Deck 30: Sources of the Magnetic Field

Question 1

Two long parallel wires separated by 5.0 mm each carry a current of 60 A.These two currents are oppositely directed.What is the magnitude of the magnetic field at a point that is between the two wires and 2.0 mm from one of the two wires?

A)2.0 mT
B)10 mT
C)8.0 mT
D)1.6 mT
E)7.2 mT

Answer 1

10 mT

Question 2

A segment of wire of total length 3.0 m carries a 15-A current and is formed into a semicircle.Determine the magnitude of the magnetic field at the center of the circle along which the wire is placed.

A)1.6 μT
B)4.9 μT
C)1.0 μT
D)9.8 μT
E)15 μT

Answer 2

4.9 μT

Question 3

Two long parallel wires carry unequal currents in the same direction.The ratio of the currents is 3 to 1.The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT.What is the larger of the two currents?

A)5.3 A
B)3.8 A
C)4.5 A
D)3.0 A
E)0.5 A

Answer 3

3.0 A

Question 4

A straight wire (length = 8.0 m)is bent to form a square.If the wire carries a current of 20 A,what is the magnitude of the magnetic field at the center of the square?

A)17 μT
B)14 μT
C)11 μT
D)20 μT
E)36 μT

Question 5

Each of two parallel wires separated by 6.0 mm carries a 40-A current.These two currents are in the same direction.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

A)2.6 mT
B)zero
C)1.9 mT
D)1.6 mT
E)3.2 mT

Question 6

Two very long parallel wires carry currents in the positive x direction.One wire (current = 15 A)is coincident with the x axis.The other wire (current = 50 A)passes through the point (0,4.0 mm,0).What is the magnitude of the magnetic field at the point (0,0,3.0 mm)?

A)3.8 mT
B)2.7 mT
C)2.9 mT
D)3.0 mT
E)0.6 mT

Question 7

A long straight wire carries a current of 40 A in a region where a uniform external magnetic field has a 30-μT magnitude and is parallel to the current.What is the magnitude of the resultant magnetic field at a point that is 20 cm from the wire?

A)70 μT
B)40 μT
C)10 μT
D)50 μT
E)36 μT

Question 8

A 2.0-cm length of wire centered on the origin carries a 20-A current directed in the positive y direction.Determine the magnetic field at the point x = 5.0 m on the x-axis.

A)1.6 nT in the negative z direction
B)1.6 nT in the positive z direction
C)2.4 nT in the negative z direction
D)2.4 nT in the negative z direction.
E)None of the above

Question 9

Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in opposite directions.What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the 30-A current and 25 cm from the other wire?

A)51 μT
B)33 μT
C)72 μT
D)64 μT
E)46 μT

Question 10

Three long wires parallel to the x axis carry currents as shown.If I = 20 A,what is the magnitude of the magnetic field at the origin?

A)37 μT
B)28 μT
C)19 μT
D)47 μT
E)58 μT

Question 11

If a = 2.0 cm,b = 5.0 cm,and I = 20 A,what is the magnitude of the magnetic field at the point P?

A)4.5 μT
B)7.5 μT
C)9.0 μT
D)6.0 μT
E)3.6 μT

Question 12

Two long straight wires carry currents perpendicular to the xy plane.One carries a current of 50 A and passes through the point x = 5.0 cm on the x axis.The second wire has a current of 80 A and passes through the point y = 4.0 cm on the y axis.What is the magnitude of the resulting magnetic field at the origin?

A)200 μT
B)600 μT
C)450 μT
D)300 μT
E)400 μT

Question 13

Each of two long straight parallel wires separated by a distance of 16 cm carries a current of 20 A in the same direction.What is the magnitude of the resulting magnetic field at a point that is 10 cm from each wire?

A)57 μT
B)80 μT
C)64 μT
D)48 μT
E)40 μT

Question 14

One long wire carries a current of 30 A along the entire x axis.A second long wire carries a current of 40 A perpendicular to the xy plane and passes through the point (0,4,0)m.What is the magnitude of the resulting magnetic field at the point y = 2.0 m on the y axis?

A)4.0 μT
B)5.0 μT
C)3.0 μT
D)7.0 μT
E)1.0 μT

Question 15

A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns.If the wire carries a 1.2-A current,determine the magnitude of the magnetic field at the center of the loop.

A)79 μT
B)69 μT
C)59 μT
D)89 μT
E)9.4 μT

Question 16

Two long parallel wires carry unequal currents in opposite directions.The ratio of the currents is 3 to 1.The magnitude of the magnetic field at a point in the plane of the wires and 10 cm from each wire is 4.0 μT.What is the larger of the two currents?

A)0.5 A
B)1.0 A
C)1.5 A
D)2.0 A
E)3.0 A

Question 17

If a = 1.0 cm,b = 3.0 cm,and I = 30 A,what is the magnitude of the magnetic field at point P?

A)0.62 mT
B)0.59 mT
C)0.35 mT
D)0.31 mT
E)0.10 mT

Question 18

Two long parallel wires each carry a current of 5.0 A directed to the east.The two wires are separated by 8.0 cm.What is the magnitude of the magnetic field at a point that is 5.0 cm from each of the wires?

A)72 μT
B)48 μT
C)24 μT
D)96 μT
E)32 μT

Question 19

Two long parallel wires separated by 4.0 mm each carry a current of 24 A.These two currents are in the same direction.What is the magnitude of the magnetic field at a point that is between the two wires and 1.0 mm from one of the two wires?

A)4.8 mT
B)6.4 mT
C)3.2 mT
D)9.6 mT
E)5.3 mT

Question 20

Each of two parallel wires separated by 8.0 mm carries a 20-A current.These two currents are oppositely directed.Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.

A)2.0 mT
B)1.6 mT
C)1.3 mT
D)1.8 mT
E)1.0 mT

Question 21

The figure shows a cross section of three parallel wires each carrying a current of 5.0 A out of the paper.If the distance R = 6.0 mm,what is the magnitude of the magnetic force on a 2.0-m length of any one of the wires?

A)2.5 mN
B)3.3 mN
C)2.2 mN
D)2.9 mN
E)1.7 mN

Question 22

A hollow cylindrical (inner radius = 1.0 mm,outer radius = 3.0 mm)conductor carries a current of 80 A parallel to its axis.This current is uniformly distributed over a cross section of the conductor.Determine the magnitude of the magnetic field at a point that is 2.0 mm from the axis of the conductor.

A)8.0 mT
B)3.0 mT
C)5.3 mT
D)16 mT
E)1.2 mT

Question 23

Three long,straight,parallel wires all lie in the yz plane and each carries a current of 20 A in the positive z direction.The two outer wires are each 4.0 cm from the center wire.What is the magnitude of the magnetic force on a 50-cm length of either of the outer wires?

A)1.0 mN
B)0.50 mN
C)1.1 mN
D)1.5 mN
E)2.0 mN

Question 24

The figure shows a cross section of three parallel wires each carrying a current of 20 A.The currents in wires A and B are out of the paper,while that in wire C is into the paper.If the distance R = 5.0 mm,what is the magnitude of the force on a 2.0-m length of wire A?

A)23 mN
B)64 mN
C)32 mN
D)46 mN
E)55 mN

Question 25

In the figure,if a = 2.0 cm,b = 4.0 cm,and I = 2.0 A,what is the magnitude of the magnetic field at point P?

A)49 μT
B)39 μT
C)50 μT
D)69 μT
E)13 μT

Question 26

Two long parallel wires are separated by 6.0 mm.The current in one of the wires is twice the other current.If the magnitude of the force on a 3.0-m length of one of the wires is equal to 8.0 μN,what is the greater of the two currents?

A)0.20 A
B)0.40 A
C)40 mA
D)20 mA
E)0.63 A

Question 27

The segment of wire (total length = 6R,including the incoming and outgoing portions of the wire)is formed into the shape shown and carries a current I.What is the magnitude of the resulting magnetic field at the point P?

A)
B)
C)
D)
E)

Question 28

What is the magnitude of the magnetic field at point P if a = R and b = 2R?

A)
B)
C)
D)
E)

Question 29

Two long parallel wires are separated by 4.0 cm.One of the wires carries a current of 20 A and the other carries a 30-A current.Determine the magnitude of the magnetic force on a 2.0-m length of the wire carrying the greater current.

A)7.0 mN
B)6.0 mN
C)8.0 mN
D)9.0 mN
E)4.0 mN

Question 30

A long straight wire (diameter = 2.0 mm)carries a current of 40 A.What is the magnitude of the magnetic field 1.5 mm from the axis of the wire?

A)3.0 mT
B)12 mT
C)5.3 mT
D)7.4 mT
E)8.0 mT

Question 31

What is the magnitude of the magnetic field at point P if a = R and b = 2R?

A)
B)
C)
D)
E)

Question 32

A long straight wire (diameter = 2.0 mm)carries a current of 25 A.What is the magnitude of the magnetic field 0.50 mm from the axis of the wire?

A)5.0 mT
B)10 mT
C)0.63 mT
D)2.5 mT
E)0.01 mT

Question 33

The figure shows a cross section of three parallel wires each carrying a current of 24 A.The currents in wires B and C are out of the paper,while that in wire A is into the paper.If the distance R = 5.0 mm,what is the magnitude of the force on a 4.0-m length of wire A?

A)15 mN
B)77 mN
C)59 mN
D)12 mN
E)32 mN

Question 34

Two long parallel wires are separated by 2.0 cm.The current in one of the wires is three times the other current.If the magnitude of the force on a 2.0-m length of one of the wires is equal to 60 μN,what is the greater of the two currents?

A)2.0 A
B)1.0 A
C)3.0 A
D)9.0 A
E)1.5 A

Question 35

What is the magnitude of the magnetic field at point P in the figure if a = 2.0 cm,b = 4.5 cm,and I = 5.0 A?

A)87 μT,into the paper
B)87 μT,out of the paper
C)0.23 mT,out of the paper
D)0.23 mT,into the paper
E)23 μT,into the paper

Question 36

Three long,straight,parallel wires each carry a current of 10 A in the positive x direction.If the distance between each wire and the other two is 10 cm,what is the magnitude of the magnetic force on a 20-cm length of either of the wires?

A)57 μN
B)40 μN
C)69 μN
D)50 μN
E)20 μN

Question 37

The segment of wire (total length including portions of incoming and outgoing wire = 6R)is formed into the shape shown and carries a current I.What is the magnitude of the resulting magnetic field at the point P?

A)
B)
C)
D)
E)

Question 38

What is the magnitude of the magnetic field at point P if a = R and b = 2R?

A)
B)
C)
D)
E)

Question 39

The figure shows a cross section of three parallel wires each carrying a current of 15 A.The currents in wires A and C are out of the paper,while that in wire B is into the paper.If the distance R = 5.0 mm,what is the magnitude of the force on a 4.0-m length of wire C?

A)90 mN
B)54 mN
C)30 mN
D)18 mN
E)36 mN

Question 40

A long cylindrical wire (radius = 2.0 cm)carries a current of 40 A that is uniformly distributed over a cross section of the wire.What is the magnitude of the magnetic field at a point which is 1.5 cm from the axis of the wire?

A)0.53 mT
B)28 mT
C)0.30 mT
D)40 mT
E)1.9 mT

Question 41

A long,straight wire (radius = 2.0 mm)carries a current of 2.0 A distributed uniformly over a cross section perpendicular to the axis of the wire.What is the magnitude of the magnetic field at a distance of 1.0 mm from the axis of the wire?

A)0.40 mT
B)0.80 mT
C)0.10 mT
D)0.20 mT
E)0.75 mT

Question 42

A long hollow cylindrical conductor (inner radius = 2.0 mm,outer radius = 4.0 mm)carries a current of 24 A distributed uniformly across its cross section.A long wire which is coaxial with the cylinder carries an equal current in the opposite direction.What is the magnitude of the magnetic field 3.0 mm from the axis?

A)0.82 mT
B)0.93 mT
C)0.70 mT
D)0.58 mT
E)0.40 mT

Question 43

Two long parallel wires lie in the xz plane.One wire passes through the point (−2 m,0,0)and the other through the point (+2 m,0,0).The wires carry equal currents in the positive z direction.

Question 44

A long wire is known to have a radius greater than 4.0 mm and to carry a current uniformly distributed over its cross section.If the magnitude of the magnetic field is 0.285 mT at a point 4.0 mm from the axis of the wire and 0.200 mT at a point 10 mm from the axis,what is the radius of the wire?

A)4.6 mm
B)7.1 mm
C)5.3 mm
D)12 mm
E)10 mm

Question 45

The magnetic field at (+1 m,0,0)is in the positive y direction.

Question 46

A long solenoid (n = 1200 turns/m,radius = 2.0 cm)has a current of a 0.30 A in its winding.A long wire carrying a current of 20 A is parallel to and 1.0 cm from the axis of the solenoid.What is the magnitude of the resulting magnetic field at a point on the axis of the solenoid?

A)0.60 mT
B)0.85 mT
C)52 μT
D)0.40 mT
E)0.75 mT

Question 47

A long solenoid (diameter = 5.0 cm)is wound with 960 turns per meter of thin wire through which a current of 300 mA is maintained.A wire carrying 12 A is inserted along the axis of the solenoid.What is the magnitude of the magnetic field at a point 2.0 cm from the axis?

A)0.41 mT
B)0.48 mT
C)0.38 mT
D)0.56 mT
E)0.24 mT

Question 48

The magnetic field at (?3 m,0,0)is in the negative y direction.

Question 49

A conducting hollow cylinder (inner radius = a,outer radius = b)carries a current of 40 A that is uniformly distributed over the cross section of the conductor.If a = 3.0 mm and b = 6.0 mm,what is the magnitude of the (line)integral
Around a circular path (radius = 5.0 mm)centered on the axis of the cylinder and in a plane perpendicular to that axis?

A)50 μT ⋅ m
B)30 μT ⋅ m
C)22 μT ⋅ m
D)37 μT ⋅ m
E)47 μT ⋅ m

Question 50

A hollow cylindrical (inner radius = 2.0 mm,outer radius = 4.0 mm)conductor carries a current of 24 A parallel to its axis.This current is uniformly distributed over a cross section of the conductor.Determine the magnitude of the magnetic field at a point that is 5.0 mm from the axis of the conductor.

A)0.96 mT
B)1.7 mT
C)0.55 mT
D)1.2 mT
E)0.40 mT

Question 51

A long straight wire (diameter = 2.0 mm)carries a current of 30 A.What is the magnitude of the magnetic field 2.5 mm from the axis of the wire?

A)3.2 mT
B)2.8 mT
C)2.4 mT
D)3.6 mT
E)3.0 mT

Question 52

A long solenoid (1500 turns/m)carries a current of 20 mA and has an inside diameter of 4.0 cm.A long wire carries a current of 2.0 A along the axis of the solenoid.What is the magnitude of the magnetic field at a point that is inside the solenoid and 1.0 cm from the wire?

A)78 μT
B)55 μT
C)48 μT
D)68 μT
E)2.0 μT

Question 53

A single circular (radius = R)loop of wire is located in the yz plane with its center at the origin.The loop has a clockwise current as seen from the point (+R,0,0).The direction of the magnetic field at the point

A)(0,0,0)is −i and at the point (+R,0,0)is −i.
B)(0,0,0)is −i and at the point (0,+2R,0)is −i.
C)(0,0,0)is +i and at the point (+R,0,0)is +i.
D)(0,0,0)is +i and at the point (0,+2R,0)is +i.
E)None of the above

Question 54

A long solenoid (1000 turns/m)carries a current of 25 mA and has an inside radius of 2.0 cm.A long wire which is parallel to and 4.0 cm from the axis of the solenoid carries a current of 6.0 A.What is the magnitude of the magnetic field at a point on the axis of the solenoid?

A)51 μT
B)61 μT
C)43 μT
D)81 μT
E)1.4 μT

Question 55

A long hollow cylindrical conductor (inner radius = 2.0 mm,outer radius = 4.0 mm)carries a current of 12 A distributed uniformly across its cross section.A long wire which is coaxial with the cylinder carries an equal current in the same direction.What is the magnitude of the magnetic field 3.0 mm from the axis?

A)1.1 mT
B)1.4 mT
C)1.7 mT
D)2.0 mT
E)0.2 mT

Question 56

A solenoid 4.0 cm in radius and 4.0 m in length has 8 000 uniformly spaced turns and carries a current of 5.0 A.Consider a plane circular surface (radius = 2.0 cm)located at the center of the solenoid with its axis coincident with the axis of the solenoid.What is the magnetic flux through this surface? (1 Wb = 1 T ⋅ m²)

A)63 μWb
B)16 μWb
C)0.25 mWb
D)10 μWb
E)5.0 μWb

Question 57

Two long parallel wires lie in the xz plane. One wire passes through the point (-2 m, 0, 0) and the other through the point (+2 m, 0, 0). The wires carry equal currents in the positive z direction.

1. The magnetic field at (-3 m, 0, 0) is in the negative y direction.
2. The magnetic field at (-1 m, 0, 0) is in the positive y direction.
3. The magnetic field at (+1 m, 0, 0) is in the positive y direction.
4. The magnetic field at (+3 m, 0, 0) is in the negative y direction.

A)1 and 2 are correct.
B) 1 and 4 are correct.
C) 2 and 3 are correct.
D) 3 and 4 are correct.
E) None of the above are correct.

Question 58

A current-carrying 2.0-cm long segment of wire is inside a long solenoid (radius = 4.0 cm,n = 800 turns/m,current = 50 mA).The wire segment is oriented perpendicularly to the axis of the solenoid.If the current in the wire segment is 12 A,what is the magnitude of the magnetic force on this segment?

A)22 μN
B)16 μN
C)18 μN
D)12 μN
E)0 μN

Question 59

The magnetic field at (+3 m,0,0)is in the negative y direction.

A)1 and 2 are correct.
B)1 and 4 are correct.
C)2 and 3 are correct.
D)3 and 4 are correct.
E)None of the above are correct.

Question 60

A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm,n = 900 turns/m,current = 30 mA).What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects.

A)34 μT
B)64 μT
C)30 μT
D)45 μT
E)4.0 μT

Question 61

A solenoid consists of 100 circular turns of copper wire.Parts of three turns,A,B and C,are shown below.
When a current flows through the coil,

A)both A and C are repelled by B.
B)A is attracted to B;C is repelled by B.
C)neither A nor C is attracted to or repelled by B.
D)A is repelled by B;C is attracted to B.
E)both A and C are attracted to B.

Question 62

The field at (0,1.0 m,0)is in the negative y direction.

Question 63

A toroid is made of 2 000 turns of wire of radius 2.00 cm formed into a donut shape of inner radius 10.0 cm and outer radius 14.0 cm.When a 30.0-A current is present in the toroid,the magnetic field at a distance of 11.0 cm from the center of the toroid is

A)0.0857 T.
B)0.109 T.
C)0.120 T.
D)0.600 T.
E)0.685 T.

Question 64

Which diagram correctly shows the magnetic field lines created by a circular current loop in which current flows in the direction shown?

A)
B)
C)
D)
E)

Question 65

A thin infinitely large current sheet lies in the y-z plane.Current of magnitude J_s per unit length along the z axis travels in the y-axis direction,which is up out of the page.Which diagram below correctly represents the direction of the magnetic field on either side of the sheet?

A)
B)
C)
D)
E)

Question 66

A 0.50-m long solenoid consists of 1 000 turns of copper wire wound with a 4.0 cm radius.When the current in the solenoid is 18 A,the magnetic field at a point 1.0 cm from the central axis of the solenoid is

A)0.090 mT.
B)0.36 mT.
C)23 mT.
D)36 mT.
E)45 mT.

Question 67

Two solenoids are each made of 2 000 turns of copper wire per meter.Solenoid I is 2 m long,while solenoid II is 1 m long.When equal currents are present in the two solenoids,the ratio of the magnetic field B_I along the axis of solenoid I to the magnetic field B_II along the axis of solenoid II,B_I/B_II,is

A)1/4.
B)1/2.
C)1.
D)2
E)4.

Question 68

The field at (1.0 m,0,0)is zero.

Question 69

The field at (0,0,1.0 m)is in the positive z direction.

Question 70

A long wire lies in a tangle on the surface of a table,as shown below.When a current is run through the wire as shown,the largest component of the magnetic field at X points

A)into the table.
B)out of the table.
C)parallel to the nearest segment of wire.
D)antiparallel to the nearest segment of wire.
E)along a circle which has its center at the center of the overall loop.

Question 71

Two solenoids of equal length are each made of 2000 turns of copper wire per meter.Solenoid I has a 5.00 cm radius;solenoid II a 10.0 cm radius.When equal currents are present in the two solenoids,the ratio of the magnitude of the magnetic field B_I along the axis of solenoid I to the magnitude of the magnetic field B_II along the axis of solenoid II,B_I/B_II,is

A)1/4.
B)1/2.
C)1.
D)2.
E)4.

Question 72

When a microwave filter consisting of vertical parallel metal rods is in the absorbing position,oscillating currents are set up in the rods.At any one instant,the current in each rod has the same magnitude and direction.At that instant

A)the rods will try to move apart horizontally.
B)the rods will try to move together horizontally.
C)the rods will try to shift vertically upwards.
D)the rods will try to shift vertically downwards.
E)the rods will not be affected because the source of current is not a battery.

Question 73

The following statements all refer to the human brain when mental activity is occurring.Which statement is correct?

A)In order to detect electric currents in the brain,you must open the skull and make direct electrical contact with the brain.
B)The electric currents in the brain can be detected outside the brain by detecting the magnetic fields they produce.
C)The electric currents in the brain can be mapped by shaving a person's head and dropping iron filings on the head.
D)The electric currents in the brain produce an aura that can be detected visually.
E)The electric currents in the brain cannot be detected by any means.

Question 74

The field at (0,0,1.0 m)is in the negative y direction.

A)3 and 4
B)1 and 3
C)2 and 4
D)1 and 2
E)None of these

Question 75

By using a compass to measure the magnetic field direction at various points adjacent to a long straight wire,you can show that the wire's magnetic field lines are

A)straight lines in space that go from one magnetic charge to another.
B)straight lines in space that are parallel to the wire.
C)straight lines in space that are perpendicular to the wire.
D)circles that have their centers on the wire and lie in planes perpendicular to the wire.
E)circles that have the wire lying along a diameter of the circle.

Question 76

When the number of turns in a solenoid and its length are both doubled,the ratio of the magnitude of the new magnetic field inside to the magnitude of the original magnetic field inside is:

A)0.25
B)0.50
C)1
D)2
E)4

Question 77

A current element (length = 1.0 cm)lies along the x axis with its center at x = 0 and carries a 20-A current in the positive x direction.Consider only the field of this current element and decide which combination of the following statements is correct.

Question 78

At a point in space where the magnetic field is measured,the magnetic field produced by a current element

A)points radially away in the direction from the current element to the point in space.
B)points radially in the direction from the point in space towards the current element.
C)points in a direction parallel to the current element.
D)points in a direction parallel to but opposite in direction to the current element.
E)points in a direction that is perpendicular to the current element and perpendicular to the radial direction.

Question 79

Gauss's Law states that the net electric flux,
,through any closed surface is proportional to the charge enclosed:
)The analogous formula for magnetic fields is:

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

Question 80

A conducting rod with a square cross section (3.0 cm × 3.0 cm)carries a current of 60 A that is uniformly distributed across the cross section.What is the magnitude of the (line)integral
Around a square path (1.5 cm × 1.5 cm)if the path is centered on the center of the rod and lies in a plane perpendicular to the axis of the rod?

A)14 μT ⋅ m
B)75 μT ⋅ m
C)19 μT ⋅ m
D)57 μT ⋅ m
E)38 μT ⋅ m