Deck 30: Magnetic Fields and Forces

Question 1

What is the magnitude of the magnetic force on a charged particle (Q = 5.0 μC) moving with a speed of 80 km/s in the positive x direction at a point where Bx = 5.0 T, By = −4.0 T, and Bz = 3.0 T?

A)2.8 N
B)1.6 N
C)1.2 N
D)2.0 N
E)0.4 N

Answer 1

2.0 N

Question 2

An electron has a velocity of 6.0 × 106 m/s in the positive x direction at a point where the magnetic field has the components Bx = 3.0 T, By = 1.5 T, and Bz = 2.0 T. What is the magnitude of the acceleration of the electron at this point?

A)2.1 × 1018 m/s²
B)1.6 × 1018 m/s²
C)2.6 × 1018 m/s²
D)3.2 × 1018 m/s²
E)3.7 × 1018 m/s²

Answer 2

2.6 × 1018 m/s²

Question 3

A straight wire is bent into the shape shown. Determine the net magnetic force on the wire when the current I travels in the direction shown in the magnetic field . ​ ​

A)2IBL in the −z direction
B)2IBL in the +z direction
C)4IBL in the +z direction
D)4IBL in the −z direction
E)zero

Answer 3

2IBL in the +z direction

Question 4

A 2.0-C charge moves with a velocity of m/s and experiences a magnetic force of N. The x component of the magnetic field is equal to zero. Determine the y component of the magnetic field.

A)−3.0 T
B)+3.0 T
C)+5.0 T
D)−5.0 T
E)+6.0 T

Question 5

A segment of wire carries a current of 25 A along the x axis from x = −2.0 m to x = 0 and then along the y axis from y = 0 to y = 3.0 m. In this region of space, the magnetic field is equal to 40 mT in the positive z direction. What is the magnitude of the force on this segment of wire?

A)2.0 N
B)5.0 N
C)1.0 N
D)3.6 N
E)3.0 N

Question 6

A 2.0-m wire carries a current of 15 A directed along the positive x axis in a region where the magnetic field is uniform and given by B = mT. What is the resulting magnetic force on the wire?

A)(+1.2 ) N
B)(−1.2 ) N
C)(−1.5 ) N
D)(+1.5 ) N
E)(+0.90 ) N

Question 7

A straight wire carries a current of 40 A in a uniform magnetic field (magnitude = 80 mT). If the force per unit length on this wire is 2.0 N/m, determine the angle between the wire and the magnetic field.

A)either 39° or 141°
B)either 25° or 155°
C)either 70° or 110°
D)either 42° or 138°
E)either 65° or 115°

Question 8

A particle (mass = 2.0 mg, charge = −6.0 μC) moves in the positive direction along the x axis with a velocity of 3.0 km/s. It enters a magnetic field of mT. What is the acceleration of the particle?

A) m/s²
B) m/s²
C) m/s²
D) m/s²
E) m/s²

Question 9

A particle (mass = 6.0 mg) moves with a speed of 4.0 km/s in a direction that makes an angle of 37° above the positive x axis in the xy plane. At the instant it enters a magnetic field of (5.0 ) mT it experiences an acceleration of (8.0 ) m/s². What is the charge of the particle?

A)−4.8 μC
B)4.0 μC
C)−4.0 μC
D)4.8 μC
E)−5.0 μC

Question 10

A 2.0-C charge moves with a velocity of ( m/s and experiences a magnetic force of N. The x component of the magnetic field is equal to zero. Determine the z component of the magnetic field.

A)−3.0 T
B)+3.0 T
C)+5.0 T
D)−5.0 T
E)+6.0 T

Question 11

A straight wire of length 70 cm carries a current of 50 A and makes an angle of 60° with a uniform magnetic field. If the force on the wire is 1.0 N what is the magnitude of ?

A)41 mT
B)33 mT
C)55 mT
D)87 mT
E)57 mT

Question 12

A particle (q = 5.0 nC, m = 3.0 μg) moves in a region where the magnetic field has components Bx = 2.0 mT, By = 3.0 mT, and Bz = −4.0 mT. At an instant when the speed of the particle is 5.0 km/s and the direction of its velocity is 120° relative to the magnetic field, what is the magnitude of the acceleration of the particle?

A)33 m/s²
B)17 m/s²
C)39 m/s²
D)25 m/s²
E)45 m/s²

Question 13

A particle (q = −4.0 μC, m = 5.0 mg) moves in a uniform magnetic field with a velocity having a magnitude of 2.0 km/s and a direction that is 50° away from that of the magnetic field. The particle is observed to have an acceleration with a magnitude of 5.8 m/s². What is the magnitude of the magnetic field?

A)5.3 mT
B)4.9 mT
C)5.1 mT
D)4.7 mT
E)3.6 mT

Question 14

A segment of wire carries a current of 25 A along the x axis from x = −2.0 m to x = 0 and then along the z axis from z = 0 to z = 3.0 m. In this region of space, the magnetic field is equal to 40 mT in the positive z direction. What is the magnitude of the force on this segment of wire?

A)1.0 N
B)5.0 N
C)2.0 N
D)3.6 N
E)3.0 N

Question 15

A straight wire is bent into the shape shown. Determine the net magnetic force on the wire.

A)Zero
B)IBL in the +z direction
C)IBL in the −z direction
D)1.7 IBL in the +z direction
E)1.4 IBL in the −z direction

Question 16

A charged particle (mass = m, charge = q > 0) moves in a region of space where the magnetic field has a constant magnitude of B and a downward direction. What is the magnetic force on the particle at an instant when it is moving horizontally toward the north with speed v?

A)qvB toward the east
B)Zero
C)qvB toward the west
D)qvB upward
E)qvB toward the south

Question 17

A straight wire of length L carries a current I in the positive z direction in a region where the magnetic field is uniform and specified by Bx = 3B, By = −2B, and Bz = B, where B is a constant. What is the magnitude of the magnetic force on the wire?

A)3.2 ILB
B)5.0 ILB
C)4.2 ILB
D)3.6 ILB
E)1.0 ILB

Question 18

A charged particle (mass = 4.0 μg, charge = 5.0 μC) moves in a region where the only force on it is magnetic. What is the magnitude of the acceleration of the particle at a point where the speed of the particle is 5.0 km/s, the magnitude of the magnetic field is 8.0 mT, and the angle between the direction of the magnetic field and the velocity of the particle is 60°?

A)39 km/s²
B)43 km/s²
C)48 km/s²
D)52 km/s²
E)25 km/s²

Question 19

An electron moving in the positive x direction experiences a magnetic force in the positive z direction. If Bx = 0, what is the direction of the magnetic field?

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

Question 20

A positively charged particle has a velocity in the negative z direction at point P. The magnetic force on the particle at this point is in the negative y direction. Which one of the following statements about the magnetic field at point P can be determined from this data?

A)Bx is positive.
B)Bz is positive.
C)By is negative.
D)By is positive.
E)Bx is negative.

Question 21

What current must be maintained in a square loop (50 cm on a side) to create a torque of 1.0 N ⋅ m about an axis through its center and parallel to one of its sides when a magnetic field of magnitude 70 mT is directed at 40° to the plane of the loop?

A)66 A
B)89 A
C)61 A
D)75 A
E)37 A

Question 22

A proton with a kinetic energy of 0.20 keV follows a circular path in a region where the magnetic field is uniform and has a magnitude of 60 mT. What is the radius of this path?

A)4.1 cm
B)2.9 cm
C)3.4 cm
D)5.1 cm
E)2.4 cm

Question 23

A deuteron is accelerated from rest through a 10-kV potential difference and then moves perpendicularly to a uniform magnetic field with B = 1.6 T. What is the radius of the resulting circular path? (deuteron: m = 3.3 × 10−27 kg, q = 1.6 × 10−19 C)

A)19 mm
B)13 mm
C)20 mm
D)10 mm
E)9.0 mm

Question 24

Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.40 T) with speeds of 5000 km/s follow circular paths that differ in diameter by 5.0 cm. What is the difference in the mass of these two ions?

A)2.6 × 10−28 kg
B)6.4 × 10−28 kg
C)3.2 × 10−28 kg
D)5.1 × 10−28 kg
E)1.1 × 10−28 kg

Question 25

The boundary shown is that of a uniform magnetic field directed in the positive z direction. An electron enters the magnetic field with a velocity pointing along the x axis and exits 0.63 μs later at point A. What is the magnitude of the magnetic field?

A)18 μT
B)14 μT
C)28 μT
D)34 μT
E)227 μT

Question 26

The figure shows the orientation of a rectangular loop consisting of 80 closely wrapped turns each carrying a current I. The magnetic field in the region is ( ) mT. The loop can turn about the y axis. If θ = 30°, a = 0.40 m, b = 0.30 m, and I = 8.0 A, what is the magnitude of the torque exerted on the loop? ​ ​

A)2.5 N ⋅ m
B)1.5 N ⋅ m
C)3.1 N ⋅ m
D)2.7 N ⋅ m
E)0.34 N ⋅ m

Question 27

A circular coil (radius = 0.40 m) has 160 turns and is in a uniform magnetic field. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.16 N ⋅ m when the current in the coil is 4.0 mA. What is the magnitude of the magnetic field?

A)0.37 T
B)1.6 T
C)0.50 T
D)1.2 T
E)2.5 T

Question 28

A straight 10-cm wire bent at its midpoint so as to form an angle of 90° carries a current of 10 A. It lies in the xy plane in a region where the magnetic field is in the positive z direction and has a constant magnitude of 3.0 mT. What is the magnitude of the magnetic force on this wire?

A)3.2 mN
B)2.1 mN
C)5.3 mN
D)4.2 mN
E)6.0 mN

Question 29

A circular loop (radius = 0.50 m) carries a current of 3.0 A and has unit normal vector of /3. What is the x component of the torque on this loop when it is placed in a uniform magnetic field of T?

A)4.7 N ⋅ m
B)3.1 N ⋅ m
C)19 N ⋅ m
D)9.4 N ⋅ m
E)12 N ⋅ m

Question 30

A square loop (L = 0.20 m) consists of 50 closely wrapped turns, each carrying a current of 0.50 A. The loop is oriented as shown in a uniform magnetic field of 0.40 T directed in the positive y direction. What is the magnitude of the torque on the loop?

A)0.21 N ⋅ m
B)0.20 N ⋅ m
C)0.35 N ⋅ m
D)0.12 N ⋅ m
E)1.73 N ⋅ m

Question 31

What is the radius of curvature of the path of a 3.0-keV proton in a perpendicular magnetic field of magnitude 0.80 T?

A)9.9 mm
B)1.1 cm
C)1.3 cm
D)1.4 cm
E)7.6 mm

Question 32

A charged particle (m = 5.0 g, q = −70 μC) moves horizontally at a constant speed of 30 km/s in a region where the free fall gravitational acceleration is 9.8 m/s² downward, the electric field is 700 N/C upward, and the magnetic field is perpendicular to the velocity of the particle. What is the magnitude of the magnetic field in this region?

A)47 mT
B)zero
C)23 mT
D)35 mT
E)12 mT

Question 33

A wire (mass = 50 g, length = 40 cm) is suspended horizontally by two vertical wires which conduct a current I = 8.0 A, as shown in the figure. The magnetic field in the region is into the paper and has a magnitude of 60 mT. What is the tension in either wire?

A)0.15 N
B)0.68 N
C)0.30 N
D)0.34 N
E)0.10 N

Question 34

What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mT and is directed at an angle of 20° away from the wire?

A)1.5 N
B)1.3 N
C)1.1 N
D)1.7 N
E)3.1 N

Question 35

A proton moves around a circular path (radius = 2.0 mm) in a uniform 0.25-T magnetic field. What total distance does this proton travel during a 1.0-s time interval? (m = 1.67 × 10−27 kg, q = 1.6 × 10−19 C)

A)82 km
B)59 km
C)71 km
D)48 km
E)7.5 km

Question 36

A current of 4.0 A is maintained in a single circular loop having a circumference of 80 cm. An external magnetic field of 2.0 T is directed so that the angle between the field and the plane of the loop is 20°. Determine the magnitude of the torque exerted on the loop by the magnetic forces acting upon it.

A)0.41 N ⋅ m
B)0.14 N ⋅ m
C)0.38 N ⋅ m
D)0.27 N ⋅ m
E)0.77 N ⋅ m

Question 37

A 500-eV electron and a 300-eV electron trapped in a uniform magnetic field move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits?

A)2.8
B)1.7
C)1.3
D)4.0
E)1.0

Question 38

A rectangular coil (0.20 m × 0.80 m) has 200 turns and is in a uniform magnetic field of 0.30 T. When the orientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is 0.080 N ⋅ m. What is the current in the coil?

A)5.0 mA
B)1.7 A
C)8.3 mA
D)1.0 A
E)42 mA

Question 39

An electron follows a circular path (radius = 15 cm) in a uniform magnetic field (magnitude = 3.0 G). What is the period of this motion?

A)0.12 μs
B)1.2 ms
C)0.18 μs
D)1.8 ms
E)1.8 μs

Question 40

The figure shows the orientation of a flat circular loop consisting of 50 closely wrapped turns each carrying a current I. The magnetic field in the region is directed in the positive z direction and has a magnitude of 50 mT. The loop can turn about the y axis. If θ = 20°, R = 0.50 m, and I = 12 A, what is the magnitude of the torque exerted on the loop? ​ ​

A)8.1 N ⋅ m
B)24 N ⋅ m
C)22 N ⋅ m
D)13 N ⋅ m
E)16 N ⋅ m

Question 41

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed up out of the page, the direction of the magnetic field at P is closest to the direction of

A)E.
B)F.
C)G.
D)H.
E)A.

Question 42

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed into the page, the direction of the magnetic field at P is closest to the direction of

A)A
B)B.
C)C.
D)D.
E)E.

Question 43

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is

A)D.
B)E.
C)F.
D)G.
E)H.

Question 44

Equal charges, one at rest, the other having a velocity of 104 m/s, are released in a uniform magnetic field. Which charge has the largest force exerted on it by the magnetic field?

A)The charge that is at rest.
B)The charge that is moving, if its velocity is parallel to the magnetic field direction when it is released.
C)The charge that is moving if its velocity makes an angle of 45o with the direction of the magnetic field when it is released.
D)The charge that is moving if its velocity is perpendicular to the magnetic field direction when it is released.
E)All the charges above experience equal forces when released in the same magnetic field.

Question 45

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is

A)E.
B)F.
C)G.
D)H.
E)A.

Question 46

A magnetic field is directed out of the page. Two charged particles enter from the top and take the paths shown in the figure. Which statement is correct?

A)Particle 1 has a positive charge and particle 2 has a negative charge.
B)Both particles are positively charged.
C)Both particles are negatively charged.
D)Particle one has a negative charge and particle 2 has a positive charge.
E)The direction of the paths depends on the magnitude of the velocity, not on the sign of the charge.

Question 47

A proton is accelerated from rest through a potential difference of 150 V. It then enters a region of uniform magnetic field and moves in a circular path (radius = 12 cm). What is the magnitude of the magnetic field in this region?

A)18 mT
B)12 mT
C)15 mT
D)22 mT
E)10 mT

Question 48

One reason why we know that magnetic fields are not the same as electric fields is because the force exerted on a charge +q

A)is in opposite directions in electric and magnetic fields.
B)is in the same direction in electric and magnetic fields.
C)is parallel to a magnetic field and perpendicular to an electric field.
D)is parallel to an electric field and perpendicular to a magnetic field.
E)is zero in both if the charge is not moving.

Question 49

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is

A)E.
B)F.
C)G.
D)H.
E)A.

Question 50

You stand near the Earth's equator. A positively charged particle that starts moving parallel to the surface of the Earth in a straight line directed east is initially deflected upwards. If you know there are no electric fields in the vicinity, a possible reason why the particle does not initially acquire a downward component of velocity is because near the equator the magnetic field lines of the Earth are directed

A)upward.
B)downward.
C)from south to north.
D)from north to south.
E)from east to west.

Question 51

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T that are perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed up out of the page, the direction of the magnetic field at P is closest to the direction of

A)E.
B)F.
C)G.
D)H.
E)A

Question 52

What is the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E = 4.0 kV/m and B = 8.0 mT?

A)0.65 eV
B)0.71 eV
C)0.84 eV
D)0.54 eV
E)1.4 eV

Question 53

What value of B should be used in a velocity selector to separate out 2.0-keV protons if E is fixed at 80 kV/m?

A)0.18 T
B)0.11 T
C)0.15 T
D)0.13 T
E)0.23 T

Question 54

The diagram below shows the position of a long straight wire perpendicular to the page and a set of directions labeled A through H. When the current in the wire is directed up out of the page, the direction of the magnetic field at point P is

A)A.
B)B.
C)C.
D)D.
E)E.

Question 55

A velocity selector uses a fixed electric field of magnitude E and the magnetic field is varied to select particles of various energies. If a magnetic field of magnitude B is used to select a particle of a certain energy and mass, what magnitude of magnetic field is needed to select a particle of equal mass but twice the energy?

A)0.50 B
B)1.4 B
C)2.0 B
D)0.71 B
E)1.7 B

Question 56

A coaxial cable has an inner cylindrical conductor surrounded by cylindrical insulation and an outer cylindrical conducting shell. The outer shell carries the same current but in the opposite direction from that in the inner conductor as shown. If the coaxial cable sits in a uniform magnetic field directed upwards with respect to the cable, the effect of the field on the cable is

A)a net force to the left.
B)a net force to the right.
C)a net force upwards.
D)no net force but a slight shift of the inner conductor to the left and the outer conductor to the right.
E)no net force but a slight shift of the inner conductor to the right and the outer conductor to the left.

Question 57

A current loop is oriented in three different positions relative to a uniform magnetic field. In position 1 the plane of the loop is perpendicular to the field lines. In positionS 2 and 3 the plane of the loop is parallel to the field as shown. The torque on the loop is maximum in ​ ​

A)position 1.
B)position 2.
C)position 3
D)positions 2 and 3.
E)all three positions.

Question 58

Three particles of equal charge, X, Y, and Z, enter a uniform magnetic field . X has velocity of magnitude v parallel to the field. Y has velocity of magnitude v perpendicular to the field. Z has equal velocity components v parallel and perpendicular to the field. Rank the radii of their orbits from least to greatest.

A)Rx = Ry < Rz.
B)Rx < Ry < Rz.
C)Rx = Ry = Rz.
D)Rx > Ry > Rz.
E)Rx < Ry = .

Question 59

A proton is accelerated from rest through a potential difference of 2.5 kV and then moves perpendicularly through a uniform 0.60-T magnetic field. What is the radius of the resulting path?

A)15 mm
B)12 mm
C)18 mm
D)24 mm
E)8.5 mm

Question 60

The point P lies along the perpendicular bisector of the line connecting two long straight wires S and T perpendicular to the page. A set of directions A through H is shown next to the diagram. When the two equal currents in the wires are directed into the page, the direction of the magnetic field at P is closest to the direction of

A)E.
B)F.
C)G.
D)H.
E)A.

Question 61

An unusual lightning strike has a vertical portion with a positive current of +400 A upwards. The Earth's magnetic field at that location is parallel to the ground and has a magnitude of 30 μT. In N, the force exerted by the Earth's magnetic field on the 25-m-long current is

A)0.
B)0.012 N, East.
C)0.012 N, West.
D)0.30 N, West.
E)300 N, East.

Question 62

A thin ribbon of a silver alloy 2.00-cm wide and 0.0150-mm thick carries a current of 6.98 A perpendicular to a magnetic field. The Hall voltage is found to be 1.24 × 10−4 V when the magnetic field is 2.50 T. Calculate n, the number of charge carriers per cubic meter.

Question 63

The magnetic dipole moment of an electron (charge = −e; mass = me) moving in a circular orbit of radius r with speed v about a nucleus of mass mN is proportional to

A)r.
B)v.
C)vr.
D)evr.
E)mNvr.

Question 64

The magnetic field in a region of space is parallel to the surface of a long flat table. Imagine that this page is lying flat on the table. When current is present in the coil, which is lying on the table, the coil tends to rotate so that the left side moves up and the right side moves down. The magnetic field is

A)directed parallel to the page and downwards.
B)directed parallel to the page and upwards.
C)directed parallel to the page and to the right.
D)directed parallel to the page and to the left.
E)in a direction that cannot be determined in this experiment

Question 65

An unusual lightning strike has a vertical portion with a current of −400 A downwards. The Earth's magnetic field at that location is parallel to the ground and has a magnitude of 30 μT. In N, the force exerted by the Earth's magnetic field on the 25 m-long current is

A)0.
B)0.012 N, East.
C)0.012 N, West.
D)0.30 N, West.
E)300 N, East.

Question 66

A stream of electrons passes through a velocity filter where the crossed magnetic and electric fields are 0.020 T and 5.00 × 104 V/m, respectively. Find the kinetic energy (in electron volts) of the electrons passing through the filter. [1 eV = 1.60 × 10−19 J]

Question 67

A physicist claims that she has found a new particle with a mass 200,000 times the mass of the proton (1.67 × 10−27 kg) and a charge of 3.20 × 10−19 C. If she is correct, such a particle traveling in a circle in a uniform 5.00-T magnetic field at a velocity of 2 500 m/s will have a radius of

A)0.261 m.
B)0.522 m.
C)1.04 m.
D)3.27 m.
E)3.13 × 1026 m.

Question 68

Two wires, each having a weight per unit length of 1.0 × 10−4 N/m, are strung parallel, one 0.10 m above the other. If the wires carry the same current, though in opposite directions, how great must the current in each wire be for the magnetic field of the lower conductor to balance the weight of the upper conductor?

Question 69

On the average, in a ferromagnetic domain permanent atomic magnetic moments are aligned ____ to one another.

A)antiparallel
B)parallel
C)perpendicular
D)alternately parallel and antiparallel
E)randomly relative

Question 70

When a ferromagnetic material that has been magnetized is brought to a temperature greater than the Curie temperature, what happens to its residual magnetism?

A)Nothing happens to the residual magnetism.
B)The residual magnetism disappears.
C)The residual magnetism reaches it's highest value.
D)All the magnetic domains causing magnetism become a single domain.
E)The material of the magnet melts causing currents that are magnetic.

Question 71

The reason the north pole of a bar magnet free to rotate points north is because

A)the south geographic pole of the earth is the Earth's magnetic north pole.
B)the south geographic pole of the earth is the Earth's magnetic south pole.
C)there is a net accumulation of negative magnetic charge at the Earth's south geographic pole.
D)there is a net accumulation of positive magnetic charge at the Earth's north geographic pole.
E)the north geographic pole of the Earth is the earth's magnetic north pole.

Question 72

An explorer walks into a lab in a science building. She has a compass in her hand and finds that the south pole of her compass points toward the room's east wall when she is nearer that wall and toward the west wall when she is nearer that wall. You could explain this if magnetized metal had been installed in the east and west walls with north poles pointing into the room. If no magnetic material was installed in the north or south walls of the room, she would expect that

A)the south pole of the compass would tend to point toward those walls.
B)the north pole of the compass would tend to point toward those walls.
C)the compass needle would not point in any particular direction.
D)the north pole of the compass needle would tend to point toward the centers of those walls, but the south pole would tend to point toward the sides of those walls.
E)the south pole of the compass needle would tend to point toward the centers of those walls, but the north pole would tend to point toward the sides of those walls.

Question 73

At what speed would a proton need to circle the Earth at a height of 1000 km above the equator if the Earth's magnetic field is horizontal and directed north-south, with an intensity of 4.00 × 10−8 T? (The radius of the Earth is 6400 km and the charge and mass of the proton are q = 1.60 × 10−19 C and mp = 1.67 × 10−27 kg. Ignore relativistic corrections.)

Question 74

A magnetic field of 2.00 T is applied to a bubble chamber to make the tracks of protons and other charged particles identifiable by the radius of the circles they move in. If a high-energy proton moves along an arc of a 3.30-m circle, what is the momentum of the proton? [q = 1.60 × 10−19 C, m = 1.67 × 10−27 kg]

Question 75

Bert says that a charged particle in a vacuum can travel in a helix only if a uniform electric field and a uniform magnetic field are both present and both parallel to the axis of the helix. Stuart says that only a magnetic field with a component parallel to the axis of the helix is needed. Which one, if either, is correct, and why?

A)Bert, because the charged particle's velocity can have a vertical component only if an electric field in the vertical direction is present.
B)Stuart, because a component of velocity in the vertical direction is not changed by a vertical component of a magnetic field.
C)Bert, because a component of velocity in the vertical direction is changed by a vertical component of a magnetic field.
D)Stuart, because an electric field in the vertical direction would cause the particle to come to a complete stop.
E)Neither, because particles cannot move in helical paths in the presence of magnetic and electric fields.