Deck 28: Magnetic Fields of Moving Charges

Question 1

A long solenoid (diameter = 5.00 cm)is wound with thin wire through which a constant 0.292 A current is maintained.A wire carrying an 8.5 A current is inserted along the axis of the solenoid.The magnitude of the magnetic field at a point 5.00 mm from the axis is 0.650 mT.What are the number of turns per unit length for this solenoid?

A)1510 turns/m
B)1000 turns/m
C)2000 turns/m
D)2120 turns/m
E)1250 turns/m

Answer 1

1510 turns/m

Question 2

Two long parallel wires are separated by 2.5 mm.The current in one of the wires is twice the other current.If the magnitude of the force on a 2.0-m length of one of the wires is equal to 4.0 µN,what is the larger of the two currents?

A)0.11 A
B)0.22 A
C)0.42 A
D)0.84 A
E)1.7 A

Answer 2

0.22 A

Question 3

A long solenoid (diameter = 5.00 cm)is wound with1000 turns per meter of thin wire through which a constant 0.292 A current is maintained.A wire carrying 10.0 A current is inserted along the axis of the solenoid.How far from the axis of the solenoid and inside the solenoid is the magnitude of the magnetic field 0.650 mT?

A)5.0 mm
B)10.mm
C)2.5 mm
D)6.1 mm
E)3.7 mm

Answer 3

3.7 mm

Question 4

Two long wires are parallel to each other.The wires carry currents of different magnitudes.If the amount of current in each wire is halved,the magnitude of the force between the wires will be

A)twice the original force.
B)four times the original force.
C)the same as the original force.
D)half the original force.
E)one fourth the original force.

Question 5

A long solenoid (diameter = 4.00 cm)is wound with 1500 turns per meter of thin wire through which a current of 0.220 A is maintained.A wire carrying 5.00 A is inserted along the axis of the solenoid.What is the magnitude of the magnetic field at a point 1.00 cm from the axis?

A)0.0673 mT
B)0.114 mT
C)0.294 mT
D)0.372 mT
E)0.427 mT

Question 6

An electron is shot from an electron gun with a speed of 5.0 * 10⁵ m/s parallel to and a distance of 2.0 cm above a long straight wire carrying a current of 10A. Determine the magnitude of the acceleration of the electron the instant it leaves the electron gun.

A)8.0 * 10^-18 N
B)5.7 * 10^-18 N
C)7.2 * 10^-18 N
D)9.3 * 10^-18 N

Question 7

The Biot-Savart Law for magnetic fields is analogous to which law for electric fields?

A)Gauss's Law
B)Coulomb's Law
C)Newton's 2nd Law of Motion
D)None are correct.

Question 8

A circular piece of wire connected to the terminals of a battery is lying on a table.The surface of the table is in the horizontal plane.As viewed from above,electrons move through the wire in the counterclockwise direction.In which direction is the magnetic field at the center of the circular wire?

A)up
B)down
C)clockwise
D)counterclockwise

Question 9

When using Ampere's Law,which currents can and must be included in the calculation?

A)all currents
B)only those currents which form a closed loop
C)only those currents generated by positive charges
D)None are correct.

Question 10

An electron is shot from an electron gun with a speed of 5.0 * 10⁵ m/s parallel to and a distance of 2.0 cm above a long straight wire carrying a current of 10 A. Determine the magnitude of the acceleration of the electron the instant it leaves the electron gun.

A)6.2 * 10¹² m/s²
B)7.9 * 10¹² m/s²
C)8.2 * 10¹² m/s²
D)8.8 * 10¹² m/s²

Question 11

A current of 18 A runs vertically up through a wire that passes through a table.A compass is placed 13 cm due north of where the wire passes through the table.The magnetic field of the earth at this location is 2.6 *10^-5 T due north.Determine the magnitude of the magnetic field at the location of the compass.

A)3.45 * 10^-5 T
B)5.37 * 10^-5 T
C)4.14 *10^-5 T
D)46.8 ^$\circ$ east of due north
E)3.80 * 10^-5 T

Question 12

An ideal solenoid has a field of magnitude 0.10 T when carrying a current of 200A. The solenoid is 5.0 m long.What is the number of turns for the coils of the solenoid?

A)1.0 * 10³
B)2.0 * 10³
C)3.0 * 10³
D)4.0 * 10³

Question 13

Two long parallel wires are separated by 4.0 mm.The current in one of the wires is twice the other current.If the magnitude of the force on a 0.5-m length of one of the wires is equal to 9.0 µN,what is the smaller of the two currents?

A)0.11 A
B)0.22 A
C)0.42 A
D)0.84 A
E)1.7 A

Question 14

Each of two long straight parallel wires separated by a distance of 24.0 cm carries a current of 5.00 A in the same direction.What is the magnitude of the resulting magnetic field at a point that is 14.0 cm from each wire?

A)1.25 µT
B)4.27 µT
C)7.36 µT
D)12.8 µT
E)18.4 µT

Question 15

A long solenoid (diameter = 5.00 cm)is wound with 2000 turns per meter of thin wire through which a constant current is maintained.A wire carrying 8.50 A is inserted along the axis of the solenoid.The magnitude of the magnetic field at a point 5.00 mm from the axis is 0.650 mT.What is the current through the solenoid?

A)0.292 A
B)517 A
C)0.220 A
D)7.80 mA
E)22.7 A

Question 16

The current in a wire is uniformly distributed over the cross-sectional area of the wire.The radius of the wire is r.Where is the magnitude of the magnetic field generated by the current flowing through the wire greatest?

A)at the center of the wire
B)on the surface of the wire
C)at a perpendicular distance r from the surface of the wire
D)None are correct.

Question 17

Each of two long straight parallel wires separated by a distance of 24.0 cm carries a current in the same direction.If the resulting magnetic field at a point that is 14.0 cm from each wire is 12.8 µT,what is the current flowing through one of the wires?

A)7.09 A
B)7.78 A
C)5.00 A
D)8.70 A
E)5.63 A

Question 18

A long solenoid (diameter = 5.00 cm)with 1000 turns per meter of thin wire through which a constant 0.292 A current is maintained.A wire carrying a current is inserted along the axis of the solenoid.The magnitude of the magnetic field at a point 5.00 mm from the axis is 0.650 mT.What is the current through the wire on the axis of the solenoid?

A)8.50 A
B)13.4 A
C)16.2 A
D)7.80 A
E)11.7 A

Question 19

Ampere's Law of magnetic fields is analogous to which law for electric fields?

A)Gauss's Law
B)Coulomb's Law
C)Newton's 2nd Law of Motion
D)None are correct.

Question 20

An electron is shot from an electron gun with a speed parallel to and a distance of 2.0 cm above a long straight wire carrying a current of 10A. The magnitude of its acceleration at the instant it leaves the electron gun is 6.1 * 10¹¹ m/s .What is the speed of the electron.

A)1.3 * 10⁴ m/s
B)2.2 * 10⁴ m/s
C)3.5 * 10⁴ m/s
D)4.8 * 10⁴ m/s

Question 21

Assume there is a current of 3.0 A traveling clockwise in a loop around this piece of paper (which is approximately 22 cm wide and 28 cm long).There is an infinitely long wire that runs parallel to the top edge of the paper that carries a current of 5.0 A.If the distance between the top edge and the wire is 50 cm find the magnitude of the torque on the current loop.

A)zero
B)2.4 10^-7 N ^. m
C)2.9 10^-7 N ^. m
D)3.0 10^-7 N ^. m

Question 22

A 7.5-m long extension cord carries a current of 12 amps.The cord is made of two wires,carrying currents in opposite directions,separated by a distance of 4.9 mm.Find the force between those two wires.

A)0.0059 N
B)0.044 N
C)0.33 N
D)1.2 N
E)9.0 N

Question 23

A wire of radius R = 1.5 mm and carries a current.The current density is given by the function J = J₀ (1 - r/R)where r is measured from the center of the wire and J₀ = 1.06 * 10⁵ A/m².Use Ampère's law to find the magnetic field at the surface of the wire.What is the magnitude of B if I = 1A,R = 1.5 mm.

A)148 µT
B)12 µT
C)100 µT
D)33 µT
E)37 µT

Question 24

Proton A travels northward with a constant velocity.Due north of proton A is proton B,traveling to the east at a different constant velocity.In what direction is the magnetic force on B?

A)to the south
B)to the west
C)upward,out of the ground
D)down into the ground
E) There is no force on B.

Question 25

Proton A travels northward with a constant velocity.Due north of proton A is proton B,traveling to the east at a different constant velocity.In what direction is the magnetic force on A?

A)to the south
B)to the west
C)upward,out of the ground
D)down into the ground

Question 26

Wire 1 has a semicircular section of radius R followed by a straight section of length R as shown in the figure,and carries a current I₁.Wire 2,which is perpendicular to the page,carries a current I₂,where I₂ flows out of the page.If R is doubled,by what factor will the magnitude of the magnetic force on wire 1 due to the magnetic field created by wire 2 change?

A)2
B)1
C)0.5
D)4

Question 27

A square loop of wire,20 cm long on each side carries a current of 0.3 A.What is the magnetic field in the center of the square loop?

A)0.5 µT
B)1.2 µT
C)1.9 µT
D)2.3 µT

Question 28

A current of flows along the length of a long solid cylindrical conductor.The radius of the cylinder is 8.5 cm.The current is uniformly distributed through the conductor.If the magnitude of the magnetic field is 2.00 * 10^-6 T at a distance of 2.4 cm from the center of the cylinder,what is the size of the current in the wire?

A)2.33 A
B)3.01 A
C)2.78 A
D)4.10 A
E)2.45 A

Question 29

A current of 2.45 A flows along the length of a long solid cylindrical conductor.The radius of the cylinder is 8.5 cm.The current is uniformly distributed through the conductor.Find where,relative to the center of the wire and inside the wire the magnitude of the magnetic field is 2.00 * 10^-6 T.

A)1.2 cm
B)2.4 cm
C)3.6 cm
D)1.8 cm
E)2.9 cm

Question 30

In a coaxial cable,the solid inner conductor carries a current of I.The shield,which also carries a current of I but in the opposite direction,has an inner radius of a and an outer radius of b.The current density is equally distributed over each conductor.What is the magnitude of at a radial distance of 1.05 mm from the center of the coaxial cable if a = 1 mm,b = 1.1 mm and I = 100 mA?

A)1.5 mT
B)10 mT
C)10 µT
D)0 T

Question 31

A current of 2.45 A flows along the length of a long solid cylindrical conductor.The radius of the cylinder is 8.5 cm.The current is uniformly distributed through the conductor.Calculate the magnitude of the magnetic field 2.4 cm from the center of the cylinder.

A)5.65 * 10^-8 T
B)1.76 * 10^-6 T
C)2.95 * 10^-5 T
D)1.63 * 10^-6 T
E)6.64 * 10^-7 T

Question 32

Two wires,A and B,are parallel to each other and separated by a distance of 30 cm.Wire A carries a current of 1.2 A in one direction while wire B carries a current of 3.1 A in the opposite direction.Where is the magnetic field equal to zero?

A)between the wires and 8 cm from A
B)between the wires and 10 cm from A
C)exactly halfway between the wires
D)outside the wires and 4 cm from A
E)outside the wires and 19 cm from A

Question 33

A large 1 m by 1 m sheet conductor in the x-y plane carries a uniform current flowing in the x-direction.The current density is 1.7 A/cm.What is the direction of the magnetic field just above the center of the sheet at z = 2 mm (not close to any edges).

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

Question 34

A wire of radius R carries a current I.The current density is given by the function J = J₀ (1 - r/R)where r is measured from the center of the wire and J₀ is a constant.Use Ampère's law to find the magnetic field inside the wire at a distance r < R from the axis.What is the magnitude of B if I = 1A,R = 1.5 mm,and r = 1 mm?

A)12 mT
B)37 µT
C)1.5 T
D)45 mT
E)148 µT

Question 35

Two wires,A and B,are parallel to each other and separated by a distance of 25 cm.Both wires carry a current of 1.5 A in the same direction.Where is the magnetic field equal to zero?

A)exactly halfway between the wires
B)outside the wires and 5 cm from A
C)outside the wires and 5 cm from B
D)B and C only are correct.
E)nowhere

Question 36

A coaxial wire consists of a copper wire of radius 1 mm surrounded by a copper sheath of inside radius 1.5 mm and an outside radius 2 mm.A 3-A current flows in one direction down the core and in the opposite direction down the sheath.What is the magnitude of the magnetic field at a radius of 3 mm from the center of the wire?

A)0 T
B)1.25 µT
C)3.15 µT
D)4.20 µT
E)5.15 µT

Question 37

In a solenoid magnet in which the wires are wound such that each winding touches the previous,which of the following will increase the magnetic field inside the magnet?

A)making the winding radius smaller
B)increasing the wire radius
C)increasing the radius of the solenoid
D)decreasing the wire radius
E)immersion of the solenoid in gasoline

Question 38

Find the magnitude of the magnetic force on a wire,which has semicircular section of radius R followed by a straight section of length R as shown in the figure,carrying a current I₁= 10 A,due to the magnetic field created by a second wire,which is perpendicular to the page,carrying a current I₂ = 10 A.I₂ flows out of the page and R = 10 cm.

A)55 mN
B)0 N
C)12 mN
D)8.1 µN
E)13.9 µN

Question 39

Assume there is a current of 3.0 A traveling clockwise in a loop around this piece of paper (which is approximately 22 cm wide and 28 cm long).There is an infinitely long wire that runs parallel to the top edge of the paper that carries a current of 5.0 A.If the distance between the top edge and the wire is 50 cm find the magnitude of the force between the wire and the loop.

A)zero
B)1.3 * 10^-7 N
C)4.7 * 10^-7 N
D)2.2 * 10^-6 N

Question 40

A current of 2.45 A flows along the length of a long solid cylindrical conductor.The current is uniformly distributed through the conductor.Find the radius of the wire if the magnitude of the magnetic field inside the wire and at a distance of 2.4 cm from the center of the wire is 2.00 * 10^-6.

A)2.4 cm
B)7.7 cm
C)9.0 cm
D)8.5 cm
E)4.8 cm

Question 41

A coil of wire 20 cm length and 200 turns carries a current of 10 A.A bar of titanium (magnetic susceptibility 1.81 x 10^-4)is positioned within the coil.The magnetic field inside the titanium bar is

A)7.590 x 10^-4 T.
B)4.145 x 10^-4 T.
C)12.6 x 10^-4 T.
D)1.257 x 10^-2 T.

Question 42

A square,clamping ammeter has four sides each with a length of 3.0 cm.The four sides of the ammeter are capable of measuring the magnetic field at the position of the sides.When the ammeter is clamped around a cylindrical wire carrying a 5.0 A DC current as shown in the figure,what is the average magnetic field measured in the sides of the clamp?

A)0.13 G
B)0.25 G
C)0.52 G
D)1.0 G
E)2.0 G

Question 43

The figure shows the cross section through 3 long wires with linear mass density 100 g/m.They carry currents I₁,I₂,and I₃ in the directions shown.Wires 2 and 3 are 10 cm apart and are attached to a vertical surface,and each carry a current of 600 A.What current I₁ will allow wire 1 on the right to "float" such that its distance from the vertical surface is 10 cm?

A)1021 A
B)512 A
C)700 A
D)256 A

Question 44

Two wires carry different currents in the opposite directions as shown.Where is it possible for the magnetic field produced by the wires to be zero?

A)A only
B)B only
C)C only
D)A or C
E)nowhere

Question 45

Two 100 turn coils of wire with a diameter of 1.0 m are placed a distance of 0.25 m apart as shown in the figure.A current of 3.0 A is in the wires of both coils and the direction of the current is clockwise (CW)for both coils when viewed from one end.What is the magnitude of the magnetic field in the center between the two coils?

A)0 T
B)1.9 * 10^-4 T
C)3.4 * 10^-4 T
D)6.9 * 10^-4 T
E)7.5 * 10^-4 T

Question 46

A particle with a mass of 1 mg and a charge q is seen to travel with a speed of 1000 m/s parallel to a straight current carrying wire along a horizontal path 10 cm below the wire as shown in the figure.Determine q if the magnitude of current in the wire is 10 A.

A)1.0 C
B)0.49 C
C)0.24 C
D)2.0 C

Question 47

A long,straight wire is located along the x-axis (y = 0 and z = 0).The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0),when it has a velocity of 300 m/s in the +z-direction?

A)0.0 N
B)1.5 * 10^-4 N
C)2.7 * 10^-4 N
D)3.0 * 10^-4 N
E)6.0 * 10^-4 N

Question 48

A very long wire carrying a current I = 5.0 A is bent into a semi-circle with a diameter of 10 cm as shown in the figure.What is the magnitude of the magnetic field at the point P,halfway between the ends of the straight sections of wire and at the center of curvature of the semi-circle?

A)2.0 * 10^-5 T
B)3.1 * 10^-5 T
C)5.1 * 10^-5 T
D)6.3 * 10^-5 T
E)8.3 * 10^-5 T

Question 49

A long wire located at Z = 0 carries current i₁ = 3.00 A to the right as shown.A second long wire located a distance d = 0.240 m above the first wire carries a current i₂ = 1.10 A to the left as shown.Where in the Z direction (in m)does the magnetic field from the two wires sum to zero?

A)0.285
B)0.379
C)0.504
D)0.670
E)0.892

Question 50

A square,clamping ammeter has four sides each with a length of 3.0 cm.The four sides of the ammeter are capable of measuring the magnetic field at the position of the sides.When the ammeter is clamped around a cylindrical wire carrying a DC current as shown in the figure,the average magnetic field measured in the sides of the clamp is 2.0

A)0.14 A
B)0.30 A
C)0.57 A
D)5.0 A
E)19 A

Question 51

A solenoid is made up of 100 turns of a wire carrying 0.25 A of current,and is 5.0 cm long.The radius of the solenoid is 1.5cm.You are looking at the solenoid end-on,such that the current circulates counter-clockwise from your point of view.A complete circuit is made by having the wire from one end of the solenoid connect to the wire at the other end,and running down the middle of the solenoid,therefore carrying current in the +z direction along the z-axis.What is the magnetic field at a point (x,y)= (-0.75 cm,0.0 cm)?

A)
B)
C)
D)
E)None are correct.

Question 52

A wire of radius R = 4 mm carries a uniformly distributed current of 2 A.The magnetic field inside the wire at a radial distance R/2 from the axis of the wire is

A)2 * 10^-4 T.
B)5 * 10^-5 T.
C)1 * 10^-4 T.
D)1 * 10^-5 T.

Question 53

Two long wires (mass per unit length 1.9 g/m)are suspended by threads attached from the ceiling so that they are parallel to each other and to the ceiling above.They each carry an electric current of 15A,in opposite directions.When they carry no current,the wires hang such that they are touching all along their length,and the threads are vertical and immediately adjacent to one another.If the angle between the threads is 10.0 ^$\circ$ ,what is the length of the threads from which the wires hang?

A)0.039 m
B)0.16 m
C)0.50 m
D)2.0 m

Question 54

The overhead cable for a street trolley is strung horizontally 5 m above the ground.A long straight section of it carries a 100 A current due west.What is the magnetic field due to the current in the cable at street level directly under the cable?

A)4·10^-6 T,pointing west
B)500 T,pointing south
C)500 T,pointing west
D)4·10^-6 T,pointing south
E)2·10^-8 T,pointing east

Question 55

Two parallel wires,separated by the distance of 2 cm,carry the currents I₁ = 1 A and I₂ = 2 A in the same direction.How far from the wire carrying the current I₁ is the magnetic field zero?

A)never 0
B)1.00 cm
C)0.667 cm
D)3.00 cm
E)2.00 cm

Question 56

Two long wires are suspended by 16-cm long threads attached from the ceiling so that they are parallel to each other and to the ceiling above.They each carry an electric current of 15A,in opposite directions.When they carry no current,the wires hang such that they are touching all along their length,and the threads are vertical and immediately adjacent to one another.If the angle between the threads is 10.0 ^$\circ$ ,what is the mass per unit length of the wires?

A)0.47 g/m
B)1.9 g/m
C)3.8 g/m
D)24 g/m
E)48 g/m

Question 57

A long,straight wire is located along the x-axis (y = 0 and z = 0).The wire carries a current of 5.0 A in the +x direction.What is the magnitude of the force on a 2.0 C charged particle located at (+2.0 m,+1.0 m,0),when it has a velocity of 300 m/s in the +x-direction?

A)0.0 N
B)1.5 * 10^-4 N
C)2.7 * 10^-4 N
D)3.0 * 10^-4 N
E)6.0 * 10^-4 N

Question 58

Two long wires lie parallel to the x-axis;one at y = 0.0 m,the other at y = 0.12 m.The first carries current of 1.0 A in the positive x direction,while the other carries current of 1.5 A in the negative x direction.Which of the below is a y-coordinate value at which there is no magnetic field?

A)4.8 cm
B)-4.8 cm
C)24 cm
D)-24 cm
E)Two or more of the choices are possible answers.