direction.
E) undeviated in its motion.

Question 39

A positively charged particle moves with velocity v along the x axis. A uniform magnetic field -B exists in the negative z direction. You want to balance the magnetic force with an electric field so that the particle will continue along a straight line. The electric field should be in the

A) positive x direction.
B) positive z direction.
C) negative y direction.
D) negative x direction.
E) negative z direction.

Question 40

A small positively charged body is moving horizontally and westward. If it enters a uniform horizontal magnetic field that is directed from north to south, the body is deflected

A) upward.
B) downward.
C) toward the north.
D) toward the south.
E) not at all.

Question 41

An electric field of 3.0 kV/m is perpendicular to a magnetic field of 0.20 T. An electron moving in a direction perpendicular to both and is not deflected if it has a velocity of

A) 6 km/s
B) 9 km/s
C) 12 km/s
D) 15 km/s
E) 6.7 m/s

Question 42

A beam of charged particles moving with a speed of 10⁶ m/s enters a uniform magnetic field of 0.1 T at right angles to the direction of motion. If the particles move in a radius of 0.2 m, then calculate their period of motion.

A) 6.3 *10^-7 s
B) 1.3* 10^-7 s
C) 1.3 *10^-6 s
D) 4.1 * 10^-7 s
E) none of the above

Question 43

A beam of electrons moving at a speed of 8 *10⁴ m/s is undeflected when it passes through an electric field of 5 N/C perpendicular to its path and a magnetic field that is perpendicular to its path and also to that of the electric field. Calculate the strength of the magnetic field.

A) 1.60 *10⁴ T
B) 6.25 * 10^-5 T
C) 7.81 *10^-10 T
D) 3.13 * 10^-5 T
E) 1.25 *10^-4 T

Question 44

The track ABC in the figure is a reproduction of the path of a charged particle in a cloud chamber. If the magnetic field is perpendicular to this sheet of paper and directed into the paper, the particle

A) has a positive charge and has moved from C to A.
B) has a negative charge and has moved from C to A.
C) has a positive charge and has moved from A to C.
D) has a negative charge and has moved from A to C.
E) is an alpha particle.

Question 45

Use the diagram for the next two problems.

-A circular current loop lies in the xy plane and has radius R = 10 cm. The loop has 20 turns and carries a current I = 4 A. A magnetic field of strength 0.3 T is applied at an angle of $\theta$ = 30 $\degree$ to the loop. The potential energy of the magnetic dipole is

A) 0.163 J
B) 0.544 J
C) 0.314 J
D) 0.653 J
E) 0.377 J

Question 46

A circular 20-turn coil with a radius of 10 cm carries a current of 3 A. It lies in the xy plane in a uniform magnetic field = 0.4 T + 0.3 T . The potential energy of the system is

A) -0.263 J
B) -0.461 J
C) -0.564 J
D) 0.564 J
E) 0.461 J

Question 47

A uniform magnetic field is parallel to and in the direction of the positive z axis. For an electron to enter this field and not be deflected by the field, the electron must be traveling in which direction?

A) any direction as long as it is in the xy plane.
B) any direction as long as it is in the xz plane.
C) along the positive x axis.
D) along the positive y axis.
E) along the positive z axis.

Question 48

A compass needle is in a homogeneous magnetic field with its south pole pointing in the positive direction of . The net force on the compass needle is

A) zero.
B) in the same direction as .
C) at a right angle to .
D) at right angles to the plane of and the needle.
E) in the opposite direction of .

Question 49

The track in the figure is a reproduction of the path of a charged particle in a cloud chamber. If the magnetic field is perpendicular to this sheet of paper, and directed out of the paper, the particle

A) has a positive charge and has moved from C to A.
B) has a negative charge and has moved from C to A.
C) has a positive charge and has moved from A to C.
D) has a negative charge and has moved from A to C.
E) is an alpha particle.

Question 50

Use the diagram for the next two problems.
A circular current loop lies in the xy plane and has radius R = 10 cm. The loop has 20 turns and carries a current I = 4 A. The magnetic dipole of the loop is

A)
B)
C)
D)
E)

Question 51

A positive ion is shown midway between the two dees of a cyclotron; at this instant its velocity is in the positive x direction. Which of the five arrangements of the electric, , and magnetic, , fields shown is applicable to the situation depicted?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 52

When a compass needle is in stable equilibrium in a magnetic field ,

A) the needle axis is at 45º to the field.
B) the south pole points in the positive direction of .
C) the north pole points in the positive direction of .
D) the needle axis is perpendicular to .
E) none of these occurs.

Question 53

The radius of the orbit of an electron moving with a speed of 10⁸ m/s perpendicular to a magnetic field of 5.0 * 10^-3 T is approximately

A) 1.1 m
B) 0.11 m
C) 0.34 m
D) 0.011 m
E) 8.9 m

Question 54

A circular, 20-turn coil of radius 5.0 cm is oriented in such a way that its axis makes a 30º angle with a uniform magnetic field of 0.15 T. What is the torque on the coil when it carries a current of 2.5 A?

A) 1.5 *10^-3 N · m
B) 9.4 * 10^-3 N · m
C) 2.9 * 10^-2 N · m
D) 5.1 * 10^-2 N · m
E) 0.59 N · m

Question 55

An alpha particle with a charge 2e and mass 4m is moving with velocity v when it enters a magnetic field B at right angles to its direction of motion. A deuteron of charge e and mass 2m also enters the field in the same direction and the same speed. Calculate the difference in radius of motion between the alpha particle and the deuteron in the magnetic field region.

A) mv/eB
B) 0
C) 2mv/eB
D) mv/2eB
E) mv/4eB

Question 56

In a mass spectrometer ions of Ni with mass 9.62 * 10^-26 kg and charge +2e are accelerated through a potential difference of X volts and then deflected in a magnetic field of 0.15 T. If the radius of curvature of the ions is 0.55 m, then calculate the value of the potential difference X.

A) 5.7 kV
B) 274 kV
C) 137 kV
D) 11.3 kV
E) none of the above

Question 57

A small permanent magnet is placed in a uniform magnetic field of magnitude 0.35 T. If the maximum torque experienced by the magnet is 0.50 N · m, what is the magnitude of the magnetic moment of the magnet?

A) 1.4 A · m²
B) 0.70 A · m²
C) 0.18 A · m²
D) 2.8 A · m²
E) 0.35 A · m²

Question 58

A positively charged particle is moving through uniform fields and , which are directed in the positive x and positive y directions, respectively. If there is no resultant force on the particle, then its velocity is in the

A) positive x direction.
B) positive y direction.
C) negative x direction.
D) positive z direction.
E) negative z direction.

Question 59

A circular, 20-turn coil has a radius of 5.0 cm. What is the magnitude of the magnetic moment of the coil when it carries a current of 2.5 A?

A) 1.5 A · m²
B) 0.16 A · m²
C) 2.0 *10^-2 A · m²
D) 0.39 A · m²
E) 3.9 kA · m²

Question 60

A rectangle is bent on two sides at 90 $\degree$ so that one end lies along the xy plane while the other end lies along the xz plane. The length of each bent portion is illustrated on the Figure. A current I flows through the loop. The magnetic dipole of the rectangle is

A)
B)
C)
D)
E) None of these is correct.

Question 61

Which of the following statements correctly describes the torque-potential energy relationship for a current-carrying coil in a uniform magnetic field?

A) The maximum potential energy occurs for the same orientation of magnetic dipole and the magnetic field that corresponds to maximum torque.
B) The potential energy of the system is constant.
C) The torque rotates the coil toward a position of lower potential energy.
D) The torque rotates the coil toward a position of higher potential energy.
E) None of these is correct.

Question 62

A circular 10-turn coil with a radius of 5.0 cm carries a current of 5 A. It lies in the xy plane in a uniform magnetic field = 0.05 T + 0.12 T . The coil rotates so that its magnetic moment, $\mu$ , is aligned with the magnetic field. The potential energy of the system when the coil's magnetic moment is aligned with the field is

A) 86.3 mJ
B) 51.1 mJ
C) 28.2 mJ
D) -28.2 mJ
E) -51.1 mJ

Question 63

The angle through which the pointer on a galvanometer rotates is

A) proportional to the current in its coil.
B) inversely proportional to the current in its coil.
C) proportional to the magnetic flux through its coil.
D) proportional to the area of its coil.
E) independent of these factors.

Question 64

A circular 20-turn coil with a radius of 10 cm carries a current of 3 A. It lies in the xy plane in a uniform magnetic field = 0.4 T + 0.3 T . The coil rotates so that its magnetic moment, $\mu$ , is aligned with the magnetic field. The potential energy of the system when the coil's magnetic moment is aligned with the field is

A) 0.282 J
B) -0.461 J
C) 0.461 J
D) -0.282 J
E) -0.564 J

Question 65

A circular 10-turn coil with a radius of 5.0 cm carries a current of 5 A. It lies in the xy plane in a uniform magnetic field = 0.05 T + 0.12 T . The potential energy of the system is

A) -4.72 mJ
B) -5.11 mJ
C) -6.34 mJ
D) 4.72 mJ
E) 5.11 mJ

Question 66

The rectangular aluminum strip in the figure is in a uniform magnetic field, . The current I is flowing perpendicular to surface 1. Negative charges will accumulate on

A) surface 1.
B) surface 2.
C) surface 3.
D) the surface opposite surface 2.
E) none of these surfaces.

Question 67

The rectangular aluminum strip in the figure is in a uniform magnetic field, . The current I is flowing perpendicular to surface 1. Positive charges will accumulate on

A) surface 1.
B) surface 2.
C) surface 3.
D) the surface opposite surface 2.
E) none of these surfaces.

Question 68

A rectangular loop of wire (0.10 m by 0.20 m) carries a current of 5.0 A in a counterclockwise direction. The loop is oriented as shown in a uniform magnetic field. The magnetic dipole moment associated with this loop has a value of

A) 0.026 A · m²
B) 0.030 A · m²
C) 0.10 A · m²
D) 0.50 A · m²
E) 1.5 A · m²

Question 69

A current I passes through a slab of metal in the presence of a magnetic field B. Between which two sides does a Hall voltage develops? Write the side with the higher potential first. The labels are: a and b the two sides on the left and right, c and d the two sides on the front and back, and e and f the top and bottom respectively.

A) a and b
B) c and d
C) e and f
D) b and a
E) d and c

Question 70

Use the following figure for the next problem.


-A metal strip 1.5 cm wide and 0.20 cm thick carries a current in a uniform magnetic field of 1.5 T. The Hall emf is 5.3 $\mu$ V. The drift velocity of the electrons in the strip is approximately

A) 3.5 mm/s
B) 0.24 mm/s
C) 0.24 cm/s
D) 3.5 cm/s
E) 4.7 cm/s

Question 71

Use the following figure for the next problem.


-A metal strip 1.5 cm wide and 0.20 cm thick carries a current of 15 A in a uniform magnetic field of 1.5 T. The Hall emf is 5.3 $\mu$ V. The electronic charge is 1.6 * 10^-19 C. The number density of the charge carriers in the strip is approximately

A) 2.6*10²⁸ electrons/m³
B) 1.3 * 10²⁶ electrons/m³
C) 1.3 * 10²⁸ electrons/m³
D) 4.7 * 10²⁸ electrons/m³
E) 2.9 * 10²³ electrons/m³