Deck 23: Electric Potential

Question 1

Direction of magnetic fields: A horizontal wire carries a current straight toward you. From your point of view, the magnetic field at a point directly below the wire points

A) directly away from you.
B) to the left.
C) to the right.
D) directly toward you.
E) vertically upward.

Answer 1

to the right.

Question 2

Field due to a long wire: 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

Answer 2

4

Question 3

Field due to a long wire: 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.

Answer 3

upward

Question 4

Direction of magnetic fields: A vertical wire carries a current straight down. To the east of this wire, the magnetic field points

A) toward the north.
B) toward the east.
C) toward the west.
D) toward the south.
E) downward.

Question 5

Field due to a long wire: 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 6

Force on parallel wires: 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 the 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 the 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 7

Force on parallel wires: 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 8

Force on parallel wires: 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 9

Force on moving charges: An electron, moving toward the west, enters a uniform magnetic field. Because of this field the electron curves upward. The direction of the magnetic field is

A) towards the north.
B) towards the south.
C) towards the west.
D) upward.
E) downward.

Question 10

Force on moving charges: An electron moving in the direction of the +x-axis enters a magnetic field. If the electron experiences a magnetic deflection in the -y direction, the direction of the magnetic field in this region points in the direction of the

A) +z-axis.
B) -z-axis.
C) -x-axis.
D) +y-axis.
E) -y-axis.

Question 11

Field due to circular loop: 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 12

Cyclotron frequency: A charged particle is moving with speed v perpendicular to a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field. If the frequency of revolution of the first particle is f, the frequency of revolution of the second particle is

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

Question 13

Field due to a long wire: 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/ o 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 14

Field due to a long wire: 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 15

Field due to a long wire: 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 16

Force on moving charges: Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure. The electric charge of each of the three particles is, respectively,

A) 1 is neutral, 2 is negative, and 3 is positive.
B) 1 is neutral, 2 is positive, and 3 is negative.
C) 1 is positive, 2 is neutral, and 3 is negative.
D) 1 is positive, 2 is negative, and 3 is neutral.
E) 1 is negative, 2 is neutral, and 3 is positive.

Question 17

Force on moving charges: A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?

A) 9R
B) 3R
C) R
D) R/
E) R/9

Question 18

Force on moving charges: Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

A) 4R
B) 3R
C) R
D) R/
E) R/2

Question 19

Force on currents: A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this current due to the field?

A) downward
B) toward the north
C) toward the south
D) toward the east
E) toward the west

Question 20

Field due to a long wire: 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.

Question 21

Solenoids: 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.

Question 22

Velocity selector: A beam of electrons is accelerated through a potential difference of 10 kV before entering a region having uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the direction in which the electron is moving. If the magnetic field in this region has a value of 0.010 T, what magnitude of the electric field is required if the particles are to be undeflected as they pass through the region?

A) 2.3 × 10³ V/m
B) 7.9 × 10³ V/m
C) 5.9 × 10⁵ V/m
D) 6.0 × 10⁵ V/m
E) 7.2 × 10⁶ V/m

Question 23

Circular motion of charges: A charged particle of mass 0.0020 kg is subjected to a magnetic field which acts at a right angle to its motion. If the particle moves in a circle of radius at a speed of what is the magnitude of the charge on the particle?

A) 0.0083 C
B) 120 C
C) 0.00040 C
D) 2500 C

Question 24

Velocity selector: The figure shows a velocity selector that can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E, which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 2.0 mm and the value of the magnetic field is 0.60 T, what voltage between the plates will allow particles of speed 5.0 × 10⁵ m/s to pass straight through without deflection?

A) 600 V
B) 1900 V
C) 3800 V
D) 190 V
E) 94 V

Question 25

Circular motion of charges: An alpha particle is moving at a speed of 5.0 × 10⁵ m/s in a direction perpendicular to a uniform magnetic field of strength 0.040 T. The charge on an alpha particle is 3.2 × 10^-19 C and its mass is 6.6 × 10^-27 kg.
(a) What is the radius of the path of the alpha particle?
(b) How long does it take the alpha particle to make one complete revolution around its path?

Question 26

Mass spectrometer: In a mass spectrometer, a singly-charged particle (charge e) has a speed of 1.0 × 10⁶ m/s and enters a uniform magnetic field of 0.20 T. The radius of the circular orbit of the particle is 0.020 m. What is the mass of this particle? (e = 1.60 × 10^-19C)

A) 3.2 × 10^-28 kg
B) 6.4 × 10^-28 kg
C) 1.7 × 10^-27 kg
D) 4.5 × 10^-27 kg

Question 27

Circular motion of charges: As shown in the figure, a small particle of charge q = - 7.0 × C and mass has velocity as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius R = 5.0 cm. Calculate the magnitude and direction of the magnetic field in the region.

Question 28

Velocity selector: A proton, with mass 1.67 × 10^-27 kg and charge +1.6 × 10^-19 C, is sent with velocity 7.1 × 10⁴ m/s in the +x direction into a region where there is a uniform electric field of magnitude 730 V/m in the +y direction. What are the magnitude and direction of the uniform magnetic field in the region, if the proton is to pass through undeflected? Assume that the magnetic field has no x-component and neglect gravitational effects.

Question 29

Force on moving charges: A particle with charge -5.00 C initially moves at = (1.00 + 7.00 ) m/s. If it encounters a magnetic field find the magnetic force vector on the particle.

A) (- 350 + 50.0
) N
B) (- 350 - 50.0
) N
C) ( 350 + 50.0
) N
D) ( 350 - 50.0
) N

Question 30

Force on currents: A wire in the shape of an "M" lies in the plane of the paper. It carries a current of 2.0 A, flowing from points A to E, as shown in the figure. It is placed in a uniform magnetic field of 0.75 T in the same plane, directed as shown on the right side of the figure. The figure indicates the dimensions of the wire. What are the magnitude and direction of the force acting on (a) section AB of this wire?
(b) section BC of this wire?
(c) section CD of this wire?
(d) section DE of this wire?
(e) the entire wire?

Question 31

Circular motion of charges: A proton is first accelerated from rest through a potential difference V and then enters a uniform 0.750-T magnetic field oriented perpendicular to its path. In this field, the proton follows a circular arc having a radius of curvature of 1.84 cm. What was the potential difference V? (m_proton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19C)

Question 32

Circular motion of charges: A proton starting from rest travels through a potential of 1.0 kV and then moves into a uniform 0.040-T magnetic field. What is the radius of the proton's resulting orbit? (m_proton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19C)

A) 0.080 m
B) 0.11 m
C) 0.14 m
D) 0.17 m

Question 33

Force on currents: A straight wire that is 0.60 m long is carrying a current of 2.0 A. It is placed in a uniform magnetic field of strength 0.30 T. If the wire experiences a force of 0.18 N, what angle does the wire make with respect to the magnetic field?

A) 25°
B) 30°
C) 35°
D) 60°
E) 90°

Question 34

Velocity selector: An electron moving with a velocity = 5.0 × 10⁷ m/s enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is = . What magnetic field will allow the electron to go through the region without being deflected?

A) = +2.0 × 10^-4 T

B) = -2.0 × 10^-4 T

C) = +2.0 × 10^-4 T

D) = -2.0 × 10^-4 T

E) = +5.0 × 10^-4 T

Question 35

Ampere's law: A very long, hollow, thin-walled conducting cylindrical shell (like a pipe) of radius R carries a current along its length uniformly distributed throughout the thin shell. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?

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

Question 36

Force on moving charges: An electron moves with a speed of 8.0 × 10⁶ m/s along the +x-axis. It enters a region where there is a magnetic field of 2.5 T, directed at an angle of 60° to the +x-axis and lying in the xy-plane. (1 eV = 1.60 × 10^-19 C, mel = 9.11 × 10^-31 kg) Calculate the magnitude of
(a) the magnetic force on the electron.
(b) the acceleration of the electron.

Question 37

Solenoids: 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 38

Velocity selector: A uniform magnetic field of magnitude 0.80 T in the negative z-direction is present in a region of space, as shown in the figure. A uniform electric field is also present. An electron that is projected with an initial velocity in the positive x-direction passes through the region without deflection. What is the electric field vector in the region?

A) - 73 kV/m
B) + 73 kV/m
C) + 110 kV/m
D) + 110 kV/m
E) - 110 kV/m

Question 39

Force on currents: A thin copper rod that is 1.0 m long and has a mass of 0.050 kg is in a magnetic field of 0.10 T. What minimum current in the rod is needed in order for the magnetic force to cancel the weight of the rod?

A) 1.2 A
B) 2.5 A
C) 4.9 A
D) 7.6 A
E) 9.8 A

Question 40

Ampere's law: A very long, solid, conducting cylinder of radius R carries a current along its length uniformly distributed throughout the cylinder. Which one of the graphs shown in the figure most accurately describes the magnitude B of the magnetic field produced by this current as a function of the distance r from the central axis?

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

Question 41

Force on currents: An L-shaped metal machine part is made of two equal-length segments that are perpendicular to each other and carry a 4.50-A current as shown in the figure. This part has a total mass of 3.80 kg and a total length of 3.00 m, and it is in an external 1.20-T magnetic field that is oriented perpendicular to the plane of the part, as shown. What is the magnitude of the NET magnetic force that the field exerts on the part?

A) 8.10 N
B) 11.5 N
C) 16.2 N
D) 22.9 N
E) 32.4 N

Question 42

Torque: A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field.
(a) What is the magnitude of the magnetic moment of the loop?
(b) What torque does the magnetic field exert on the loop?

Question 43

Force on currents: A wire segment 1.2 m long carries a current I = 3.5 A and is oriented as shown in the figure. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. The +z-axis points directly into the page. What is the magnetic force vector on the wire segment?

A) +1.6 N
B) -1.6 N
C) +1.6 N
D) (+1.3 - 1.6
) N
E) (+1.3 + 1.6
) N

Question 44

Torque: A rigid rectangular loop, which measures 0.30 m by 0.40 m, carries a current of 5.5 A, as shown in the figure. A uniform external magnetic field of magnitude 2.9 T in the negative x direction is present. Segment CD is in the xz-plane and forms a 35° angle with the z-axis, as shown. Find the magnitude of the external torque needed to keep the loop in static equilibrium.

A) 1.1 N ∙ m
B) 0.73 N ∙ m
C) 1.3 N ∙ m
D) 1.4 N ∙ m
E) 1.6 N ∙ m

Question 45

Potential energy of a current loop: A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A ∙ m². A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy. The work done by this external torque is closest to

A) 0.20 J
B) 0.30 J
C) 0.40 J
D) 0.50 J
E) 0.60 J

Question 46

Field of a long wire: A very long thin wire produces a magnetic field of at a distance of 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 47

Force on currents: A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field.
(a) Which way should the magnetic field point?
(b) What is the magnitude of the weakest possible magnetic field you could use?

Question 48

Field of a long wire: 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 49

Torque: A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A. It is placed in a magnetic field of with the plane of the coil making an angle of 30° with the magnetic field. What is the magnetic torque on the coil?

A) 0.15 N ∙ m
B) 0.088 N ∙ m
C) 0.29 N ∙ m
D) 0.40 N ∙ m
E) 0.076 N ∙ m

Question 50

Force on currents: A wire along the z-axis carries a current of 6.8 A in the +z direction. Find the magnitude and direction of the force exerted on a 6.1-cm long length of the wire by a uniform magnetic field with magnitude 0.36 T in the -x direction.

Question 51

Biot-Savart law: A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at 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 52

Force on currents: A wire carries a 4.0-A current along the +x-axis through a magnetic field = (5.0 + 7.0 ) T. If the wire experiences a force of 30 N as a result, how long is the wire?

A) 1.1 m
B) 0.87 m
C) 1.5 m
D) 0.63 m

Question 53

Force on currents: A wire segment 1.2 m long carries a current I = 3.5 A, and is oriented as shown in the figure. The +x-axis points directly into the page. A uniform magnetic field of magnitude 0.50 T pointing toward the -x direction is present as shown. What is the magnetic force vector on the wire segment?

A) (+1.1 - 1.8
) N
B) (-1.1 + 1.8
) N
C) (-1.1 - 1.8
) N
D) (+1.8 - 1.1
) N
E) (+1.8 + 1.1
) N

Question 54

Biot-Savart law: A point charge Q moves on the x-axis in the positive direction with a speed of A point P is on the y-axis at The magnetic field produced at point P, as the charge moves through the origin, is equal to When the charge is at 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 55

Torque: A rectangular loop of wire carrying a 4.0-A current is placed in a magnetic field of 0.60 T. The magnitude of the torque acting on this wire when the plane of the loop makes a 30° angle with the field is measured to be 1.1 N ∙ m. What is the area of this loop?

A) 0.20 m²
B) 0.40 m²
C) 0.26 m²
D) 0.80 m²
E) 0.53 m²

Question 56

Field of a long wire: 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

Question 57

Torque: A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T . The normal to the loop is parallel to a unit vector = -0.60 - 0.80 . Calculate the magnitude of the torque on the loop due to the magnetic field.

A) 4.7 × 10^-4 N ∙ m
B) 2.8 × 10^-4 N ∙ m
C) 0.60 × 10^-4 N ∙ m
D) 1.2 × 10^-4 N ∙ m
E) zero

Question 58

Potential energy of a current loop: A round loop of diameter 12 cm, carrying a current of 0.40 A, is placed inside a magnetic field = 0.20 T + 0.40 T . The normal to the loop is parallel to the unit vector = -0.60 - 0.80 . What is the potential energy of the loop?

A) -4.5 × 10^-3 J
B) +2.0 × 10^-3 J
C) -2.0 × 10^-3 J
D) -2.3 × 10^-3 J
E) +4.5 × 10^-3 J

Question 59

Field of a long wire: 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 60

Torque: A rigid circular loop has a radius of 0.20 m and is in the xy-plane. A clockwise current I is carried by the loop, as shown. The magnitude of the magnetic moment of the loop is 0.75 A · m². A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present. (a) What is the current in the loop?
(b) Find the magnitude of the magnetic torque exerted on the loop.
(c) If the loop is released from rest, in what direction will points a and c initially move?

Question 61

Force on parallel wires: 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 62

Field of a circular loop: A long straight very thin wire on the y-axis carries a 10-A current in the positive y-direction. A circular loop 0.50 m in radius, also of very thin wire and lying in the yz-plane, carries a 9.0-A current, as shown. Point P is on the positive x-axis, at a distance of 0.50 m from the center of the loop. What is the magnetic field vector at point P due to these two currents? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) zero
B) -8.0 × 10^-6 T
C) (+4.0 × 10^-6 T) - (4.0 × 10^-6 T)

D) (-4.0 × 10^-6 T) - (4.0 × 10^-6 T)

E) (-4.0 × 10^-6 T) - (80 × 10^-6 T)

Question 63

Field of a circular loop: Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure. Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers. (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 0.90 × T
B) 3.9 × T
C) 1.9 × T
D) 6.3 × T
E) 9.2 × T

Question 64

Field of a long wire: 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

Question 65

Force on parallel wires: As shown in the figure, a rectangular current loop is carrying current = 3.0 A, in the direction shown, and is located near a long wire carrying a current . 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 and is directed towards the wire. (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 66

Field of a circular loop: A circular loop of wire of radius 10 cm carries a current of 6.0 A. What is the magnitude of the magnetic field at the center of the loop? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 3.8 × 10^-5 T
B) 3.8 × 10^-7 T
C) 1.2 × 10^-5 T
D) 1.2 × 10^-7 T
E) 3.8 × 10^-8 T

Question 67

Field of a long wire: 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 68

Ampere's law: 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 69

Field of a long wire: As shown in the figure, two long straight wires are separated by a distance of The currents are to the right in the upper wire and to the left in the lower wire. What are the magnitude and direction of the magnetic field at point P, which is a distance below the lower wire?

Question 70

Ampere's law: A long, straight wire with current flowing through it produces magnetic field strength at its surface. If the wire has a radius R, where within the wire is the field strength equal to of the field strength at the surface of the wire? Assume that the current density is uniform throughout the wire. (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 0.36 R
B) 0.060 R
C) 0.64 R
D) 0.030 R

Question 71

Force on parallel wires: 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 72

Field of a circular loop: Two circular coils of diameter 30.0 cm are parallel to each other and have their centers along the same line L but separated by 22.0 cm. When an experimenter views the coils along L, the coil closer to her carries a clockwise current of 2.50 A. Find the magnitude and sense (clockwise or counterclockwise) of the current needed in the other coil so that the net magnetic field on L midway between the two coils will have a magnitude of 4.10 µT and point away from the experimenter who is viewing the coils along L. (μ₀ = 4π × 10^-7 T ∙ m/A)

Question 73

Field of a circular loop: A wire carrying a current is shaped in the form of a circular loop of radius If the magnetic field strength that this current produces at the center of the loop is what is the magnitude of the current that flows through the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 5.3 A
B) 16 A
C) 9.1 A
D) 23 A

Question 74

Ampere's law: 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 The inner conductor carries current in one direction, and the outer conductor carries current 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 75

Ampere's law: A tube with a 3.0-mm radius has ions flowing through it along its length. To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and do not screen magnetism, what is the magnitude of the current flowing through the tube? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 66 A
B) 132 A
C) 829 A
D) 415 A

Question 76

Field of a circular loop: As shown in the figure, a wire is bent into the shape of a tightly closed omega (Ω), with a circular loop of radius 4.0 cm and two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the x-axis. The wire carries a 5.0-A current, as shown. What is the magnitude of the magnetic field at the center of the loop? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 25 µT
B) 40 µT
C) 54 µT
D) 80 µT
E) 104 µT

Question 77

Field of a long wire: 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 78

Ampere's law: The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm. A uniform current density of 1.0 A/ cm² flows through the cylinder parallel to its axis. Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder. (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 0.00 T
B) 1.5 × 10^-4 T
C) 2.5 × 10^-4 T
D) 4.5 × 10^-4 T
E) 0.50 × 10^-4 T

Question 79

Field of a circular loop: As shown in the figure, an insulated wire is bent into a circular loop of radius 6.0 cm and has two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the z-axis. The wire carries a current of 8.0 A. What is the magnitude of the magnetic field at the origin? (μ₀ = 4π × 10^-7 T ∙ m/A)

A) 75 µT
B) 81 µT
C) 88 µT
D) 110 µT
E) 120 µT

Question 80

Field of a circular loop: A long straight wire on the z-axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 1.0 × 10⁶ m/s in the negative x-direction. What is the y component of the force on the electron? (e = 1.60 × 10^-19 C, μ₀ = 4π × 10^-7 T ∙ m/A)

A) -1.0 × 10^-18 N
B) +1.0 × 10^-18 N
C) -2.0 × 10^-18 N
D) +2.0 × 10^-18 N
E) zero