Deck 19: Magnetic Forces and Fields

Question 1

A proton cyclotron has a magnetic field of 0.20 T between its poles and a radius of 0.40 m. What is the maximum energy for the protons from this machine?

A) 1.6 × 10⁻¹³ J
B) 3.2 × 10⁻¹³ J
C) 4.9 × 10⁻¹³ J
D) 3.2 × 10⁻¹⁴ J
E) 4.9 × 10⁻¹⁴ J

Answer 1

4.9 × 10⁻¹⁴ J

Question 2

What is the speed of a proton in a cyclotron having a 0.50 T magnetic field when the proton is at a distance of 25 cm from the center?

A) 3.7 × 10⁷ m/s
B) 1.2 × 10⁷ m/s
C) 6.0 × 10⁶ m/s
D) 3.2 × 10⁶ m/s
E) 1.1 × 10⁴ m/s

Answer 2

1.2 × 10⁷ m/s

Question 3

A proton is moving at 3.0 × 10⁶ m/s and experiences a magnetic force of magnitude 2.5 × 10⁻¹⁶ N. If the magnetic field makes an angle of 40° with respect to the velocity of the proton, what is the field's magnitude?

A) 1.7 × 10⁻⁴ T
B) 3.3 × 10⁻⁴ T
C) 4.1 × 10⁻⁴ T
D) 8.1 × 10⁻⁴ T
E) 1.6 × 10⁻³ T

Answer 3

8.1 × 10⁻⁴ T

Question 4

A proton is moving perpendicular to a magnetic field at 3.0 × 10⁶ m/s and experiences a magnetic force of magnitude 2.5 × 10⁻¹⁶ N. What is the magnitude of the magnetic field?

A) 0.52 T
B) 3.8 × 10⁻² T
C) 1.9 × 10⁻³ T
D) 2.6 × 10⁻⁴ T
E) 5.2 × 10⁻⁴ T

Question 5

An electron is moving at 3.0 × 10⁶ m/s at an angle of 40° to a 0.80 T magnetic field. What is the magnitude of the force on the electron?

A) 4.8 × 10⁻¹³ N
B) 3.8 × 10⁻¹³ N
C) 2.5 × 10⁻¹³ N
D) 2.9 × 10⁻¹³ N
E) 1.2 × 10⁻¹³ N

Question 6

A singly charged ⁹Be ion is accelerated from rest through a potential difference of 8000 V. The ion is then sent into a mass spectrometer where the radius of the path is 29 cm. What is the magnetic field in the spectrometer?

A) 0.27 T
B) 0.13 T
C) 0.067 T
D) 0.0028 T
E) 0.00019 T

Question 7

In ancient times permanent magnets were known to the Greeks. These magnets were chunks of iron ore now called magnetite. What is the older name for this material?

A) magnesia
B) lodestone
C) oersted
D) compass
E) None of these choices are correct.

Question 8

Find the force (magnitude and direction) exerted on an electron moving vertically upward at a speed of 2.0 × 10⁷ m/s by a horizontal magnetic field of 0.50 T directed north.

A) 1.6 × 10⁻¹² N west
B) 1.6 × 10⁻¹² N east
C) 1.8 × 10⁻¹² N west
D) 1.8 × 10⁻¹² N east

Question 9

The SI unit of magnetic field is the tesla, which is equivalent to a

A) N/C.
B) A/m.
C) N/(A·m).
D) magnon.
E) None of these choices are correct.

Question 10

A negative ion is moving east near the equator where the Earth's magnetic field is horizontal to the north. The direction of the magnetic force on the ion is

A) north.
B) south.
C) up.
D) down.
E) not meaningful since the force is zero.

Question 11

In diagrams of magnetic fields, the symbol "×" is used to represent

A) the region of no magnetic field.
B) the north magnetic field.
C) the magnetic field coming out of the paper.
D) the magnetic field going into the paper.
E) the magnetic field, regardless of direction.

Question 12

A bar magnet has a north pole and a south pole. This arrangement is referred to as a

A) monopole.
B) dipole.
C) bipole.
D) equipole.
E) oppopole.

Question 13

The magnetic force on a point charge in a given magnetic field and at a given speed is largest when the charge

A) has velocity components both parallel to and perpendicular to the field.
B) moves perpendicular to the magnetic field.
C) moves in the direction opposite to the magnetic field.
D) moves in the direction of the magnetic field.

Question 14

An electron is moving at 3.0 × 10⁶ m/s perpendicular to a uniform magnetic field. If the radius of the motion is 18 mm, what is the magnitude of the magnetic field?

A) 70 mT
B) 0.95 mT
C) 9.3 mT
D) 1.6 μT
E) 8.9 nT

Question 15

An electron is moving at 2.5 × 10⁶ m/s perpendicular to a uniform 3.5 mT magnetic field. What is the radius of its path?

A) 5.1 cm
B) 3.9 cm
C) 1.6 cm
D) 4.1 mm
E) 2.0 mm

Question 16

A cyclotron with a magnetic field of 1.2 T is used to accelerate protons. How does the time for the protons to complete one orbit change when the radius of their orbit changes from 10 cm to 22 cm?

A) It increases by a factor of 2.2.
B) It decreases by a factor of 2.2.
C) It increases by a factor of 4.8.
D) It decreases by a factor of 4.8.
E) It stays the same.

Question 17

A proton is moving at 2.0 × 10⁷ m/s in a magnetic field of 30 mT. What is the magnitude of the magnetic force on the proton?

A) 9.6 × 10⁻¹⁴ N
B) 4.8 × 10⁻¹⁴ N
C) 0.0
D) 6.0 × 10⁻⁵ N
E) More information is needed.

Question 18

A cyclotron with a magnetic field of 1.2 T is used to accelerate protons. How long does it take for the protons to make one complete trip around the cyclotron at a radius of 25 cm?

A) 11 ns
B) 28 ns
C) 32 ns
D) 48 ns
E) 55 ns

Question 19

Doubling the magnetic field in a proton cyclotron changes the maximum kinetic energy of the protons by what amount?

A) It is quadrupled.
B) It is doubled.
C) It remains the same.
D) It is halved.
E) It is quartered.

Question 20

A mass spectrometer splits a beam of ¹⁰B and ¹¹B singly charged ions having the same velocity by passing the beam through a uniform magnetic field. If the radius of the path for the ¹⁰B ions is 12.0 cm, what will be the radius for the ¹¹B ions?

A) 9.90 cm
B) 10.9 cm
C) 12.0 cm
D) 13.2 cm
E) 14.5 cm

Question 21

If the charge carriers are positive instead of negative, what difference will result when measuring the Hall voltage?

A) There is no difference.
B) Hall voltages will be double for positive charge carriers.
C) Hall voltages will be double for negative charge carriers.
D) The polarity of the voltage will be reversed.
E) Hall voltages cannot be measured for positive charge carriers.

Question 22

When measuring the Hall voltage, what happens to the reading when the current is increased 20%?

A) It increases 20%.
B) It increases 40%.
C) It increases 44%.
D) It decreases 20%.
E) It decreases 44%.

Question 23

The magnetic forces exerted on each other by two parallel wires with unequal currents flowing in opposite directions are

A) repulsive and unequal in magnitude.
B) attractive and unequal in magnitude.
C) repulsive and equal in magnitude.
D) attractive and equal in magnitude.

Question 24

In a velocity selector for ions, when the electric field is increased by 50%, what change in the magnetic field is necessary to select the same speed as before?

A) a 50% decrease
B) a 25% decrease
C) no change
D) a 25% increase
E) a 50% increase

Question 25

A velocity selector for ions uses perpendicular electric and magnetic fields. If the electric field used were 800 V/m, what magnetic field would allow the selection of a velocity of 4000 m/s?

A) 0.0400 T
B) 0.0800 T
C) 0.160 T
D) 0.200 T
E) 0.500 T

Question 26

A long straight wire is carrying a current of 2.4 A in a region where a uniform magnetic field is perpendicular to the wire. If the magnetic field is 0.52 mT, what is the magnitude of the force on 3.0 m of the wire?

A) 1.2 × 10⁻³ N
B) 3.7 × 10⁻³ N
C) 7.2 × 10⁻³ N
D) 3.7 N
E) 7.2 N

Question 27

If a charged particle is moving through a magnetic field with its velocity at an angle of 45 degrees with respect to the field, what happens to the magnetic force on it if both the speed and magnetic field are doubled?

A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It increases by a factor of 5.66.

Question 28

In a velocity selector for ions, when the velocity of the ions is double the value for which the selector is set, how do the magnetic force F_M and the electric force F_E compare?

A) F_M = 4 F_E
B) F_M = 2 F_E
C) F_M = F_E/2
D) F_M = F_E/4
E) F_M = 1.414 F_E

Question 29

A long straight wire is carrying a current of 2.4 A in a region with a uniform magnetic field. If the magnetic field is 0.52 mT and makes an angle of 60° with the wire, what is the magnitude of the force on 3.0 m of the wire?

A) 3.2 N
B) 6.5 N
C) 1.6 × 10⁻³ N
D) 3.2 × 10⁻³ N
E) 6.5 × 10⁻³ N

Question 30

A flat conductor of thickness 0.500 mm is placed in a magnetic field of 0.200 T perpendicular to the flat surface. If there are 8.00 × 10²⁴ charge carriers (i.e., electrons) per m³, what is the Hall voltage generated when 3.40 A flows along the conductor?

A) 0.266 mV
B) 0.531 mV
C) 0.797 mV
D) 1.06 mV
E) 2.12 mV

Question 31

A 3.0 cm section of a horizontal wire, carrying a 6.7 A current from east to west, is placed in a horizontal north-to-south 0.42 T uniform magnetic field in the lab. What is the magnitude of the force on the 3.0 cm section of the wire?

A) 0.084 N
B) 0.17 N
C) 0.25 N
D) 0.0017 N
E) 0.0025 N

Question 32

A 3.0 cm section of a horizontal wire, carrying a 6.7 A current from east to west, is placed in a horizontal north-to-south 0.42 T uniform magnetic field in the lab. In what direction is the magnetic force on the 3.0 cm section?

A) north
B) south
C) up
D) down
E) southwest

Question 33

A 300-turn coil of area 25 cm² is placed in an 80 mT magnetic field. If the coil carries a current of 3.3 A, what is the magnitude of the maximum magnetic torque it could experience?

A) 20 N·m
B) 6.0 N·m
C) 0.13 N·m
D) 0.20 N·m
E) 0.060 N·m

Question 34

The magnetic field in a cyclotron is 0.50 T. What is the radius of the vacuum chamber for a maximum proton velocity of 1.0 × 10⁷ m/s?

A) 0.11 m
B) 1.2 m
C) 0.21 m
D) 0.013 m

Question 35

The magnetic field in a cyclotron is 0.50 T. Find the magnitude of the magnetic force on a proton with velocity of 1.0 × 10⁷ m/s in a plane perpendicular to the field.

A) 6.0 × 10⁻¹⁴ N
B) 6.0 × 10⁻¹³ N
C) 8.0 × 10⁻¹⁴ N
D) 8.0 × 10⁻¹³ N

Question 36

Cathode rays are

A) x-rays.
B) γ-rays.
C) electrons.
D) protons.
E) neutrons.

Question 37

An electron is moving at 3.0 × 10⁶ m/s at an angle of 40° to a 0.80 T magnetic field. What is the magnitude of the acceleration of the electron?

A) 2.7 × 10¹⁷ m/s²
B) 1.4 × 10¹⁷ m/s²
C) 5.2 × 10¹⁷ m/s²
D) 7.8 × 10¹⁷ m/s²
E) 9.8 × 10¹⁷ m/s²

Question 38

A 10 m long wire carrying a current of 22 A makes an angle of 37° with the Earth's magnetic field of 0.51 mT. What is the magnetic force on the wire?

A) 0.11 N
B) 0.068 N
C) 0.19 N
D) 0.090 N
E) 0.011 N

Question 39

A 300-turn coil of area 25 cm² is placed in an 80 mT magnetic field. If the coil carries a current of 3.3 A and if the normal to the area of the coil makes an angle of 20° with the direction of the magnetic field, what is the magnitude of the torque on the coil?

A) 0.20 N·m
B) 0.19 N·m
C) 0.072 N·m
D) 0.068 N·m
E) 0.039 N·m

Question 40

An electric field perpendicular to a magnetic field is used as a velocity selector for Li⁺ ions, selecting the velocity v₁. Next, Li⁺⁺ ions are sent through the same velocity selector, selecting velocity v₂. If neither the electric nor magnetic fields have changed between the two processes, how do v₁ and v₂ compare?

A) v₂ = v₁
B) v₂ = 2 v₁
C) v₂ = v₁/2
D) v₂ = 4 v₁
E) v₂ = v₁/4

Question 41

What current is necessary to generate a field of 0.20 T inside a solenoid with 300 turns per cm?

A) 530 A
B) 5.3 A
C) 33 A
D) 0.33 A
E) 3.1 A

Question 42

All materials fall into one of three magnetic categories. Select the category that is invalid.

A) ferromagnetic
B) nonmagnetic
C) diamagnetic
D) paramagnetic

Question 43

One wire, lying on the x-axis, carries a current of 8.0 A in the positive x-direction. Another wire, lying on the y-axis, carries a current of 12 A in the positive y-direction. What is the magnitude of the magnetic field at (x, y) = (8.0 cm, 12.0 cm)?

A) 1.3 × 10⁻⁵ T
B) 3.0 × 10⁻⁵ T
C) 1.7 × 10⁻⁵ T
D) 4.3 × 10⁻⁵ T
E) 4.0 × 10⁻¹⁰ T

Question 44

Which of the following magnetic materials has domains?

A) paramagnetic
B) diamagnetic
C) solenoidic
D) amperic
E) ferromagnetic

Question 45

A charged particle having electric charge Q = 4.0e enters a region of magnetic field 1.2 T at an angle of 37 degrees relative to the magnetic field direction. If the speed of the particle upon entering the region is 2.8 × 10⁴ m/s, what is the magnitude of the force on the particle?

A) 1.8 × 10⁻¹⁴ N
B) 1.3 × 10⁻¹⁴ N
C) 3.3 × 10⁻¹⁵ N
D) 1.1 × 10⁻¹⁴ N
E) 1.4 × 10⁻¹⁴ N

Question 46

A power line carries 1000 A at a height of 20 m above the ground. What is the resulting magnetic field at ground level?

A) 50 mT
B) 0.13 mT
C) 13 μT
D) 10 μT
E) 5.0 μT

Question 47

A cyclotron is designed to accelerate protons (mass 1.67 × 10⁻²⁷ kg) up to a kinetic energy of 2.5 × 10⁻¹³ J. If the magnetic field in the cyclotron is 0.75 T, what is the radius of the dipole magnets in the cyclotron?

A) 14 cm
B) 24 cm
C) 17 cm
D) 5.8 cm

Question 48

If the magnetic field from a long, straight, current-carrying wire has a magnitude B₀ at a distance d, what is the magnitude of the field at a distance 2d?

A) also B₀
B) 0.707 B₀
C) 0.693 B₀
D) B₀/2
E) B₀/4

Question 49

A proton and electron, each travelling with the same velocity, enter a region of uniform magnetic field. They experience

A) forces in the same direction and having ratio F_p/F_e = m_e/m_p.
B) forces equal in magnitude, but opposite in direction.
C) forces opposite in direction and having ratio F_p/F_e = m_e/m_p.
D) the same force.

Question 50

A straight wire is carrying a current upward. Observed from above (i.e., looking downward towards the wire), the magnetic field lines are

A) radially outward.
B) radially inward.
C) clockwise circles.
D) counter-clockwise circles.
E) directed toward the observer.

Question 51

The magnetic field lines inside a bar magnet go in what direction?

A) from south pole to north pole
B) from north pole to south pole
C) from side to side
D) There are no magnetic field lines inside a bar magnet.

Question 52

The magnetic field inside a solenoid having 100 turns per cm and a current of 5.0 A is

A) 2.0 × 10⁻² T.
B) 1.0 × 10⁻² T.
C) 1.0 × 10⁻⁴ T.
D) 6.3 × 10⁻⁴ T.
E) 6.3 × 10⁻² T.

Question 53

The temperature at which ferromagnetic materials transform into paramagnetic materials is called the

A) Celsius temperature.
B) Carnot temperature.
C) Crossover temperature.
D) Curie temperature.
E) Chaos temperature.

Question 54

Two parallel wires are each carrying 10 A and are separated by 4.0 m. If the currents are in opposite directions, what is the magnitude of the magnetic field halfway between them?

A) 0.0
B) 1.0 μT
C) 2.0 μT
D) 4.0 μT
E) 1.4 μT

Question 55

Doubling the current, number of turns, the area, and the ambient magnetic field for a coil changes the maximum torque it can experience by what factor?

A) 2
B) 4
C) 8
D) 16
E) 32

Question 56

A solenoid of radius 1.1 cm, carrying a current of 2.2 A, produces a magnetic field at its center of 0.28 T. How many turns per unit length does the solenoid have?

A) 1.0 × 10⁵ m⁻¹
B) 1.0 × 10⁻⁹ m⁻¹
C) 1.1 × 10³ m⁻¹
D) 2.2 × 10³ m⁻¹
E) 7.0 × 10³ m⁻¹

Question 57

A charged particle having electric charge Q = 4.0e enters a region of magnetic field 1.2 T at an angle of θ relative to the magnetic field direction. If the speed of the particle upon entering the region is 2.8 × 10⁴ m/s, and the magnitude of the force on it is 1.3 × 10^-14 N, which of the following could be the angle θ?

A) 47°
B) 37°
C) 53°
D) 65°

Question 58

Two parallel wires run in a north-south direction. The eastern wire carries 15.0 A southward while the western wire carries 6.0 A northward. If the wires are separated by 30 cm, what is the magnitude of the magnetic field at a point between the wires 10 cm from the western wire?

A) 3.0 μT
B) 6.0 μT
C) 15 μT
D) 27 μT
E) 90 μT

Question 59

A cyclotron is designed to accelerate protons (mass 1.67 × 10⁻²⁷ kg) up to a kinetic energy of 2.5 × 10⁻¹³ J. If the radius of the dipole magnets is 96 cm, what is the magnetic field used in the cyclotron?

A) 35 mT
B) 0.13 T
C) 0.19 T
D) 0.21 T

Question 60

Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of 8.46 A circulating clockwise and has a radius of 6.20 cm. The smaller loop has a radius of 4.42 cm. What is the magnitude and direction of the current in the smaller loop if the total magnetic field at the center of the system is zero?

A) 6.03 A CCW
B) 6.03 A CW
C) 12.8 A CCW
D) 12.8 A CW

Question 61

A charged particle of enters a region of uniform magnetic field at a speed of 2.8 × 10⁶m/s, at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is 1.2 T and the charge of the particle is +e, and the radius of the helical path is 8.8 cm, what is the particle's mass?

A) 7.7 × 10⁻²⁷ kg
B) 6.1 × 10⁻²⁷ kg
C) Insufficient information is given.
D) 1.0 × 10⁻²⁶ kg

Question 62

A wire bearing current of 1.25 A crosses a region in which there is a uniform B field of magnitude 1.0 T in the +y direction. The wire is inclined at an angle of 75 degrees above the +x direction, in the xy-plane. What is the magnitude of the force on the wire, if the magnetic field region spans 15 cm in the x direction?

A) 0.19 N
B) 0.70 N
C) 0.18 N
D) 0.05 N

Question 63

A charged particle of mass 1.0 × 10⁻²⁶ kg enters a region of uniform magnetic field at a speed of 2.8 × 10⁶ m/s, at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is 1.2 T what will be the radius of the helical path it takes?

A) Insufficient information given.
B) 15 cm.
C) 8.9 cm.
D) 11 cm.

Question 64

A coil of 150 turns of wire is in the form of a circle of radius 7.5 cm and sits in the center of a region of uniform magnetic field of strength 1.5 T. The torque on the coil has a maximum value of 0.25 N·m. What is the current in the coils?

A) 9.4 A
B) 200 mA
C) 4.7 mA
D) 63 mA
E) 94 mA

Question 65

A charged particle of mass 1.0 × 10⁻²⁶ kg enters a region of uniform magnetic field at a speed of 2.8 × 10⁶ m/s, at an angle of 37 degrees relative to the magnetic field direction. If the magnetic field strength is 1.2 T and the charge of the particle is +e, what will be the radius of the helical path it takes?

A) Insufficient information is given.
B) 15 cm
C) 11 cm
D) 8.8 cm

Question 66

A 2.5 cm-long horizontal wire segment has a mass of 0.15 g and carries a current sufficiently large that it levitates when the segment is in a region of uniform B field of magnitude 1.5 T. Assume that the B field is horizontal and perpendicular to the wire segment. The current is passed to the segment by way of massless electrical leads. What is the magnitude of the current in the wire?

A) 39 mA
B) 25 A
C) 4.0 mA
D) Not enough information is given.

Question 67

A charged particle enters a region of uniform magnetic field at a speed of 2.8 × 10⁴ m/s, at an angle of 37 degrees relative to the magnetic field direction. What will be the magnitude of the component of the particle's velocity that is parallel to the magnetic field while it is in this region?

A) Insufficient information is given.
B) 2.2 × 10⁴ m/s
C) 2.1 × 10⁴ m/s
D) 1.7 × 10⁴ m/s
E) 2.8 × 10⁴ m/s

Question 68

A coil of 150 turns of wire is in the form of a circle, carries a current of 63 mA, and sits in the center of a region of uniform magnetic field of strength 1.5 T. The torque on the coil has a maximum value of 0.25 N·m. What is the radius of the coils?

A) 9.2 cm
B) 13 cm
C) 0.56 cm
D) 7.5 cm