Deck 20: Induced Voltages and Inductance: Part A

Question 1

The magnetic force on a charged particle moving at a constant speed in a uniform magnetic field will be halved when the angle between the velocity of the particle and the direction of the magnetic field changes from 25.0° to

A) 50.0°.
B) 12.5°.
C) 57.7°.
D) 12.2°.

Answer 1

12.2°.

Question 2

A proton moving with a speed of 6.0 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.20 T will follow which of the paths described below? (q_p = 1.6 × 10−¹⁹ C and m_p = 1.67 × 10−²⁷ kg)

A) a circular path of 1.6-cm radius
B) a circular path of 3.1-cm radius
C) a circular path of 6.3-cm radius
D) a straight line path

Answer 2

a circular path of 3.1-cm radius

Question 3

A proton is released such that it has an initial speed of 5.0 × 10⁵ m/s from left to right across the page.A magnetic field of 1.2 T is present at an angle of 30° to the horizontal direction (or positive x axis).What is the magnitude of the force experienced by the proton? (q_p = 1.6 × 10−¹⁹ C)

A) 3.8 × 10−¹⁴ N
B) 7.5 × 10³ N
C) 4.8 × 10−¹⁴ N
D) 1.3 × 10−¹⁹ N

Answer 3

4.8 × 10−¹⁴ N

Question 4

A proton moves across the Earth's equator in a northwesterly direction.At this point the Earth's magnetic field has a direction due north and is parallel to the surface.What is the direction of the force acting on the proton at this instant?

A) toward the northeast
B) into the Earth's surface
C) toward the northwest
D) out of the Earth's surface

Question 5

A proton moving at a speed of 3.8 × 10⁶ m/s cuts across the lines of a magnetic field at an angle of 40°.The strength of the field is 0.25 × 10−⁴ T.What is the magnitude of the force acting on the proton? (q_p = 1.6 × 10−¹⁹ C)

A) 1.4 × 10−¹⁷ N
B) 2.3 × 10−¹⁷ N
C) 9.8 × 10−¹⁸ N
D) 5.1 × 10−¹⁸ N

Question 6

If an electron is released at the equator and falls toward the Earth under the influence of gravity,the magnetic force on the electron will be toward the:

A) south.
B) east.
C) west.
D) north.

Question 7

A proton,mass 1.67 × 10−²⁷ kg and charge +1.6 × 10−¹⁹ C,moves in a circular orbit perpendicular to a uniform magnetic field of 0.50 T.Find the time for the proton to make one complete circular orbit.

A) 8.7 × 10−⁸ s
B) 1.3 × 10−⁷ s
C) 9.8 × 10−⁷ s
D) 4.3 × 10−⁸ s

Question 8

A proton and an alpha particle are moving perpendicular to a uniform magnetic field with the same speed.If the velocity of the proton is at an angle of 20° with respect to the magnetic field direction,at what angle to the magnetic field direction would the alpha particle be moving if it experiences the same magnitude acceleration as the proton? The alpha particle has 4 times the mass of the proton and twice its charge.

A) 43°
B) 10°
C) 62°
D) 9.8°

Question 9

A proton and an alpha particle are moving perpendicular to a uniform magnetic field with the same speeds.If the velocity of the proton is at an angle of 20° with respect to the magnetic field direction,at what angle to the magnetic field direction would the alpha particle be moving if it experiences the same magnitude magnetic force as the proton? The alpha particle has 4 times the mass of the proton and twice its charge.

A) 10°
B) 62°
C) 43°
D) 9.8°

Question 10

Three identical bar magnets,each 2 cm long,are placed in a straight line on a frictionless surface with their ends equally spaced with 2 cm between ends.They are constrained so they cannot rotate,but they can slide along the straight line.The left magnet has its north pole nearest the north pole of the middle magnet,and the right magnet has its south pole toward the middle magnet's south pole.Once they are in place and released from rest,which of the following best describes the motion of the magnets?

A) The end magnets will move away from the center magnet.
B) The magnets will not move since they are equally spaced.
C) The magnets will snap together.
D) None of the above would happen.

Question 11

At the Fermilab accelerator in Weston,Illinois,singly-charged ions with momentum 3.2 × 10−¹⁶ kg⋅m/s are held in a circular orbit of radius 1 km by an upward magnetic field.What B-field must be used to maintain the ions in this orbit? (qion = 1.6 × 10−¹⁹ C)

A) 4 T
B) 2 T
C) 1 T
D) 3 T

Question 12

A proton with initial kinetic energy E is moving in circular motion in a uniform magnetic field.When it has completed one fourth of a revolution,what is its kinetic energy?

A) 1.4 E
B) 0.71 E
C) E
D) The value is not given.

Question 13

A bar magnet is attached solidly to a frictionless surface and its length is aligned with the x axis.To the right of the first magnet a short distance away is a second bar magnet with its center placed on the x axis and its length perpendicular to the x axis.The second magnet is free to move.Once placed in position at rest,which best describes the initial motion of the second magnet?

A) The magnet will move away from the fixed magnet.
B) The magnet will not move.
C) The magnet will move toward the fixed magnet.
D) The magnet will start to rotate.

Question 14

An electron which moves with a speed of 7.5 × 10³ m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 × 10−¹⁹ C)

A) 1.9 × 10−¹⁵ N
B) zero
C) 2.2 × 10−²⁴ N
D) 4.8 × 10−¹⁴ N

Question 15

A deuteron,with the same charge but twice the mass of a proton,moves with a speed of 6.0 × 10⁵ m/s perpendicular to a uniform magnetic field of 0.20 T.Which of the paths described below would it follow? (q_p = 1.6 × 10−¹⁹ C and m_d = 3.34 × 10−²⁷ kg)

A) a circular path of 6.3-cm radius
B) a circular path of 1.6-cm radius
C) a circular path of 3.1-cm radius
D) a straight line path

Question 16

A proton,which moves perpendicular to a magnetic field of 0.60 T in a circular path of radius 0.080 m,has what speed? (q_p = 1.6 × 10−¹⁹ C and m_p = 1.67 × 10−²⁷ kg)

A) 9.2 × 10⁶ m/s
B) 4.6 × 10⁶ m/s
C) 9.6 × 10⁶ m/s
D) 3.4 × 10⁶ m/s

Question 17

An electron is released such that its initial velocity is from right to left across this page.The electron's path,however,is deflected in a direction toward the bottom edge of the page due to the presence of a uniform magnetic field.What is the direction of this field?

A) from bottom edge to top edge of the page
B) into the page
C) from right to left across the page
D) out of the page

Question 18

An electron is moving at a speed of 12 × 10⁶ m/s at an angle of 30° with respect to a uniform magnetic field of 8.0 × 10^-4 T.What is the radius of the resulting helical path? (m_e = 9.11 × 10^-31 kg,q_e = 1.6 × 10^-19 C)

A) 2.1 cm
B) 3.7 cm
C) 4.3 cm
D) 8.5 cm

Question 19

The magnetic force on a charged particle moving at a constant speed in a uniform magnetic field will be doubled when the angle between the velocity of the particle and the direction of the magnetic field changes from 25.0° to

A) 57.7°.
B) 12.5°.
C) 12.2°.
D) 50.0°.

Question 20

Assume that a uniform magnetic field is directed into this page.If a proton is released with an initial velocity directed from the bottom edge to the top edge of the page,which of the following describes the direction of the resultant force acting on the proton?

A) into the page
B) to the left
C) to the right
D) out of the page

Question 21

Niobium metal becomes a superconductor (with electrical resistance equal to zero)when cooled below 9 K.If superconductivity is destroyed when the surface magnetic field exceeds 0.100 T,determine the maximum current a 2.00-mm diameter niobium wire can carry and remain superconducting.(µ₀ = 4π × 10−⁷ T⋅m/A)

A) 2000 A
B) 1000 A
C) 125 A
D) 500 A

Question 22

A horizontal wire of length 3.6 m carries a current of 6.0 A and is oriented so that the current direction is 50° S of W.The Earth's magnetic field is due north at this point and has a strength of 0.14 × 10−⁴ T.What is the size of the force on the wire?

A) 1.6 × 10−⁴ N
B) 0.28 × 10−⁴ N
C) 1.9 × 10−⁴ N
D) 2.5 × 10−⁴ N

Question 23

Superconductors can carry very large currents with no resistance.If a superconducting wire is formed into a solenoid of length 50.0 cm with 250 turns,what is the magnetic field inside the solenoid when the current is 10⁴ A? (µ₀ = 4π × 10−⁷ T⋅m/A)

A) 12.6 T
B) 2.50 T
C) 1.25 T
D) 6.28 T

Question 24

Two parallel wires are separated by 0.25 m.Wire A carries 4.1 A and Wire B carries 10 A,both currents in the same direction.The magnetic permeability in empty space µ₀ = 4π × 10−⁷ T⋅m/A.The magnitude of the force on 1.4 m of Wire A is:

A) 2.6 × 10^-5 N.
B) 4.6 × 10^-5 N.
C) less than 1.0 × 10^-5 N.
D) 3.2 × 10^-5 N.

Question 25

A 2.0-m wire segment carrying a current of 0.60 A oriented parallel to a uniform magnetic field of 0.25 T experiences a force of what magnitude?

A) 0.30 N
B) 6.7 N
C) 0.15 N
D) zero

Question 26

Two long parallel wires 40 cm apart are carrying currents of 10 A and 30 A in the same direction.What is the magnitude of the magnetic field halfway between the wires?

A) 4.0 × 10^-5 T
B) 1.0 × 10^-5 T
C) 3.0 × 10^-5 T
D) 2.0 × 10^-5 T

Question 27

A current-carrying wire of length 50 cm is positioned perpendicular to a uniform magnetic field.If the current is 10.0 A and it is determined that there is a resultant force of 7.5 N on the wire due to the interaction of the current and field,what is the magnetic field strength?

A) 1.8 × 10^-3 T
B) 1.5 T
C) 6.7 × 10^-3 T
D) 0.60 T

Question 28

A high-voltage power line 20 m above the ground carries a current of 5000 A.What is the magnetic field due to the current directly underneath the power line? (µ₀ = 4π × 10−⁷ T⋅m/A)

A) 14 mT
B) 35 µT
C) 20 µT
D) 50 µT

Question 29

An electron moves through a region of crossed electric and magnetic fields.The electric field E = 3200 V/m and is directed straight down.The magnetic field B = 0.80 T and is directed to the left.For what velocity v of the electron into the paper will the electric force exactly cancel the magnetic force?

A) 2500 m/s
B) 5000 m/s
C) 4000 m/s
D) 8000 m/s

Question 30

A superconducting solenoid is to be designed to generate a magnetic field of 2.50 T.If the solenoid winding has 1000 turns/m,what is the required current? (µ₀ = 4π × 10−⁷ T⋅m/A)

A) 5000 A
B) 1990 A
C) 3980 A
D) 1000 A

Question 31

A circular loop carrying a current of 3.0 A is oriented in a magnetic field of 0.35 T.The loop has an area of 0.24 m² and is mounted on an axis,perpendicular to the magnetic field,which allows the loop to rotate.If the plane of the loop is oriented parallel to the field,what torque is created by the interaction of the loop current and the field?

A) 0.017 N⋅m
B) 0.084 N⋅m
C) 0.25 N⋅m
D) 5.8 N⋅m

Question 32

A superconducting wire carries a current of 10⁴ A.Find the magnetic field at a distance of 0.25 m from the wire.(µ₀ = 4π × 10−⁷ T⋅m/A)

A) 1.6 × 10−² T
B) 2 × 10−³ T
C) 8 × 10−³ T
D) 3.2 × 10−² T

Question 33

Two long parallel wires are a distance d apart.The current in one wire is 10 A and the current in the other wire is 30 A.The currents are in the same direction.If the 30-A current is increased to 50 A,by what factor does the magnitude of the magnetic field midway between the wires change?

A) 2
B) 4
C) 25/9
D) 5/3

Question 34

A 100-m long wire carrying a current of 4.0 A will be accompanied by a magnetic field of what strength at a distance of 0.040 m from the wire? (magnetic permeability in empty space µ₀ = 4π × 10−⁷ T⋅m/A)

A) zero
B) 1.6 × 10−⁵ T
C) 2.0 × 10−⁵ T
D) 4.0 × 10−⁵ T

Question 35

A copper wire of length 10 cm is in a magnetic field of 0.30 T.If it has a mass of 20 g,what minimum current through the wire would cause a magnetic force equal to its weight?

A) 4.9 A
B) 6.5 A
C) 2.0 A
D) 1.3 A

Question 36

A circular loop carrying a current of 3.0 A is oriented in a magnetic field of 0.35 T.The loop has an area of 0.24 m² and is mounted on an axis,perpendicular to the magnetic field,which allows the loop to rotate.What is the torque on the loop when its plane is oriented at a 50° angle to the field?

A) 4.6 N⋅m
B) 0.16 N⋅m
C) 0.076 N⋅m
D) 0.23 N⋅m

Question 37

A solenoid with 500 turns,0.10 m long,carrying a current of 2.0 A and with a radius of 10−² m will have what strength magnetic field at its center? (magnetic permeability in empty space µ₀ = 4π × 10−⁷ T⋅m/A)

A) 31 × 10−⁴ T
B) 1.3 × 10−² T
C) 2.5 × 10−² T
D) 62 × 10−⁴ T

Question 38

A horizontal wire of length 3.6 m carries a current of 6.0 A and is oriented so that the current direction is 50° S of W.The Earth's magnetic field is due north at this point and has a strength of 0.14 × 10−⁴ T.What is the direction of the force on the wire?

A) 40° S of E
B) out of the Earth's surface
C) toward the Earth's surface
D) due east

Question 39

Two long parallel wires 40 cm apart are carrying currents of 10 A and 30 A in the opposite direction.What is the magnitude of the magnetic field halfway between the wires?

A) 3.0 × 10^-5 T
B) 2.0 × 10^-5 T
C) 1.0 × 10^-5 T
D) 4.0 × 10^-5 T

Question 40

Two long parallel wires 15 cm apart carry currents of 5.0 A and 8.0 A in the same direction.Is there any point between the two wires where the magnetic field is zero?

A) yes,midway between the wires
B) yes,9.2 cm from the 5 A wire
C) no
D) yes,5.8 cm from the 5 A wire

Question 41

A charged particle moving perpendicular to a magnetic field has a magnet force on it.But when an observer moves with the particle,so that the particle has a relative velocity of zero with respect to the observer,one would expect there would be no magnetic force.Yet there is still a force.If it is not a magnetic force,then what is the source of this force?

A) It is an electrical force.
B) It is due to the ether.
C) It is a gravitational force.
D) It is something other than any of the above.

Question 42

Which of the following devices makes use of an electromagnet?

A) relay
B) motor
C) both A and B
D) None of the above.

Question 43

Four long wires are perpendicular to the x-y plane.Each wire carries the same magnitude current.Wire 1 goes through point (a,a,0)on the x-y plane,wire 2 goes through the point (-a,a,0),wire 3 goes through the point (-a,-a,0),and wire 4 goes through the point (a,-a,0).Wires 1 and 3 carry their currents in the positive z direction and wires 2 and 4 carry their currents in the -z direction.What is the direction of the resulting magnetic field at the origin?

A) in the +x direction
B) in the -y direction
C) in the -x direction
D) There is no direction since the field is zero at this point.

Question 44

Four long wires are perpendicular to the x-y plane.Each wire carries the same magnitude current.Wire 1 goes through point (a,a,0)on the x-y plane,wire 2 goes through the point (-a,a,0),wire 3 goes through the point (-a,-a,0),and wire 4 goes through the point (a,-a,0).Wires 1 and 2 carry their currents in the positive z direction and wires 3 and 4 carry their currents in the -z direction.What is the direction of the resulting magnetic field at the origin?

A) the -x direction
B) the -y direction
C) the +x direction
D) There is no direction since the field is zero at this position.

Question 45

The magnetic domains in a magnetized piece of iron are characterized by which orientation?

A) anti-parallel (opposite direction)to the magnetic axis
B) perpendicular to the magnetic axis
C) parallel to the magnetic axis
D) random

Question 46

A square loop of wire has a current going around it.The magnetic field from the current on each side of the loop results in a magnetic force on the wire on the opposite side.Each resulting magnetic force on the opposite side wire

A) pushes inward on the loop.
B) is actually zero since a current cannot push on itself.
C) depends on whether the current is clockwise of counterclockwise.
D) pushes outward on the loop.