Deck 28: Magnetic Fields of Charged Particles in Motion

Question 1

The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact.The magnitude of the current is the same in all the wires,and the directions of current flow are as indicated.For which (if any)configuration will the magnetic field at the center of the square formed by the wires be equal to zero?

A) A
B) B
C) C
D) D
E) The field is not equal to zero in any of these cases.

Answer 1

C

Question 2

The magnetic field at a distance of 2 cm from a current carrying wire is 4 μT.What is the magnetic field at a distance of 4 cm from the wire?

A) 1/2 µT
B) 1 µT
C) 2 µT
D) 4 µT
E) 8 µT

Answer 2

2 µT

Question 3

Consider a solenoid of length L,N windings,and radius b (L is much longer than b).A current I is flowing through the wire.If the radius of the solenoid were doubled (becoming 2b),and all other quantities remained the same,the magnetic field inside the solenoid would

A) remain the same.
B) become twice as strong.
C) become one half as strong.

Answer 3

remain the same.

Question 4

Two very long parallel wires in the xy-plane,a distance 2a apart,are parallel to the y-axis and carry equal currents I as shown in the figure.The +z direction points perpendicular to the xy-plane in a right-handed coordinate system.If both currents flow in the +y direction,which one of the graphs shown in the figure below best represents the z component of the net magnetic field,in the xy-plane,as a function of x? (Caution: These graphs are not magnetic field lines.)

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

Question 5

At what distance from the central axis of a long straight thin wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of the Earth's magnetic field of about 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T • m/A)

A) 1.0 cm
B) 2.0 cm
C) 3.0 cm
D) 4.0 cm
E) 5.0 cm

Question 6

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ₀ = 4π × 10^-7 T • m/A)

A) 1.5 µT
B) 3.3 µT
C) 6.7 µT
D) 33 µT
E) 67 µT

Question 7

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the magnitude of the magnetic field midway between the two wires?
(μ₀ = 4π × 10^-7 T • m/A)

A) 1.0 × 10^-5 T
B) 2.0 × 10^-5 T
C) 3.0 × 10^-5 T
D) 4.0 × 10^-5 T
E) 5.0 × 10^-5 T

Question 8

A negatively charged particle is moving to the right,directly above a wire having a current flowing to the right,as shown in the figure.In which direction is the magnetic force exerted on the particle?

A) into the page
B) out of the page
C) downward
D) upward
E) The magnetic force is zero since the velocity is parallel to the current.

Question 9

A point charge Q moves on the x-axis in the positive direction with a speed of 370 m/s.A point P is on the y-axis at y = +80 mm.The magnetic field produced at point P,as the charge moves through the origin,is equal to When the charge is at x = +40 mm,what is the magnitude of the magnetic field at point P? (μ₀ = 4π × 10^-7 T • m/A)

A) 0.57 μT
B) 0.74 μT
C) 0.92 μT
D) 1.1 μT
E) 1.3 μT

Question 10

The figure shows three long,parallel current-carrying wires.The magnitudes of the currents are equal and their directions are indicated in the figure.Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?

A) A
B) B
C) C
D) D
E) The magnetic force on current 1 is equal to zero.

Question 11

Two very long parallel wires are a distance d apart and carry equal currents in opposite directions.The locations where the net magnetic field due to these currents is equal to zero are

A) midway between the wires.
B) a distance d/2 to the left of the left wire and also a distance d/2 to the right of the right wire.
C) a distance d to the left of the left wire and also a distance d to the right of the right wire.
D) a distance d/ to the left of the left wire and also a distance d/
to the right of the right wire.
E) The net field is not zero anywhere.

Question 12

A point charge Q moves on the x-axis in the positive direction with a speed of 280 m/s.A point P is on the y-axis at y = +70 mm.The magnetic field produced at the point P,as the charge moves through the origin,is equal to What is the charge Q? (μ₀ = 4π × 10^-7 T • m/A)

A) -53 μC
B) +53 μC
C) -39 μC
D) +39 μC
E) +26 μC

Question 13

A very long thin wire produces a magnetic field of 0.0050 × 10^-4 T at a distance of 3.0 mm from the central axis of the wire.What is the magnitude of the current in the wire? (μ₀ = 4π × 10^-7 T • m/A)

A) 7.5 mA
B) 1.7 mA
C) 3300 mA
D) 24,000 mA

Question 14

The figure shows three long,parallel,current-carrying wires.The current directions are indicated for currents I₁ and I₃.The arrow labeled F represents the net magnetic force acting on current I₃.The three currents have equal magnitudes.What is the direction of the current I₂?

A) into the picture (in the direction opposite to that of I₁ and I₃)
B) horizontal to the right
C) vertically upward
D) vertically downward
E) out of the picture (in the same direction as I₁ and I₃)

Question 15

A ring with a clockwise current (as seen from above the ring)is situated with its center directly above another ring,which has a counter-clockwise current,as shown in the figure.In what direction is the net magnetic force exerted on the top ring?

A) upward
B) downward
C) to the right
D) to the left
E) The net force is zero.

Question 16

The figure shows two long wires carrying equal currents I₁ and I₂ flowing in opposite directions.Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire?

A) A
B) B
C) C
D) D
E) The magnetic field is zero at that point.

Question 17

Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions.The wire on your right carries current toward you,and the wire on your left carries current away from you.From your point of view,the magnetic field at the point exactly midway between the two wires

A) points upward.
B) points downward.
C) points toward you.
D) points away from you.
E) is zero.

Question 18

A long straight conductor has a constant current flowing to the right.A wire rectangle is situated above the wire,and also has a constant current flowing through it (as shown in the figure).Which of the following statements is true?

A) The net magnetic force on the wire rectangle is upward, and there is also a net torque on it.
B) The net magnetic force on the wire rectangle is zero, and the net torque on it is zero.
C) The net magnetic force on the wire rectangle is downward, and there is also a net torque on it.
D) The net magnetic force on the wire rectangle is zero, but there is a net torque on it.
E) The net magnetic force on the wire rectangle is downward, and the net torque on it is zero.

Question 19

Consider a solenoid of length L,N windings,and radius b (L is much longer than b).A current I is flowing through the wire.If the length of the solenoid became twice as long (2L),and all other quantities remained the same,the magnetic field inside the solenoid would

A) remain the same.
B) become twice as strong.
C) become one half as strong.

Question 20

Two very long parallel wires in the xy-plane,a distance 2a apart,are parallel to the y-axis and carry equal currents I as shown in the figure.The +z direction points perpendicular to the xy-plane in a right-handed coordinate system.If the left current flows in the +y direction and the right current flows in the -y direction,which one of the graphs shown in the figure below best represents the z component of the net magnetic field,in the xy-plane,as a function of x? (Caution: These graphs are not magnetic field lines.)

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

Question 21

A coaxial cable consists of an inner cylindrical conductor of radius R₁ = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R₂ = 0.080 m and outer radius R₃ = 0.090 m. The inner conductor carries current I₁= 4.40 A in one direction,and the outer conductor carries current I₂ = 7.70 A in the opposite direction.What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ₀ = 4π × 10^-7 T • m/A)
(a)At r = 0.060 m (in the gap midway between the two conductors)
(b)At r = 0.150 m (outside the cable)

Question 22

The figure shows two long,parallel current-carrying wires.The wires carry equal currents
I₁ = I₂ = 20 A in the directions indicated and are located a distance d = 0.5 m apart.Calculate the magnitude and direction of the magnetic field at the point P that is located an equal distance d from each wire.(μ₀ = 4π × 10^-7 T • m/A)

A) 8 µT downward
B) 8 µT upward
C) 4 µT downward
D) 4 µT upward
E) 4 µT to the right

Question 23

As shown in the figure,a rectangular current loop is carrying current I₁ = 3.0 A,in the direction shown,and is located near a long wire carrying a current I_w.The long wire is parallel to the sides of the rectangle.The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire,as shown.We measure that the net force on the rectangular loop is 4.9 × 10^-6 N and is directed towards the wire.(μ₀ = 4π × 10^-7 T • m/A)
(a)What is the magnitude of the current I_w?
(b)In which direction does I_w flow: from top to bottom or from bottom to top in the sketch?

Question 24

A solenoid having N turns and carrying a current of 2.000 A has a length of 34.00 cm.If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT,what is the value of N?
(μ₀ = 4π × 10^-7 T • m/A)

A) 860.0
B) 1591
C) 2318
D) 3183
E) 1218

Question 25

A rectangular loop of wire measures 1.0 m by 1.0 cm.If a 7.0-A current flows through the wire,what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop? (μ₀ = 4π × 10^-7 T • m/A)

A) 9.8 × 10^-6 N
B) 7.8 × 10^-7 N
C) 9.8 × 10^-8 N
D) 4.9 × 10^-6 N

Question 26

A type of transmission line for electromagnetic waves consists of two parallel conducting plates (assumed infinite in width)separated by a distance a.Each plate carries the same uniform surface current density of 16.0 A/m,but the currents run in opposite directions.What is the magnitude of the magnetic field between the plates at a point 1.00 mm from one of the plates if a = 0.800 cm? (μ₀ = 4π × 10^-7 T • m/A)

A) 3.20 × 10^-3 T
B) 1.00 × 10^-5 T
C) 4.63 × 10^-5 T
D) 2.01 × 10^-5 T
E) 7.07 × 10^-4 T

Question 27

A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A.What is the magnitude of the magnetic field inside the solenoid at the central radius? (μ₀ = 4π × 10^-7 T • m/A)

A) 8.1 mT
B) 51 mT
C) 16 mT
D) 81 mT
E) zero

Question 28

As shown in the figure,two long straight wires are separated by a distance of d = 0.80 m.The currents are I₁ = 2.0 A to the right in the upper wire and I₂ = 7.0 A to the left in the lower wire.What are the magnitude and direction of the magnetic field at point P,which is a distance d/2 = 0.40 m below the lower wire? (μ₀ = 4π × 10^-7 T • m/A)

Question 29

A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other.When a 0.10 A current is sent through the wire,what is the magnitude of the magnetic field on the axis of the solenoid near its center?
(μ₀ = 4π × 10^-7 T • m/A)

A) 6.6 × 10^-5 T
B) 2.5 × 10^-5 T
C) 1.3 × 10^-5 T
D) 3.6 × 10^-5 T
E) 9.8 × 10^-5 T

Question 30

A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward.The wires are parallel to each other and are 42 cm apart.Calculate the force on a 6.4 m length of one of the wires.(μ₀ = 4π × 10^-7 T • m/A)

A) 8.0 × 10^-7 N
B) 5.1 × 10^-4 N
C) 8.0 × 10^-5 N
D) 5.1 × 10^-6 N
E) 2.2 × 10^-4 N

Question 31

A solenoid of length 18 cm consists of closely spaced coils of wire wrapped tightly around a wooden core.The magnetic field strength is 2.0 mT inside the solenoid near its center when a certain current flows through the coils.If the coils of the solenoid are now pulled apart slightly,stretching it to 21 cm without appreciably changing the size of the coils,what does the magnetic field become near the center of the solenoid when the same current flows through the coils? (μ₀ = 4π × 10^-7 T • m/A)

A) 1.7 mT
B) 3.4 mT
C) 0.85 mT
D) 2.0 mT

Question 32

A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long.The windings carry a current I in the sense that is shown in the figure.The current produces a magnetic field,of magnitude 4.3 mT,near the center of the solenoid.Find the current in the solenoid windings.(μ₀ = 4π × 10^-7 T • m/A)

A) 1.8 A
B) 1.5 A
C) 1.3 A
D) 2.2 A
E) 2.0 A

Question 33

A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long.If this solenoid carries a current of 12 A,what is the magnitude of the magnetic field near the center of the solenoid?
(μ₀ = 4π × 10^-7 T • m/A)

A) 16 mT
B) 4.9 mT
C) 15 mT
D) 6.0 mT
E) 9.0 mT

Question 34

A toroidal solenoid has a central radius of 0.50 m and a cross-sectional diameter of 10 cm.When a current passes through the coil of the solenoid,the magnetic field inside the solenoid at its CENTER has a magnitude of 2.0 μT.What is the largest value of the magnetic field inside the solenoid when this current is flowing? (μ₀ = 4π × 10^-7 T • m/A)

A) 3.5 µT
B) 1.8 µT
C) 2.2 µT
D) 0.50 µT
E) 2.8 µT

Question 35

Three very long,straight,parallel wires each carry currents of 4.00 A,directed out of the page as shown in the figure.The wires pass through the vertices of a right isosceles triangle of side 2.00 cm.What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle?

A) 4.42 × 10^-6 T
B) 1.77 × 10^-5 T
C) 5.66 × 10^-5 T
D) 1.26 × 10^-4 T
E) 1.77 × 10^-6 T