Deck 7: Sources of the Magnetic Field

Question 1

A particle with charge q = 5 $\mu$ C is moving with velocity . At t = 0, it is located at the origin. The magnetic field at at t = 0 is

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

Answer 1

Question 2

A positively charged body is moving in the positive x direction as shown. The direction of the magnetic field at the origin due to the motion of this charged body is

A) 1
B) 2
C) 3
D) 4
E) None of these is correct, as this charged body does not create a magnetic field along the axis of its motion.

Answer 2

4

Question 3

The magnitude of the magnetic field due to the presence of a charged body

A) varies directly with the speed of the body.
B) varies directly with the charge carried by the body.
C) varies inversely with the square of the distance between the charged body and the field point.
D) depends on the magnetic properties of the space between the charged body and the field point.
E) is described by all of these.

Answer 3

is described by all of these.

Question 4

Two wires lying in the plane of this page carry equal currents in opposite directions, as shown. At a point midway between the wires, the magnetic field is

A) zero.
B) into the page.
C) out of the page.
D) toward the top or bottom of the page.
E) toward one of the two wires.

Question 5

A point charge is moving with speed 2 *10⁷ m/s along the x axis. At t = 0, the charge is at x = 0 m and the magnitude of the magnetic field at x = 4 m is B₀. The magnitude of the magnetic field at x = 4m when t = 0.1 $\mu$ s is

A) B₀/2
B) B₀
C) B₀/4
D) 2B₀
E) 4B₀

Question 6

A positively charged body is moving in the negative z direction as shown. The direction of the magnetic field due to the motion of this charged body at point P is

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

Question 7

The top diagram shows the velocity of a positively charged particle. The direction of the magnetic field due to the moving charge at r is best represented by

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

Question 8

At a certain instant of time a particle with charge q = 25 $\mu$ C is located at x = 4.0 m, y = 2.0 m; its velocity at that time is v = -20 m/s . If you are at the origin, what do you measure as the magnitude of the magnetic field due to this moving point charge?

A) 6.8 pT
B) 1.1 pT
C) 5.6 pT
D) 2.2 pT
E) 4.4 pT

Question 9

A point charge of q₁ = 5.8 nC is moving with speed 2.5 * 10⁷ m/s parallel to the z axis along the line x = 3 m. The magnetic field produced by this charge at the origin when it is at the point x = 3 m, z = 4 m is approximately

A) 0.70 nT
B) -0.70 nT
C) 3.2 nT
D) -1.6 nT
E) -0.35 nT

Question 10

At the instant the positively charged body is at the origin, the magnetic field at point P due to the motion of this charged body is in the negative x direction. The charged body must be moving

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

Question 11

In a simple picture of the hydrogen atom, the electron moves in circular orbits around the central proton attracted by the Coulomb force. The lowest (n = 1) energy orbit that is allowed for the electron is at a radius of 5.29*10^-11 m and the second (n = 2) lowest allowed orbit is at 4 times this radius. Calculate the magnetic field strength at the proton due to the orbital motion of the electron in the n = 2 state.

A) 0 T
B) 6.3 T
C) 0.39 T
D) 12.5 T
E) None of the above

Question 12

The Biot-Savart law is similar to Coulomb's law in that both

A) are inverse square laws.
B) include the permeability of free space.
C) deal with excess charges.
D) are not electrical in nature.
E) are described by none of the above.

Question 13

The magnetic field due to the presence of a charged body

A) depends on whether the charged body is moving.
B) depends on the direction the charged body is moving in relationship to the location of the field point.
C) varies inversely with the square of the distance between the charged body and the field point.
D) depends on the magnetic properties of the space between the charged body and the field point.
E) is described by all of these.

Question 14

In a simple picture of the hydrogen atom, the electron moves in circular orbits around the central proton attracted by the Coulomb force. The lowest (n = 1) energy orbit that is allowed for the electron is at a radius of 5.29 *10^-11 m and the second (n = 2) lowest allowed orbit is at 4 times this radius. How many times stronger is the magnetic field strength at the proton due to the orbital motion of the electron in the n = 1 state than the n = 2 state?

A) 64
B) 16
C) 4
D) 1
E) 32

Question 15

At the instant the negatively charged body is at the origin, the magnetic field at point P due to its motion is in the negative x direction. The charged body must be moving

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

Question 16

A wire carries an electric current straight upward. What is the direction of the magnetic field due to the current north of the wire?

A) north
B) east
C) west
D) south
E) upward

Question 17

What is the direction of the magnetic field around a wire carrying a current perpendicularly into this page?

A) The field is parallel to and in the same direction as the current flow.
B) It is parallel to but directed opposite to the current flow.
C) It is counterclockwise around the wire in the plane of the page.
D) It is clockwise around the wire in the plane of the page.
E) None of these is correct.

Question 18

Two positively charged bodies are moving in opposite directions on parallel paths that lie in the xz plane. Their speeds are equal and their trajectories are equidistant from the x axis. The magnetic field at the origin, due to the motion of these charged bodies will be

A) in the x direction.
B) in the y direction.
C) in all directions.
D) in the z direction.
E) zero.

Question 19

A point charge of q₁ = 3.6 nC is moving with speed 4.5 * 10⁷ m/s parallel to the y axis along the line x = 3 m. The magnetic field produced by this charge at the origin when it is at the point x = 3 m, y = 4 m is approximately

A) 0.39 nT
B) -0.78 nT
C) -0.39 nT
D) 0.78 nT
E) 2.0 nT

Question 20

At a certain instant of time a particle with charge q = 15 $\mu$ C is located at x = 2.0 m, y = 5.0 m; its velocity at that time is v = 40 m/s . If you are at the origin, what do you measure as the magnitude of the magnetic field due to this moving point charge?

A) 1.9 pT
B) 3.8 pT
C) 2.7 pT
D) 4.1 pT
E) 5.9 pT

Question 21

Four wires carry equal currents along the four parallel edges of a cube. A parallel current-carrying wire through the center of the cube is free to move. The vector that might represent the direction in which the center wire will move is

A)
B)
C)
D)
E)

Question 22

The magnetic field at a distance of 50 cm from a long, straight wire carrying a current of 5.0 A is approximately

A) 10 $\mu$ T
B) 50 $\mu$ T
C) 5.0 $\mu$ T
D) 32 $\mu$ T
E) 2.0 $\mu$ T

Question 23

The sketch shows a circular coil in the xz plane carrying a current I. The direction of the magnetic field at point O is

A) x
B) -x
C) y
D) -y
E) -z

Question 24

An electron beam travels counterclockwise in a circle in the magnetic field produced by the Helmholtz coils, as shown. Assuming that Earth's field is downward, one can conclude that

A) the Helmholtz field equals Earth's field.
B) the current in the coils moves in the same direction as the electron beam.
C) the current in the coils moves in the direction opposite to the electron beam.
D) the Helmholtz field curves in the direction of the electron beam.
E) the Helmholtz field curves in a direction opposite to the electron beam.

Question 25

At great axial distances x from a current-carrying loop the magnetic field varies as

A) x²
B) x^-3
C) x^-2
D) x³
E) x^-1

Question 26

The current in a wire along the x axis flows in the positive x direction. If a proton, located as shown in the figure, has an initial velocity in the positive z direction, it experiences

A) a force in the direction of positive x.
B) a force in the direction of negative x.
C) a force in the direction of positive z.
D) a force in the direction of positive y.
E) no force.

Question 27

A circular loop of wire 10 cm in radius carries a current of 20 A. The axial magnetic field 15 cm from the center of the loop is approximately

A) 37 $\mu$ T
B) 13 $\mu$ T
C) 21 $\mu$ T
D) 41 $\mu$ T
E) 18 $\mu$ T

Question 28

A solenoid carries a current I. An electron is injected with velocity along the axis AB of the solenoid. When the electron is at C, it experiences a force that is

A) zero.
B) not zero and along AB.
C) not zero and along BA.
D) not zero and perpendicular to the page.
E) None of these is correct.

Question 29

A long conductor carrying current I lies in the xz plane parallel to the z axis. The current travels in the negative z direction, as shown in the figure. The vector that represents the magnetic field at the origin O is

A)
B)
C)
D)
E)

Question 30

When the positive current in a long wire is flowing in a direction from S to N, it creates a magnetic field below the wire that is directed

A) from E to W.
B) from N to S.
C) from NE to SW.
D) from S to N.
E) from W to E.

Question 31

Each of the figures shown is the source of a magnetic field. In which figure does the magnetic dipole vector ( ) point in the direction of the negative x axis?

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

Question 32

The graph that best represents the magnetic field B between the coils of radius R of a Helmholtz pair as a function of distance along the axis of the pair is

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

Question 33

In a circular loop of wire lying on a horizontal floor, the current is constant and, to a person looking downward, has a clockwise direction. The accompanying magnetic field at the center of the circle is directed

A) horizontally and to the east.
B) horizontally and to the north.
C) vertically upward.
D) parallel to the floor.
E) vertically downward.

Question 34

An electron beam travels counterclockwise in a circle of radius R in the magnetic field produced by the Helmholtz coils as shown. If you increase the current in the Helmholtz coils, the electron beam will

A) increase its radius.
B) decrease its radius.
C) maintain the same radius.
D) reverse and travel clockwise with the same radius.
E) reverse and travel clockwise with a larger radius.

Question 35

What is the magnetic field at the center of a circular loop with a diameter of 15.0 cm that carries a current of 1.50 A?

A) zero
B) 6.28 *10^-6 T
C) 1.26 * 10^-5 T
D) 2.51* 10^-5 T
E) 1.68* 10^-4 T

Question 36

A circular loop of wire of radius 6.0 cm has 30 turns and lies in the xy plane. It carries a current of 5 A in such a direction that the magnetic moment of the loop is along the x axis. The magnetic field on the x axis at x = 6.0 cm is approximately

A) 19 $\mu$ T
B) 0.56 mT
C) 0.11 mT
D) 47 $\mu$ T
E) 0.88 mT

Question 37

Two straight wires perpendicular to the plane of this page are shown in the figure. The currents in the wires are the same. The current in M is into the page and the current in N is out of the page. The vector that represents the resultant magnetic field at point P is

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

Question 38

Two current-carrying wires are perpendicular to each other. The current in one flows vertically upward and the current in the other flows horizontally toward the east. The horizontal wire is 1 m south of the vertical wire. What is the direction of the net magnetic force on the horizontal wire?

A) north
B) east
C) west
D) south
E) There is no net magnetic force on the horizontal wire.

Question 39

A 1000-turn solenoid is 50 cm long and has a radius of 2.0 cm. It carries a current of 8.0 A. What is the magnetic field inside the solenoid near its center?

A) 2.0 * 10^-2 T
B) 3.2 * 10^-3 T
C) 4.0 * 10^-4 T
D) 1.0 T
E) 2.0 * 10^-4 T

Question 40

A circular loop of wire 1.0 cm in radius carries a current of 30 A. The magnetic field at the center of the loop is

A) 1.9 mT
B) 2.4 mT
C) 3.8 mT
D) 12 $\mu$ T
E) 48 $\mu$ T

Question 41

Two very long, parallel conducting wires carry equal currents in opposite directions. The numbered diagrams show end views of the wires and the resultant force vectors due to current flow in each wire. Which diagram best represents the direction of the forces?

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

Question 42

Two straight rods 60 cm long and 2.0 mm apart in a current balance carry currents of 18 A each in opposite directions. What mass must be placed on the upper rod to balance the magnetic force of repulsion?

A) 0.50 g
B) 0.99 g
C) 9.7 g
D) 4.3 g
E) 1.6 g

Question 43

Two very long, parallel conducting wires carry equal currents in the same direction, as shown. The numbered diagrams show end views of the wires and the resultant force vectors due to current flow in each wire. Which diagram best represents the direction of the forces?

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

Question 44

The force per unit length between two current-carrying wires is expressed as
F/l = ( $\mu$ ₀/2 $\pi$ d)I²
Where I is the current, d the separation of the wires, and l the length of each wire. A plot of force per unit length versus I² gives a straight line, the slope of which is

A) $\mu$ ₀
B) F/l
C) (2 $\pi$ d/ $\mu$ ₀)^1/2
D) $\mu$ ₀/2 $\pi$ d
E) FI²/l

Question 45

Two long, straight parallel wires 9.3 cm apart carry currents of equal magnitude I. They repel each other with a force per unit length of 5.8 nN/m. The current I is approximately

A) 27 mA
B) 65 mA
C) 43 mA
D) 52 mA
E) 2.7 mA

Question 46

Calculate the magnetic field at the center of a circular current loop of radius R divided by the magnetic field at a distance R away from a very long straight wire carrying the same current value I. (Note the loop and wire are not in electrical contact.)

A) 3.14
B) 1.00
C) 2.00
D) 0.318
E) 0.500

Question 47

Calculate the magnetic field at the center of a circular current loop of area 0.200 m² divided by the magnetic field at the center of a square current loop of the same inside area for the same current I value.

A) 1.00
B) 1.02
C) 0.246
D) 0.985
E) 0.785

Question 48

If the magnetic field at the center of a square current loop of side L = 40 cm is
2)4 *10^-6 T calculate the current flowing around the loop.

A) 11 A
B) 3.4 A
C) 0.85 A
D) 0.21 A
E) 1.7 A

Question 49

Calculate the magnetic field and its direction at point P, which is 2.0 cm away from the top wire and 4.0 cm from the bottom wire. Assume both wires are infinitely long and each carries a current of 1.5 A.

A) 2.3 *10^-5 T directed OUT of the page
B) 7.5 *10^-6 T directed INTO the page
C) 2.3 *10^-5 T directed INTO the page
D) 7.5 * 10^-6 T directed OUT of the page
E) 1.1 * 10^-5 T directed OUT of the page

Question 50

Use the following to answer the next question:

-Two long parallel wires are a distance d apart (d = 6 cm) and carry equal and opposite currents of 5 A. Point P is distance d from each of the wires. Calculate the magnitude of the magnetic field strength at point P.

A) 2.9 * 10^-5 T
B) 8.5*10^-6 T
C) 3.3 *10^-5 T
D) 1.7* 10^-5 T
E) none of the above

Question 51

The two wires in a DC adapter cable are 5 mm apart and carry a current of 4 A. If the cable is 1.5 m long, calculate the force between the wires and state if this force is attractive or not.

A) 9.6 *10^-4 N, attractive
B) 9.6 * 10^-7 N, attractive
C) 1.1 * 10^-8 N, attractive
D) 9.6 *10^-4 N, repulsive
E) 1.1 *10^-8 N, repulsive

Question 52

Two long, parallel wires are spaced 1 m apart in air, and you have established a current of 1 A in each. The force per unit length that each wire exerts on the other is

A) 4 $\mu$$\pi$ ₀
B) 2 $\mu$$\pi$ ₀
C) $\mu$ ₀
D) $\mu$ ₀/4 $\pi$
E) $\mu$ ₀/2 $\pi$

Question 53

Two long, straight parallel wires 7.6 cm apart carry currents of equal magnitude I. They attract each other with a force per unit length of 4.3 nN/m. The current I is approximately

A) 1.6 mA
B) 40 mA
C) 37 mA
D) 59 mA
E) 4.0 mA

Question 54

The graph that best represents the magnetic field on the axis inside a solenoid as a function of position x on the axis is

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

Question 55

The magnetic field at point P, due to the current in the very long wire, varies with distance R according to

A) R²
B) R^-3
C) R^-2
D) R³
E) R^-1

Question 56

Current-carrying wires are located along two edges of a cube with the directions of the currents as indicated. The vector that indicates the resultant magnetic field at the corner of the cube is

A)
B)
C)
D)
E)

Question 57

Two straight rods 55 cm long and 1.4 mm apart in a current balance carry current I, each in opposite directions. If a mass of 1.3 g when placed on the upper rod balances the magnetic force of repulsion between the rods, then calculate the current I.

A) 160 A
B) 18 A
C) 13 A
D) 3.6 A
E) 9.0 A

Question 58

Two long, parallel wires are spaced 1 m apart in air, and you have established a current of 1 A in each. The force per unit length that each wire exerts on the other is approximately

A) 2 * 10^-6 N/m
B) 2 * 10^-5 N/m
C) 2 * 10^-7 N/m
D) 2 $\pi$ * 10^-5 N/m
E) 2 $\pi$ * 10^-6 N/m

Question 59

Two parallel wires carry currents I₁ and I₂ = 2I₁ in the same direction. Which of the following expressions shows the relationship of the forces on the wires?

A) F₁ = F₂
B) F₁ = 2F₂
C) 2F₁ = F₂
D) F₁ = 4F₂
E) 4F₁ = F₂

Question 60

Use the following to answer the next question:
Two long parallel wires are a distance d apart and carry equal and opposite currents. Point P is distance d from each of the wires. Which diagram best represents the direction of the magnetic field at point P?

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

Question 61

If the Biot-Savart relationship d = ( $\mu$ ₀/4 $\pi$ )( * d )/r³
Is used to determine the magnetic field at the point P on the axis of a circular current-carrying loop, the vector is correctly represented by

A) ₁
B) ₂
C) ₃
D) ₄
E) ₅

Question 62

A long straight wire of radius R carries a current density J = kr A/m² where k is a constant. The magnetic field for r < R is (Hint: Current enclosed .)

A) $\mu$ ₀kr²/2
B) $\mu$ ₀kr²/3
C) 2 $\pi$$\mu$ ₀kr
D) 2 $\pi$$\mu$ ₀kr/2
E) none of the above

Question 63

A coaxial cable consists of a solid inner cylindrical conductor of radius 2 mm and an outer cylindrical shell of inner radius 3 mm and outer radius 3.5 mm. A current of 15 A flows down the inner wire and an equal return current flows in the outer conductor. If we assume that the currents are uniform over the cross section of the conductors, then calculate the magnitude of the enclosed current for use in Ampere's Law at a radius of 3.25 mm.

A) 7.2 A
B) 3.8 A
C) 7.8 A
D) 11.2 A
E) 7.5 A

Question 64

A wire of radius 0.35 cm carries a current of 75 A that is uniformly distributed over its cross-sectional area. The magnetic field at the surface of the wire is approximately

A) 8.4 mT
B) 4.3 mT
C) 6.7 mT
D) 2.3 mT
E) 5.7 mT

Question 65

Use the following to answer the next question:

-A coil of radius R = 5 cm lies inside a long solenoid which carries a current I₁ = 10 A and has 800 turns/m. The coil carries a current I₂ = 4 A and the normal of the plane of the coil is at an angle $\theta$ = 30 $\degree$ with the axis of the solenoid. The magnitude of the torque on the coil is

A) 1.56 * 10^-4 N . m
B) 2.74 * 10^-4 N . m
C) 5.03 * 10^-5 N . m
D) 3.16 * 10^-4 N . m
E) none of the above

Question 66

A wire of radius 0.6 cm carries a current of 10 A that is uniformly distributed over its cross section. Calculate the magnetic field strength at r = 0.2 cm divided by that at r = 0.4 cm.

A) 1.0
B) 0.75
C) 0.50
D) 2.0
E) 3.0

Question 67

A toroid has 200 turns of wire with a current of 3 A passing through the wire. The inner radius of the toroid is 3 cm and the outer radius is 5 cm. Calculate the magnetic field strength at a radius of 2 cm.

A) 6.0 * 10^-3 T
B) 3.0 * 10^-3 T
C) 1.2* 10^-2 T
D) 4.8 F*10^-4 T
E) none of the above

Question 68

Use the following figure to answer the next problem:

-The tightly wound toroid shown consists of 100 turns of wire, each carrying a current
I = 3 A. If a = 12 cm and b = 15 cm, the magnetic field at r = 13 cm, due to the current in this toroid, is (µ₀ = 4 $\pi$ *10^-7 N/A²)

A) 333 µT
B) 462 µT
C) 500 µT
D) 600
E) zero

Question 69

Use the following figure to answer the next problem:

-The tightly wound toroid shown consists of 100 turns of wire, each carrying a current
I = 3 A. If a = 12 cm and b = 15 cm, the magnetic field at r = 18 cm, due to the current in this toroid, is (µ₀ = 4 $\pi$ *10^-7 N/A²)

A) 333 µT
B) 400 µT
C) 500 µT
D) 600
E) zero

Question 70

The graph that best represents B as a function of r for a wire of radius R carrying a current I uniformly distributed over its cross-sectional area is

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

Question 71

A wire of radius 0.35 cm carries a current of 75 A that is uniformly distributed over its cross-sectional area. The magnetic field at a distance of 5.0 cm from the center of the wire is approximately

A) 0.47 mT
B) 1.5 mT
C) 0.30 mT
D) 0.56 mT
E) 0.24 mT

Question 72

Ampère's law is valid

A) when there is a high degree of symmetry in the geometry of the situation.
B) when there is no symmetry.
C) when the current is constant.
D) when the magnetic field is constant.
E) for all of these conditions.

Question 73

Use the following to answer the next question:

-A coil of radius R = 5 cm lies inside a long solenoid which carries a current I₁ = 10 A and has 800 turns/m. The coil carries a current I₂ = 4 A and the normal of the plane of the coil is at an angle $\theta$ = 30 $\degree$ with the axis of the solenoid. The magnetic field produced by the solenoid at the center is ____ times greater than the magnetic field by the coil at the center.

A) 100
B) 200
C) 1000
D) 2000
E) 8000

Question 74

A wire of radius 0.35 cm carries a current of 75 A that is uniformly distributed over its cross-sectional area. The magnetic field 0.20 cm from the center of the wire is approximately

A) 2.5 mT
B) 8.8 $\mu$ T
C) 3.8 mT
D) 15 mT
E) 2.9 $\mu$ T

Question 75

A long solenoid of radius 3 cm has 1100 turns per m. If the solenoid wire carries a current of 1.5 A, then calculate the magnetic field inside the solenoid.

A) 2.1 * 10^-3 T
B) 1.0 *10^-3 T
C) 1.7 *10^-4 T
D) 7.0 *10^-2 T
E) none of the above

Question 76

Use the following figure to answer the next problem:

-The tightly wound toroid shown consists of 100 turns of wire, each carrying a current
I = 3 A. If a = 12 cm and b = 15 cm, the magnetic field at r = 10 cm, due to the current in this toroid, is (µ₀ = 4 $\pi$ * 10^-7 N/A²)

A) 400 µT
B) 500 µT
C) 600 µT
D) zero
E) impossible to calculate without additional information.

Question 77

The orbital magnetic moment of an atomic electron is

A) directly proportional to its angular momentum.
B) directly proportional to the electronic charge.
C) inversely proportional to the mass of the electron.
D) quantized as a consequence of the quantization of angular momentum.
E) described by all of the above.

Question 78

A wire of radius 0.6 cm carries a current of 10 A that is uniformly distributed over its cross section. Calculate the magnetic field strength at r = 0.3 cm divided by that at r = 0.9 cm.

A) 1.0
B) 0.75
C) 0.50
D) 2.0
E) 3.0

Question 79

A long straight wire of radius R carries a current density J = kr A/m² where k is a constant. The magnetic field for r > R is (Hint: Current enclosed .)

A) $\mu$ ₀kR³/3r
B) 2 $\pi$$\mu$ ₀kR³/3r
C) 2 $\pi$$\mu$ ₀kR²/r
D) 2 $\pi$$\mu$ ₀kR/2
E) none of the above

Question 80

Gauss's law for magnetism summarizes the fact(s) that

A) the magnetic flux through a closed surface is zero.
B) the magnetic flux is given by _SB dA.
C) the existence of magnetic monopoles has yet to be verified.
D) there is no point in space from which magnetic field lines diverge.
E) all of the above are true.